From ad620dfd19f56083901865bda94fbf2bbcfe87fe Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dion=20H=C3=A4fner?= Date: Wed, 25 Mar 2026 16:31:19 +0100 Subject: [PATCH 01/24] add enzyme integration proof of concept --- demo/enzyme_thermal_2d/README.md | 179 ++++ demo/enzyme_thermal_2d/enzyme/build.sh | 44 + demo/enzyme_thermal_2d/enzyme/thermal_2d.f90 | 218 +++++ demo/enzyme_thermal_2d/enzyme/wrapper.c | 186 ++++ .../inverse_heat_transfer.ipynb | 911 ++++++++++++++++++ demo/enzyme_thermal_2d/tesseract_api.py | 489 ++++++++++ demo/enzyme_thermal_2d/tesseract_config.yaml | 62 ++ .../tesseract_requirements.txt | 1 + demo/jax_thermal_2d/README.md | 58 ++ demo/jax_thermal_2d/benchmark.py | 144 +++ demo/jax_thermal_2d/tesseract_api.py | 339 +++++++ demo/jax_thermal_2d/tesseract_config.yaml | 16 + .../jax_thermal_2d/tesseract_requirements.txt | 2 + examples/enzyme_ad/README.md | 104 ++ examples/enzyme_ad/enzyme/build.sh | 41 + examples/enzyme_ad/enzyme/heat_step.f90 | 39 + examples/enzyme_ad/enzyme/wrapper.c | 87 ++ examples/enzyme_ad/tesseract_api.py | 263 +++++ examples/enzyme_ad/tesseract_config.yaml | 59 ++ examples/enzyme_ad/tesseract_requirements.txt | 1 + pyproject.toml | 1 + 21 files changed, 3244 insertions(+) create mode 100644 demo/enzyme_thermal_2d/README.md create mode 100644 demo/enzyme_thermal_2d/enzyme/build.sh create mode 100644 demo/enzyme_thermal_2d/enzyme/thermal_2d.f90 create mode 100644 demo/enzyme_thermal_2d/enzyme/wrapper.c create mode 100644 demo/enzyme_thermal_2d/inverse_heat_transfer.ipynb create mode 100644 demo/enzyme_thermal_2d/tesseract_api.py create mode 100644 demo/enzyme_thermal_2d/tesseract_config.yaml create mode 100644 demo/enzyme_thermal_2d/tesseract_requirements.txt create mode 100644 demo/jax_thermal_2d/README.md create mode 100644 demo/jax_thermal_2d/benchmark.py create mode 100644 demo/jax_thermal_2d/tesseract_api.py create mode 100644 demo/jax_thermal_2d/tesseract_config.yaml create mode 100644 demo/jax_thermal_2d/tesseract_requirements.txt create mode 100644 examples/enzyme_ad/README.md create mode 100644 examples/enzyme_ad/enzyme/build.sh create mode 100644 examples/enzyme_ad/enzyme/heat_step.f90 create mode 100644 examples/enzyme_ad/enzyme/wrapper.c create mode 100644 examples/enzyme_ad/tesseract_api.py create mode 100644 examples/enzyme_ad/tesseract_config.yaml create mode 100644 examples/enzyme_ad/tesseract_requirements.txt diff --git a/demo/enzyme_thermal_2d/README.md b/demo/enzyme_thermal_2d/README.md new file mode 100644 index 00000000..e10328ae --- /dev/null +++ b/demo/enzyme_thermal_2d/README.md @@ -0,0 +1,179 @@ +# Enzyme AD: Differentiable 2D Thermal Solver + +This example demonstrates how to obtain **exact automatic derivatives** of a production-style Fortran thermal simulation without writing any manual adjoint code, using [Enzyme](https://enzyme.mit.edu/) for automatic differentiation at the LLVM IR level. + +## What it does + +The Tesseract wraps a 2D transient heat conduction solver: + +``` +rho * cp * dT/dt = div( k(T) * grad(T) ) + Q +``` + +with: + +- **Temperature-dependent conductivity**: `k(T) = k0 + k1*T` (nonlinear material model) +- **Mixed boundary conditions**: Dirichlet (hot wall), convection (Robin), and insulated (Neumann) +- **Multi-step explicit time integration**: the Fortran kernel runs the full time-stepping loop internally + +This is representative of the thermal solvers CAE engineers run in production — a structured-grid finite difference code with nonlinear material properties, mixed BCs, and a time integration loop. The key difference from a toy example is that **the nonlinear conductivity makes the Jacobian solution-dependent**, so you can't derive it analytically and hand-coding the adjoint is error-prone. + +Enzyme differentiates through the **entire time-stepping loop** (including the nonlinear stencil operations at each step), giving exact gradients of the final temperature field with respect to all material properties, boundary conditions, and initial conditions. + +## How it works + +The compilation pipeline is identical to the [1D Enzyme example](../enzyme_ad/): + +``` +thermal_2d.f90 (Fortran source — 2D solver with k(T), mixed BCs, time loop) + │ + ▼ lfortran --show-llvm +thermal_2d.ll (LLVM IR) + │ + ▼ opt -O1 +thermal_2d_opt.ll (cleaned-up IR, ready for Enzyme) + │ + ▼ llvm-link with wrapper.c +combined.ll (Fortran IR + C wrapper with __enzyme_autodiff / __enzyme_fwddiff) + │ + ▼ opt --load-pass-plugin=LLVMEnzyme-19.so -passes=enzyme +ad.ll (LLVM IR with compiler-generated forward and reverse mode derivatives) + │ + ▼ clang -shared +libthermal_2d_ad.so (shared library: forward, JVP, VJP entry points) +``` + +At runtime, `tesseract_api.py` loads `libthermal_2d_ad.so` via `ctypes` and exposes: + +- **`apply`** — runs the full forward simulation (all time steps) +- **`jacobian_vector_product`** — Enzyme forward-mode (JVP) through the full simulation +- **`vector_jacobian_product`** — Enzyme reverse-mode (VJP) through the full simulation + +## Physics + +### Governing equation + +2D transient heat conduction with temperature-dependent conductivity and volumetric heat source: + +``` +rho * cp * dT/dt = d/dx(k(T) * dT/dx) + d/dy(k(T) * dT/dy) + Q +``` + +### Material model + +``` +k(T) = k0 + k1 * T +``` + +Default values model mild steel: `k0 = 45 W/(m·K)`, `k1 = -0.01 W/(m·K²)`. + +### Boundary conditions + +| Boundary | Type | Condition | +| ------------ | ------------------- | -------------------- | +| Bottom (y=0) | Dirichlet | T = T_hot | +| Top (y=Ly) | Convection (Robin) | -k ∂T/∂n = h(T - T∞) | +| Left (x=0) | Insulated (Neumann) | ∂T/∂x = 0 | +| Right (x=Lx) | Insulated (Neumann) | ∂T/∂x = 0 | + +### Discretization + +- Structured rectangular grid (nx × ny) +- Central differences in space with harmonic-mean conductivity at cell faces +- Explicit Euler in time + +## Why AD matters here + +With constant thermal conductivity, the Jacobian of the heat equation is a constant tridiagonal (or banded) matrix that you could derive by hand. But with `k(T) = k0 + k1*T`: + +1. The stencil coefficients depend on the current temperature field +2. The Jacobian changes at every time step +3. Hand-coding the adjoint through the nonlinear stencil and multi-step loop is tedious and error-prone +4. Finite differences require N+1 forward solves for N parameters + +Enzyme gives you exact gradients through the entire nonlinear time-stepping loop for the cost of roughly one additional forward solve (for reverse mode). This enables: + +- **Material property calibration**: fit k0, k1 to match experimental temperature measurements +- **Boundary condition estimation**: infer h_conv or T_hot from sensor data (inverse heat transfer) +- **Design optimization**: optimize geometry (Lx, Ly) or heat source placement (Q) to achieve a target temperature distribution +- **Sensitivity analysis**: understand how uncertainties in material properties propagate to the temperature field + +## Usage + +```python +from tesseract_core import Tesseract +import numpy as np + +with Tesseract.from_image("enzyme-thermal-2d:latest") as t: + nx, ny = 20, 20 + n = nx * ny + + # Uniform initial temperature + T_init = np.full(n, 293.15) # 20°C everywhere + Q = np.zeros(n) # no internal heating + + # Forward solve + result = t.apply(inputs={ + "T_init": T_init, "Q": Q, + "nx": nx, "ny": ny, "n_steps": 100, + "k0": 45.0, "k1": -0.01, + "rho": 7850.0, "cp": 460.0, + "h_conv": 25.0, "T_inf": 293.15, "T_hot": 373.15, + "Lx": 0.1, "Ly": 0.05, "dt": 0.01, + }) + T_final = result["T_final"].reshape(ny, nx) + + # Gradient of average temperature w.r.t. material properties + # (e.g., for calibrating k0 and h_conv from experimental data) + cotangent = np.full(n, 1.0 / n) # gradient of mean(T_final) + vjp = t.vector_jacobian_product( + inputs={ + "T_init": T_init, "Q": Q, + "nx": nx, "ny": ny, "n_steps": 100, + "k0": 45.0, "k1": -0.01, + "rho": 7850.0, "cp": 460.0, + "h_conv": 25.0, "T_inf": 293.15, "T_hot": 373.15, + "Lx": 0.1, "Ly": 0.05, "dt": 0.01, + }, + vjp_inputs=["k0", "k1", "h_conv", "T_hot"], + vjp_outputs=["T_final"], + cotangent_vector={"T_final": cotangent}, + ) + print(f"d(mean T)/d(k0) = {vjp['k0']:.6f}") + print(f"d(mean T)/d(k1) = {vjp['k1']:.6f}") + print(f"d(mean T)/d(h_conv)= {vjp['h_conv']:.6f}") + print(f"d(mean T)/d(T_hot) = {vjp['T_hot']:.6f}") +``` + +## Toolchain + +All tools are installed from prebuilt binaries during the Docker build (no source compilation of the toolchain itself): + +| Tool | Source | Purpose | +| ------------------------------------------- | --------------- | --------------------------------- | +| [LFortran](https://lfortran.org/) 0.61.0 | conda-forge | Fortran → LLVM IR frontend | +| [LLVM](https://llvm.org/) 19 | apt.llvm.org | IR optimization, linking, codegen | +| [Enzyme](https://enzyme.mit.edu/) (nightly) | GitHub releases | LLVM AD pass | + +## Key design choices + +- **Black-box solver.** The Fortran subroutine takes initial conditions and parameters, runs the full time integration internally, and returns the final temperature field. This mirrors how legacy Fortran solvers are structured — the user doesn't need to refactor their code to expose individual time steps. +- **Temperature-dependent conductivity via harmonic mean at cell faces.** This is the standard approach in finite volume / finite difference thermal codes — it ensures continuity of heat flux across cells with different conductivities. +- **No array intrinsics in the Fortran kernel.** Explicit `do` loops produce clean LLVM IR that Enzyme handles reliably. +- **`--no-array-bounds-checking`** is passed to LFortran. Bounds checks emit calls to LFortran's runtime which Enzyme cannot differentiate through. +- **Enzyme differentiates through the full time-stepping loop** using a store-all (tape) strategy for reverse mode. During the forward pass, Enzyme caches ~148 intermediate values per time step into dynamically allocated tapes (O(n_steps) memory). For the default problem size (~400 grid points, 100 time steps), this is ~115 KB — trivial. For very long simulations (e.g., 100,000 steps), tape memory grows linearly to ~115 MB. Enzyme's checkpointing annotations (`__enzyme_checkpoint`) could be used to trade recomputation for memory in such cases, but are not needed here. +- **Work arrays are passed from C, not allocated in Fortran.** LFortran emits `_lfortran_malloc` for variable-length arrays, which Enzyme cannot differentiate through. The C wrapper allocates `T_cur` and `T_new` on the heap and passes them to the Fortran subroutine, avoiding this issue. + +## File structure + +``` +enzyme_thermal_2d/ +├── README.md +├── tesseract_api.py # Python API wrapping ctypes calls +├── tesseract_config.yaml # Build config with LLVM/LFortran/Enzyme toolchain +├── tesseract_requirements.txt # numpy +└── enzyme/ + ├── thermal_2d.f90 # Fortran solver (2D, nonlinear, multi-step) + ├── wrapper.c # C wrapper declaring Enzyme AD entry points + └── build.sh # Full compilation pipeline script +``` diff --git a/demo/enzyme_thermal_2d/enzyme/build.sh b/demo/enzyme_thermal_2d/enzyme/build.sh new file mode 100644 index 00000000..95ca1ddf --- /dev/null +++ b/demo/enzyme_thermal_2d/enzyme/build.sh @@ -0,0 +1,44 @@ +#!/bin/bash +# Copyright 2025 Pasteur Labs. All Rights Reserved. +# SPDX-License-Identifier: Apache-2.0 +# +# Build pipeline: Fortran -> LFortran -> LLVM IR -> Enzyme AD -> shared library +# +# This script implements the full compilation pipeline: +# 1. LFortran compiles Fortran to LLVM IR +# 2. LLVM opt cleans up the IR (-O1) +# 3. Clang compiles the C wrapper (with Enzyme calls) to LLVM IR +# 4. llvm-link merges the Fortran and C IR modules +# 5. Enzyme LLVM pass generates derivative code +# 6. Clang compiles the differentiated IR to a shared library + +set -euo pipefail + +SCRIPT_DIR="$(cd "$(dirname "$0")" && pwd)" +ENZYME_LIB="${ENZYME_LIB:-/usr/local/lib/LLVMEnzyme-19.so}" +OUTPUT="${1:-${SCRIPT_DIR}/libthermal_2d_ad.so}" + +echo "=== Step 1: LFortran -> LLVM IR ===" +lfortran --show-llvm --no-array-bounds-checking \ + "${SCRIPT_DIR}/thermal_2d.f90" > /tmp/thermal_2d.ll + +echo "=== Step 2: Optimize IR ===" +opt -O3 -S /tmp/thermal_2d.ll -o /tmp/thermal_2d_opt.ll + +echo "=== Step 3: Compile C wrapper -> LLVM IR ===" +clang -emit-llvm -S -O3 "${SCRIPT_DIR}/wrapper.c" -o /tmp/wrapper.ll + +echo "=== Step 4: Link IR modules ===" +llvm-link /tmp/wrapper.ll /tmp/thermal_2d_opt.ll -S -o /tmp/combined.ll + +echo "=== Step 5: Enzyme AD pass ===" +opt --load-pass-plugin="${ENZYME_LIB}" -passes=enzyme \ + -S /tmp/combined.ll -o /tmp/ad.ll + +echo "=== Step 5b: Optimize post-Enzyme IR ===" +opt -O3 -S /tmp/ad.ll -o /tmp/ad_opt.ll + +echo "=== Step 6: Compile to shared library ===" +clang -shared -O3 /tmp/ad_opt.ll -o "${OUTPUT}" -lm + +echo "=== Built ${OUTPUT} ===" diff --git a/demo/enzyme_thermal_2d/enzyme/thermal_2d.f90 b/demo/enzyme_thermal_2d/enzyme/thermal_2d.f90 new file mode 100644 index 00000000..1a7f983b --- /dev/null +++ b/demo/enzyme_thermal_2d/enzyme/thermal_2d.f90 @@ -0,0 +1,218 @@ +! Copyright 2025 Pasteur Labs. All Rights Reserved. +! SPDX-License-Identifier: Apache-2.0 +! +! 2D transient heat conduction solver with temperature-dependent conductivity. +! +! Solves: +! +! rho * cp * dT/dt = div( k(T) * grad(T) ) + Q +! +! on a rectangular domain [0, Lx] x [0, Ly] with a structured grid. +! +! Material model: +! k(T) = k0 + k1 * T +! +! Boundary conditions: +! Bottom (y=0): Dirichlet, T = T_hot +! Top (y=Ly): Convection, -k dT/dn = h_conv * (T - T_inf) +! Left (x=0): Neumann (insulated), dT/dx = 0 +! Right (x=Lx): Neumann (insulated), dT/dx = 0 +! +! Time integration: explicit Euler with n_steps steps of size dt. +! +! Work arrays T_cur and T_new are passed in from the caller to avoid +! dynamic allocation (LFortran emits _lfortran_malloc for VLAs, which +! Enzyme cannot differentiate through). +! +! This subroutine is compiled to LLVM IR via LFortran, then +! differentiated by Enzyme to obtain exact JVP and VJP functions. + +subroutine thermal_2d_solve(n, nx, ny, n_steps, & + T_init, T_final, T_cur, T_new, & + k0, k1, rho, cp, & + h_conv, T_inf, T_hot, & + Q, Lx, Ly, dt) + implicit none + integer, intent(in) :: n, nx, ny, n_steps + double precision, intent(in) :: T_init(n) + double precision, intent(out) :: T_final(n) + double precision, intent(out) :: T_cur(n) + double precision, intent(out) :: T_new(n) + double precision, intent(in) :: k0, k1, rho, cp + double precision, intent(in) :: h_conv, T_inf, T_hot + double precision, intent(in) :: Q(n) + double precision, intent(in) :: Lx, Ly, dt + + double precision :: dx, dy + double precision :: kx_east, kx_west, ky_north, ky_south + double precision :: T_c, T_e, T_w, T_nn, T_s + double precision :: flux_x, flux_y + integer :: i, j, idx, step + + dx = Lx / dble(nx - 1) + dy = Ly / dble(ny - 1) + + ! Copy initial condition + do idx = 1, n + T_cur(idx) = T_init(idx) + end do + + ! Time integration loop + do step = 1, n_steps + + ! --- Interior points --- + do j = 2, ny - 1 + do i = 2, nx - 1 + idx = (j - 1) * nx + i + + T_c = T_cur(idx) + T_e = T_cur(idx + 1) + T_w = T_cur(idx - 1) + T_nn = T_cur(idx + nx) + T_s = T_cur(idx - nx) + + ! Harmonic-mean conductivity at cell faces + kx_east = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_e) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_e)) + kx_west = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_w) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_w)) + ky_north = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_nn) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_nn)) + ky_south = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_s) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_s)) + + flux_x = (kx_east * (T_e - T_c) - kx_west * (T_c - T_w)) / (dx * dx) + flux_y = (ky_north * (T_nn - T_c) - ky_south * (T_c - T_s)) / (dy * dy) + + T_new(idx) = T_c + dt / (rho * cp) * (flux_x + flux_y + Q(idx)) + end do + end do + + ! --- Bottom boundary (j=1): Dirichlet T = T_hot --- + do i = 1, nx + idx = i + T_new(idx) = T_hot + end do + + ! --- Top boundary (j=ny): Convection BC --- + ! -k dT/dn = h_conv * (T - T_inf) + ! (one-sided difference for the normal derivative) + do i = 2, nx - 1 + idx = (ny - 1) * nx + i + + T_c = T_cur(idx) + T_e = T_cur(idx + 1) + T_w = T_cur(idx - 1) + T_s = T_cur(idx - nx) + + kx_east = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_e) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_e)) + kx_west = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_w) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_w)) + ky_south = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_s) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_s)) + + flux_x = (kx_east * (T_e - T_c) - kx_west * (T_c - T_w)) / (dx * dx) + + T_new(idx) = T_c + dt / (rho * cp) * ( & + flux_x & + + ky_south * (T_s - T_c) / (dy * dy) & + - h_conv * (T_c - T_inf) / dy & + + Q(idx)) + end do + + ! --- Left boundary (i=1): insulated (zero flux) --- + ! Mirror: T_w = T_e => flux_x uses only east neighbor + do j = 2, ny - 1 + idx = (j - 1) * nx + 1 + + T_c = T_cur(idx) + T_e = T_cur(idx + 1) + T_nn = T_cur(idx + nx) + T_s = T_cur(idx - nx) + + kx_east = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_e) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_e)) + ky_north = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_nn) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_nn)) + ky_south = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_s) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_s)) + + ! Zero-flux left: symmetric difference gives 2*(T_e - T_c)/(2*dx^2) + flux_x = kx_east * (T_e - T_c) / (dx * dx) + flux_y = (ky_north * (T_nn - T_c) - ky_south * (T_c - T_s)) / (dy * dy) + + T_new(idx) = T_c + dt / (rho * cp) * (flux_x + flux_y + Q(idx)) + end do + + ! --- Right boundary (i=nx): insulated (zero flux) --- + do j = 2, ny - 1 + idx = (j - 1) * nx + nx + + T_c = T_cur(idx) + T_w = T_cur(idx - 1) + T_nn = T_cur(idx + nx) + T_s = T_cur(idx - nx) + + kx_west = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_w) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_w)) + ky_north = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_nn) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_nn)) + ky_south = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_s) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_s)) + + flux_x = kx_west * (T_w - T_c) / (dx * dx) + flux_y = (ky_north * (T_nn - T_c) - ky_south * (T_c - T_s)) / (dy * dy) + + T_new(idx) = T_c + dt / (rho * cp) * (flux_x + flux_y + Q(idx)) + end do + + ! --- Corners --- + ! Bottom-left and bottom-right: Dirichlet (already set above) + ! Top-left corner (i=1, j=ny) + idx = (ny - 1) * nx + 1 + T_c = T_cur(idx) + T_e = T_cur(idx + 1) + T_s = T_cur(idx - nx) + + kx_east = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_e) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_e)) + ky_south = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_s) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_s)) + + T_new(idx) = T_c + dt / (rho * cp) * ( & + kx_east * (T_e - T_c) / (dx * dx) & + + ky_south * (T_s - T_c) / (dy * dy) & + - h_conv * (T_c - T_inf) / dy & + + Q(idx)) + + ! Top-right corner (i=nx, j=ny) + idx = ny * nx + T_c = T_cur(idx) + T_w = T_cur(idx - 1) + T_s = T_cur(idx - nx) + + kx_west = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_w) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_w)) + ky_south = 2.0d0 * (k0 + k1 * T_c) * (k0 + k1 * T_s) & + / ((k0 + k1 * T_c) + (k0 + k1 * T_s)) + + T_new(idx) = T_c + dt / (rho * cp) * ( & + kx_west * (T_w - T_c) / (dx * dx) & + + ky_south * (T_s - T_c) / (dy * dy) & + - h_conv * (T_c - T_inf) / dy & + + Q(idx)) + + ! Swap: T_cur <- T_new + do idx = 1, n + T_cur(idx) = T_new(idx) + end do + + end do + + ! Copy result + do idx = 1, n + T_final(idx) = T_cur(idx) + end do + +end subroutine diff --git a/demo/enzyme_thermal_2d/enzyme/wrapper.c b/demo/enzyme_thermal_2d/enzyme/wrapper.c new file mode 100644 index 00000000..d49c7a42 --- /dev/null +++ b/demo/enzyme_thermal_2d/enzyme/wrapper.c @@ -0,0 +1,186 @@ +/* Copyright 2025 Pasteur Labs. All Rights Reserved. + * SPDX-License-Identifier: Apache-2.0 + * + * C wrapper that declares Enzyme AD entry points for the 2D thermal solver. + * After the Enzyme LLVM pass runs, the __enzyme_autodiff and __enzyme_fwddiff + * calls are replaced with compiler-generated derivative code. + * + * Work arrays (T_cur, T_new) are allocated here and passed to the Fortran + * subroutine to avoid _lfortran_malloc calls in the differentiated code. + * + * The resulting shared library exports three functions callable from Python + * via ctypes: + * + * thermal_2d_forward -- primal forward evaluation + * thermal_2d_vjp -- reverse-mode AD (vector-Jacobian product) + * thermal_2d_jvp -- forward-mode AD (Jacobian-vector product) + */ + +#include +#include + +/* Enzyme annotation sentinels (resolved by the Enzyme LLVM pass) */ +int enzyme_dup; +int enzyme_const; + +/* Fortran subroutine (Fortran ABI: everything by pointer) + * Note: n = nx*ny is passed explicitly so the Fortran side sees fixed-size + * arrays and never calls _lfortran_malloc. */ +extern void thermal_2d_solve(int* n, int* nx, int* ny, int* n_steps, + double* T_init, double* T_final, + double* T_cur, double* T_new, + double* k0, double* k1, + double* rho, double* cp, + double* h_conv, double* T_inf, double* T_hot, + double* Q, double* Lx, double* Ly, double* dt); + +/* Enzyme magic functions -- replaced by generated code after the pass */ +extern void __enzyme_autodiff(void*, ...); +extern void __enzyme_fwddiff(void*, ...); + + +/* -- Forward evaluation --------------------------------------------------- */ + +void thermal_2d_forward(int nx, int ny, int n_steps, + const double* T_init, double* T_final, + double k0, double k1, + double rho, double cp, + double h_conv, double T_inf, double T_hot, + const double* Q, double Lx, double Ly, double dt) +{ + int n = nx * ny; + int nx_ = nx, ny_ = ny, n_steps_ = n_steps, n_ = n; + double k0_ = k0, k1_ = k1, rho_ = rho, cp_ = cp; + double h_conv_ = h_conv, T_inf_ = T_inf, T_hot_ = T_hot; + double Lx_ = Lx, Ly_ = Ly, dt_ = dt; + + double* T_cur = (double*)calloc(n, sizeof(double)); + double* T_new = (double*)calloc(n, sizeof(double)); + + thermal_2d_solve(&n_, &nx_, &ny_, &n_steps_, + (double*)T_init, T_final, T_cur, T_new, + &k0_, &k1_, &rho_, &cp_, + &h_conv_, &T_inf_, &T_hot_, + (double*)Q, &Lx_, &Ly_, &dt_); + + free(T_cur); + free(T_new); +} + + +/* -- Reverse mode (VJP) --------------------------------------------------- */ + +void thermal_2d_vjp(int nx, int ny, int n_steps, + const double* T_init, double* dT_init, + const double* T_final, double* dT_final, + double k0, double* dk0, + double k1, double* dk1, + double rho, double* drho, + double cp, double* dcp, + double h_conv, double* dh_conv, + double T_inf, double* dT_inf, + double T_hot, double* dT_hot, + const double* Q, double* dQ, + double Lx, double* dLx, + double Ly, double* dLy, + double dt, double* ddt) +{ + int n = nx * ny; + int nx_ = nx, ny_ = ny, n_steps_ = n_steps, n_ = n; + double k0_ = k0, k1_ = k1, rho_ = rho, cp_ = cp; + double h_conv_ = h_conv, T_inf_ = T_inf, T_hot_ = T_hot; + double Lx_ = Lx, Ly_ = Ly, dt_ = dt; + + /* Work arrays and their shadows (zero-initialized) */ + double* T_cur = (double*)calloc(n, sizeof(double)); + double* dT_cur = (double*)calloc(n, sizeof(double)); + double* T_new = (double*)calloc(n, sizeof(double)); + double* dT_new = (double*)calloc(n, sizeof(double)); + + __enzyme_autodiff((void*)thermal_2d_solve, + enzyme_const, &n_, + enzyme_const, &nx_, + enzyme_const, &ny_, + enzyme_const, &n_steps_, + enzyme_dup, (double*)T_init, dT_init, + enzyme_dup, (double*)T_final, dT_final, + enzyme_dup, T_cur, dT_cur, + enzyme_dup, T_new, dT_new, + enzyme_dup, &k0_, dk0, + enzyme_dup, &k1_, dk1, + enzyme_dup, &rho_, drho, + enzyme_dup, &cp_, dcp, + enzyme_dup, &h_conv_, dh_conv, + enzyme_dup, &T_inf_, dT_inf, + enzyme_dup, &T_hot_, dT_hot, + enzyme_dup, (double*)Q, dQ, + enzyme_dup, &Lx_, dLx, + enzyme_dup, &Ly_, dLy, + enzyme_dup, &dt_, ddt); + + free(T_cur); + free(dT_cur); + free(T_new); + free(dT_new); +} + + +/* -- Forward mode (JVP) --------------------------------------------------- */ + +void thermal_2d_jvp(int nx, int ny, int n_steps, + const double* T_init, const double* dT_init, + double* T_final, double* dT_final, + double k0, double dk0, + double k1, double dk1, + double rho, double drho, + double cp, double dcp, + double h_conv, double dh_conv, + double T_inf, double dT_inf, + double T_hot, double dT_hot, + const double* Q, const double* dQ, + double Lx, double dLx, + double Ly, double dLy, + double dt, double ddt) +{ + int n = nx * ny; + int nx_ = nx, ny_ = ny, n_steps_ = n_steps, n_ = n; + int dnx_ = 0, dny_ = 0, dn_steps_ = 0, dn_ = 0; + double k0_ = k0, k1_ = k1, rho_ = rho, cp_ = cp; + double h_conv_ = h_conv, T_inf_ = T_inf, T_hot_ = T_hot; + double Lx_ = Lx, Ly_ = Ly, dt_ = dt; + double dk0_ = dk0, dk1_ = dk1, drho_ = drho, dcp_ = dcp; + double dh_conv_ = dh_conv, dT_inf_ = dT_inf, dT_hot_ = dT_hot; + double dLx_ = dLx, dLy_ = dLy, ddt_ = ddt; + + /* Work arrays and their tangent shadows */ + double* T_cur = (double*)calloc(n, sizeof(double)); + double* dT_cur = (double*)calloc(n, sizeof(double)); + double* T_new = (double*)calloc(n, sizeof(double)); + double* dT_new = (double*)calloc(n, sizeof(double)); + + __enzyme_fwddiff((void*)thermal_2d_solve, + enzyme_dup, &n_, &dn_, + enzyme_dup, &nx_, &dnx_, + enzyme_dup, &ny_, &dny_, + enzyme_dup, &n_steps_, &dn_steps_, + enzyme_dup, (double*)T_init, (double*)dT_init, + enzyme_dup, T_final, dT_final, + enzyme_dup, T_cur, dT_cur, + enzyme_dup, T_new, dT_new, + enzyme_dup, &k0_, &dk0_, + enzyme_dup, &k1_, &dk1_, + enzyme_dup, &rho_, &drho_, + enzyme_dup, &cp_, &dcp_, + enzyme_dup, &h_conv_, &dh_conv_, + enzyme_dup, &T_inf_, &dT_inf_, + enzyme_dup, &T_hot_, &dT_hot_, + enzyme_dup, (double*)Q, (double*)dQ, + enzyme_dup, &Lx_, &dLx_, + enzyme_dup, &Ly_, &dLy_, + enzyme_dup, &dt_, &ddt_); + + free(T_cur); + free(dT_cur); + free(T_new); + free(dT_new); +} diff --git a/demo/enzyme_thermal_2d/inverse_heat_transfer.ipynb b/demo/enzyme_thermal_2d/inverse_heat_transfer.ipynb new file mode 100644 index 00000000..491e1384 --- /dev/null +++ b/demo/enzyme_thermal_2d/inverse_heat_transfer.ipynb @@ -0,0 +1,911 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "0o7kbl9m2j69", + "metadata": {}, + "source": [ + "# Inverse Heat Transfer with Automatic Differentiation\n", + "\n", + "A steel plate is heating up. You have thermocouple readings at a handful of\n", + "locations, but you don't know the exact material properties — or even what the\n", + "temperature distribution looked like before heating started. Can you figure it out?\n", + "\n", + "This notebook solves two inverse problems of increasing ambition using a Fortran\n", + "finite-difference solver whose exact derivatives are generated automatically by\n", + "[Enzyme](https://enzyme.mit.edu/) at the LLVM IR level — no manual adjoint code,\n", + "no source modifications. Then it shows how `jax.grad` can differentiate through\n", + "the Fortran solver end-to-end via [`tesseract-jax`](https://github.com/pasteurlabs/tesseract-jax).\n", + "\n", + "1. **Part 1: Scalar calibration** — recover 2 material parameters (k₀, k₁) from 9 sensors\n", + "2. **Part 2: Thermal forensics** — recover the full 900-element initial temperature\n", + " field from 100 sensors (finite differences would need 901 forward solves per\n", + " iteration; one VJP gives all 900 gradients at once)\n", + "3. **Part 3: JAX integration** — `jax.grad` through Python → JAX → HTTP → Enzyme → Fortran\n", + " in a single call" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "sp6907y1jgf", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "from tesseract_core import Tesseract\n", + "\n", + "# Grid and simulation parameters (fixed throughout)\n", + "nx, ny = 30, 30\n", + "n = nx * ny\n", + "n_steps = 500\n", + "dt = 0.05 # 500 steps x 0.05s = 25s (CFL-safe up to k0 ~ 80)\n", + "Lx, Ly = 0.1, 0.05\n", + "\n", + "# Fixed physical parameters\n", + "rho = 7850.0 # density [kg/m^3] (mild steel)\n", + "cp = 460.0 # specific heat [J/(kg*K)]\n", + "h_conv = 25.0 # convection coefficient [W/(m^2*K)]\n", + "T_inf = 293.15 # ambient temperature [K]\n", + "T_hot = 373.15 # hot wall temperature [K]\n", + "\n", + "# Initial condition: uniform ambient temperature\n", + "T_init = np.full(n, T_inf)\n", + "Q = np.zeros(n) # no internal heating\n", + "\n", + "print(f\"Simulation: {n_steps} steps x {dt}s = {n_steps * dt:.0f}s total\")" + ] + }, + { + "cell_type": "markdown", + "id": "rkthdyekadr", + "metadata": {}, + "source": "## Part 1: Scalar calibration (2 parameters)\n\n### Generate synthetic data\n\nWe run the solver with the **true** material properties to produce a ground-truth\ntemperature field, then sample it at sparse sensor locations with added noise.\nIn practice, these would be thermocouple readings from a real component." + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8pt0ybtfm36", + "metadata": {}, + "outputs": [], + "source": [ + "# True material properties (what we want to recover)\n", + "k0_true = 45.0 # base conductivity [W/(m*K)]\n", + "k1_true = -0.02 # temperature coefficient [W/(m*K^2)]\n", + "\n", + "\n", + "def make_inputs(k0, k1):\n", + " \"\"\"Build a full input dict for the Tesseract.\"\"\"\n", + " return {\n", + " \"T_init\": T_init,\n", + " \"Q\": Q,\n", + " \"nx\": nx,\n", + " \"ny\": ny,\n", + " \"n_steps\": n_steps,\n", + " \"k0\": float(k0),\n", + " \"k1\": float(k1),\n", + " \"rho\": rho,\n", + " \"cp\": cp,\n", + " \"h_conv\": h_conv,\n", + " \"T_inf\": T_inf,\n", + " \"T_hot\": T_hot,\n", + " \"Lx\": Lx,\n", + " \"Ly\": Ly,\n", + " \"dt\": dt,\n", + " }\n", + "\n", + "\n", + "# Run the ground-truth simulation\n", + "with Tesseract.from_image(\"enzyme-thermal-2d:latest\") as t:\n", + " result_true = t.apply(inputs=make_inputs(k0_true, k1_true))\n", + " T_true = np.array(result_true[\"T_final\"]).reshape(ny, nx)\n", + "\n", + "print(f\"Ground truth: k0={k0_true}, k1={k1_true}\")\n", + "print(f\"Temperature range: {T_true.min():.2f} K to {T_true.max():.2f} K\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8z2g10uvgwl", + "metadata": {}, + "outputs": [], + "source": [ + "# Place sensors on a regular grid in the interior (away from BCs)\n", + "# This mimics a realistic thermocouple layout\n", + "sensor_ix = [7, 15, 22] # x positions\n", + "sensor_jy = [7, 15, 22] # y positions\n", + "sensor_indices = []\n", + "sensor_coords = []\n", + "\n", + "for jy in sensor_jy:\n", + " for ix in sensor_ix:\n", + " sensor_indices.append(jy * nx + ix)\n", + " sensor_coords.append((ix, jy))\n", + "\n", + "sensor_indices = np.array(sensor_indices)\n", + "n_sensors = len(sensor_indices)\n", + "\n", + "# Extract true temperatures at sensor locations and add noise\n", + "rng = np.random.default_rng(42)\n", + "noise_std = 0.5 # K — realistic thermocouple noise\n", + "T_true_flat = T_true.flatten()\n", + "T_obs = T_true_flat[sensor_indices] + rng.normal(0, noise_std, n_sensors)\n", + "\n", + "print(f\"Number of sensors: {n_sensors}\")\n", + "print(f\"Noise std: {noise_std} K\")\n", + "print(f\"Observed temperatures: {T_obs.round(2)}\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "h7wqp7wjjl4", + "metadata": {}, + "outputs": [], + "source": [ + "# Visualize the ground truth and sensor locations\n", + "fig, ax = plt.subplots(1, 1, figsize=(8, 4))\n", + "im = ax.imshow(\n", + " T_true, origin=\"lower\", cmap=\"hot\", extent=[0, Lx * 1e3, 0, Ly * 1e3], aspect=\"auto\"\n", + ")\n", + "plt.colorbar(im, ax=ax, label=\"Temperature [K]\")\n", + "\n", + "# Plot sensor locations\n", + "for ix, jy in sensor_coords:\n", + " x_mm = ix / (nx - 1) * Lx * 1e3\n", + " y_mm = jy / (ny - 1) * Ly * 1e3\n", + " ax.plot(x_mm, y_mm, \"ws\", markersize=8, markeredgecolor=\"blue\", markeredgewidth=1.5)\n", + "\n", + "ax.set_xlabel(\"x [mm]\")\n", + "ax.set_ylabel(\"y [mm]\")\n", + "ax.set_title(\n", + " f\"Ground truth temperature field (k₀={k0_true}, k₁={k1_true})\\n□ = sensor locations\"\n", + ")\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "6o9vjw5xeyw", + "metadata": {}, + "source": "## Step 2: Define the inverse problem\n\nMinimize the misfit between predicted and observed sensor temperatures:\n\n$$\nJ(k_0, k_1) = \\frac{1}{2} \\sum_{i=1}^{N_\\text{sensors}} \\left( T_\\text{pred}(\\mathbf{x}_i; k_0, k_1) - T_\\text{obs}(\\mathbf{x}_i) \\right)^2\n$$\n\nThe gradient $\\nabla_{k_0, k_1} J$ comes from a single VJP (reverse-mode AD) call.\nThe cotangent vector is the residual at sensor locations, zero elsewhere:\n\n$$\n\\bar{T}_j = \\begin{cases}\nT_\\text{pred}(\\mathbf{x}_j) - T_\\text{obs}(\\mathbf{x}_j) & \\text{if } j \\text{ is a sensor location} \\\\\n0 & \\text{otherwise}\n\\end{cases}\n$$\n\nOne VJP call gives $\\partial J / \\partial k_0$ and $\\partial J / \\partial k_1$\nsimultaneously. Finite differences would need a separate forward solve per parameter." + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ah1upfczz2e", + "metadata": {}, + "outputs": [], + "source": [ + "def objective_and_gradient(params, tesseract):\n", + " \"\"\"Compute loss and gradient for the inverse problem.\n", + "\n", + " params: [k0, k1]\n", + " Returns: (loss, [dk0, dk1])\n", + " \"\"\"\n", + " k0, k1 = params\n", + " inputs = make_inputs(k0, k1)\n", + "\n", + " # Forward solve\n", + " result = tesseract.apply(inputs=inputs)\n", + " T_pred = np.array(result[\"T_final\"])\n", + "\n", + " # Loss: sum of squared residuals at sensor locations\n", + " residuals = T_pred[sensor_indices] - T_obs\n", + " loss = 0.5 * np.sum(residuals**2)\n", + "\n", + " # Cotangent vector: residuals at sensor locations, zero elsewhere\n", + " cotangent = np.zeros(n, dtype=np.float64)\n", + " cotangent[sensor_indices] = residuals\n", + "\n", + " # One VJP call gives gradients w.r.t. both k0 and k1\n", + " vjp = tesseract.vector_jacobian_product(\n", + " inputs=inputs,\n", + " vjp_inputs=[\"k0\", \"k1\"],\n", + " vjp_outputs=[\"T_final\"],\n", + " cotangent_vector={\"T_final\": cotangent},\n", + " )\n", + "\n", + " grad = np.array([vjp[\"k0\"], vjp[\"k1\"]])\n", + " return loss, grad" + ] + }, + { + "cell_type": "markdown", + "id": "ll57ug9m2cd", + "metadata": {}, + "source": "## Step 3: Run the optimization\n\nWe start from a deliberately wrong initial guess and use `scipy.optimize.minimize`\nwith L-BFGS-B (a quasi-Newton method that uses gradient information). The bounds\nensure physical plausibility (positive conductivity, reasonable temperature dependence)." + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3iy2we25s1j", + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.optimize import minimize\n", + "\n", + "# Initial guess: 30% off on k0, wrong sign on k1\n", + "k0_init = 60.0\n", + "k1_init = 0.01\n", + "\n", + "# Track optimization history\n", + "history = {\"k0\": [k0_init], \"k1\": [k1_init], \"loss\": []}\n", + "\n", + "with Tesseract.from_image(\"enzyme-thermal-2d:latest\") as t:\n", + " # Evaluate initial loss\n", + " loss0, _ = objective_and_gradient([k0_init, k1_init], t)\n", + " history[\"loss\"].append(loss0)\n", + " print(f\"Initial guess: k0={k0_init:.2f}, k1={k1_init:.4f}, loss={loss0:.4f}\")\n", + "\n", + " def callback(params):\n", + " k0, k1 = params\n", + " loss, _ = objective_and_gradient(params, t)\n", + " history[\"k0\"].append(k0)\n", + " history[\"k1\"].append(k1)\n", + " history[\"loss\"].append(loss)\n", + " print(f\" k0={k0:.4f}, k1={k1:.6f}, loss={loss:.6f}\")\n", + "\n", + " result = minimize(\n", + " fun=lambda p: objective_and_gradient(p, t),\n", + " x0=[k0_init, k1_init],\n", + " method=\"L-BFGS-B\",\n", + " jac=True, # objective_and_gradient returns (loss, grad)\n", + " bounds=[(5.0, 80.0), (-0.08, 0.08)], # stay CFL-safe\n", + " callback=callback,\n", + " options={\"maxiter\": 50, \"ftol\": 1e-12, \"gtol\": 1e-8},\n", + " )\n", + "\n", + " # Final forward solve with recovered parameters\n", + " k0_opt, k1_opt = result.x\n", + " result_opt = t.apply(inputs=make_inputs(k0_opt, k1_opt))\n", + " T_opt = np.array(result_opt[\"T_final\"]).reshape(ny, nx)\n", + "\n", + "print(f\"\\nOptimization finished in {result.nit} iterations\")\n", + "print(f\" True: k0={k0_true:.4f}, k1={k1_true:.6f}\")\n", + "print(f\" Recovered: k0={k0_opt:.4f}, k1={k1_opt:.6f}\")\n", + "print(\n", + " f\" Error: k0: {abs(k0_opt - k0_true) / k0_true * 100:.2f}%, \"\n", + " f\"k1: {abs(k1_opt - k1_true) / abs(k1_true) * 100:.2f}%\"\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "hsdco9e9t14", + "metadata": {}, + "source": "## Step 4: Visualize results\n\n### Convergence" + }, + { + "cell_type": "code", + "execution_count": null, + "id": "zd3j2yjqer", + "metadata": {}, + "outputs": [], + "source": [ + "fig, axes = plt.subplots(1, 3, figsize=(14, 4))\n", + "\n", + "# Loss convergence\n", + "axes[0].semilogy(history[\"loss\"], \"k.-\", linewidth=1.5)\n", + "axes[0].set_xlabel(\"Iteration\")\n", + "axes[0].set_ylabel(\"Loss (sum of squared residuals)\")\n", + "axes[0].set_title(\"Convergence\")\n", + "axes[0].grid(True, alpha=0.3)\n", + "\n", + "# k0 convergence\n", + "axes[1].plot(history[\"k0\"], \"b.-\", linewidth=1.5, label=\"k₀ estimate\")\n", + "axes[1].axhline(\n", + " k0_true, color=\"b\", linestyle=\"--\", alpha=0.5, label=f\"k₀ true = {k0_true}\"\n", + ")\n", + "axes[1].set_xlabel(\"Iteration\")\n", + "axes[1].set_ylabel(\"k₀ [W/(m·K)]\")\n", + "axes[1].set_title(\"Base conductivity\")\n", + "axes[1].legend()\n", + "axes[1].grid(True, alpha=0.3)\n", + "\n", + "# k1 convergence\n", + "axes[2].plot(history[\"k1\"], \"r.-\", linewidth=1.5, label=\"k₁ estimate\")\n", + "axes[2].axhline(\n", + " k1_true, color=\"r\", linestyle=\"--\", alpha=0.5, label=f\"k₁ true = {k1_true}\"\n", + ")\n", + "axes[2].set_xlabel(\"Iteration\")\n", + "axes[2].set_ylabel(\"k₁ [W/(m·K²)]\")\n", + "axes[2].set_title(\"Temperature coefficient\")\n", + "axes[2].legend()\n", + "axes[2].grid(True, alpha=0.3)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "x9v55p3ofe", + "metadata": {}, + "source": "### Temperature fields: initial guess vs. optimized vs. ground truth" + }, + { + "cell_type": "code", + "execution_count": null, + "id": "p46li5txyl", + "metadata": {}, + "outputs": [], + "source": [ + "# Also compute the initial-guess temperature field for comparison\n", + "with Tesseract.from_image(\"enzyme-thermal-2d:latest\") as t:\n", + " result_init = t.apply(inputs=make_inputs(k0_init, k1_init))\n", + " T_init_field = np.array(result_init[\"T_final\"]).reshape(ny, nx)\n", + "\n", + "# Common color range\n", + "vmin = min(T_true.min(), T_opt.min(), T_init_field.min())\n", + "vmax = max(T_true.max(), T_opt.max(), T_init_field.max())\n", + "\n", + "fig, axes = plt.subplots(1, 4, figsize=(18, 4))\n", + "extent = [0, Lx * 1e3, 0, Ly * 1e3]\n", + "\n", + "im0 = axes[0].imshow(\n", + " T_init_field,\n", + " origin=\"lower\",\n", + " cmap=\"hot\",\n", + " extent=extent,\n", + " aspect=\"auto\",\n", + " vmin=vmin,\n", + " vmax=vmax,\n", + ")\n", + "axes[0].set_title(f\"Initial guess\\nk₀={k0_init}, k₁={k1_init}\")\n", + "\n", + "im1 = axes[1].imshow(\n", + " T_opt,\n", + " origin=\"lower\",\n", + " cmap=\"hot\",\n", + " extent=extent,\n", + " aspect=\"auto\",\n", + " vmin=vmin,\n", + " vmax=vmax,\n", + ")\n", + "axes[1].set_title(f\"Recovered\\nk₀={k0_opt:.2f}, k₁={k1_opt:.4f}\")\n", + "\n", + "im2 = axes[2].imshow(\n", + " T_true,\n", + " origin=\"lower\",\n", + " cmap=\"hot\",\n", + " extent=extent,\n", + " aspect=\"auto\",\n", + " vmin=vmin,\n", + " vmax=vmax,\n", + ")\n", + "axes[2].set_title(f\"Ground truth\\nk₀={k0_true}, k₁={k1_true}\")\n", + "\n", + "# Error field\n", + "error = np.abs(T_opt - T_true)\n", + "im3 = axes[3].imshow(error, origin=\"lower\", cmap=\"Blues\", extent=extent, aspect=\"auto\")\n", + "axes[3].set_title(f\"|Recovered - Truth|\\nmax error: {error.max():.3f} K\")\n", + "\n", + "for ax in axes:\n", + " ax.set_xlabel(\"x [mm]\")\n", + " ax.set_ylabel(\"y [mm]\")\n", + " # Mark sensor locations\n", + " for ix, jy in sensor_coords:\n", + " x_mm = ix / (nx - 1) * Lx * 1e3\n", + " y_mm = jy / (ny - 1) * Ly * 1e3\n", + " ax.plot(\n", + " x_mm, y_mm, \"ws\", markersize=5, markeredgecolor=\"blue\", markeredgewidth=1\n", + " )\n", + "\n", + "plt.colorbar(im2, ax=axes[:3].tolist(), label=\"Temperature [K]\", shrink=0.9)\n", + "plt.colorbar(im3, ax=axes[3], label=\"Error [K]\", shrink=0.9)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "y5c2ssvn3x", + "metadata": {}, + "source": [ + "## Part 2: Thermal forensics — recovering a hidden heat signature (900 parameters)\n", + "\n", + "A steel plate was subjected to an unmonitored heating event — say, a laser pulse\n", + "or a localized defect generating heat. Five seconds later, you measure temperatures\n", + "at 100 sensor locations. Can you reconstruct what the initial temperature\n", + "distribution looked like?\n", + "\n", + "This is an ill-posed inverse problem: 900 unknowns (temperature at every grid cell)\n", + "from 100 noisy observations, through a nonlinear PDE. But with exact gradients from\n", + "Enzyme's VJP, L-BFGS-B handles it comfortably.\n", + "\n", + "The cost advantage of reverse-mode AD is now dramatic:\n", + "\n", + "| Method | Forward solves per iteration | Time per iteration |\n", + "|--------|----------------------------:|-------------------:|\n", + "| Finite differences | 901 (N+1) | ~10 s |\n", + "| VJP (reverse-mode AD) | 2 (fwd + rev) | ~0.8 s |\n", + "| **Speedup** | | **~450×** |" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a5vw1rcatio", + "metadata": {}, + "outputs": [], + "source": [ + "# --- Part 2 setup ---\n", + "# Shorter simulation: 5 seconds (we want residual structure in the initial field)\n", + "n_steps_p2 = 100\n", + "dt_p2 = 0.05\n", + "\n", + "# Fixed material properties (known — we're recovering T_init, not k)\n", + "k0_p2 = 45.0\n", + "k1_p2 = -0.01\n", + "\n", + "# Build coordinate arrays for the 30x30 grid\n", + "x = np.linspace(0, Lx, nx)\n", + "y = np.linspace(0, Ly, ny)\n", + "X, Y = np.meshgrid(x, y)\n", + "X_flat, Y_flat = X.flatten(), Y.flatten()\n", + "\n", + "# True initial temperature: two Gaussian hot spots on a warm background\n", + "T_init_true = (\n", + " T_inf\n", + " + 40.0 * np.exp(-((X_flat - 0.04) ** 2 + (Y_flat - 0.025) ** 2) / 0.015**2)\n", + " + 25.0 * np.exp(-((X_flat - 0.08) ** 2 + (Y_flat - 0.035) ** 2) / 0.01**2)\n", + ")\n", + "\n", + "\n", + "# Run forward simulation with true initial field\n", + "def make_inputs_p2(T_init_field):\n", + " return {\n", + " \"T_init\": T_init_field.astype(np.float64),\n", + " \"Q\": Q,\n", + " \"nx\": nx,\n", + " \"ny\": ny,\n", + " \"n_steps\": n_steps_p2,\n", + " \"k0\": k0_p2,\n", + " \"k1\": k1_p2,\n", + " \"rho\": rho,\n", + " \"cp\": cp,\n", + " \"h_conv\": h_conv,\n", + " \"T_inf\": T_inf,\n", + " \"T_hot\": T_hot,\n", + " \"Lx\": Lx,\n", + " \"Ly\": Ly,\n", + " \"dt\": dt_p2,\n", + " }\n", + "\n", + "\n", + "with Tesseract.from_image(\"enzyme-thermal-2d:latest\") as t:\n", + " result_true_p2 = t.apply(inputs=make_inputs_p2(T_init_true))\n", + " T_final_true_p2 = np.array(result_true_p2[\"T_final\"])\n", + "\n", + "# 10x10 sensor grid (100 sensors in the interior)\n", + "sensor_ix_p2 = np.linspace(3, nx - 4, 10, dtype=int)\n", + "sensor_jy_p2 = np.linspace(3, ny - 4, 10, dtype=int)\n", + "sensor_grid = np.array([(jy * nx + ix) for jy in sensor_jy_p2 for ix in sensor_ix_p2])\n", + "n_sensors_p2 = len(sensor_grid)\n", + "\n", + "# Observed data: true final temperatures at sensors + noise\n", + "noise_std_p2 = 0.3 # K\n", + "T_obs_p2 = T_final_true_p2[sensor_grid] + rng.normal(0, noise_std_p2, n_sensors_p2)\n", + "\n", + "print(f\"Grid: {nx}x{ny} = {n} unknowns\")\n", + "print(f\"Sensors: {n_sensors_p2}\")\n", + "print(f\"Simulation: {n_steps_p2} steps x {dt_p2}s = {n_steps_p2 * dt_p2:.0f}s\")\n", + "print(f\"True T_init range: {T_init_true.min():.1f} — {T_init_true.max():.1f} K\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "lafkg3kzyuo", + "metadata": {}, + "outputs": [], + "source": [ + "import time\n", + "\n", + "from scipy.optimize import minimize as sp_minimize\n", + "\n", + "\n", + "def objective_and_gradient_p2(T_init_vec, tesseract):\n", + " \"\"\"Loss and gradient for the T_init recovery problem.\n", + "\n", + " 900 unknowns, 100 observations, 1 VJP call for all 900 gradients.\n", + " \"\"\"\n", + " inputs = make_inputs_p2(T_init_vec)\n", + "\n", + " # Forward solve\n", + " result = tesseract.apply(inputs=inputs)\n", + " T_pred = np.array(result[\"T_final\"])\n", + "\n", + " # Sensor residuals\n", + " residuals = T_pred[sensor_grid] - T_obs_p2\n", + " loss = 0.5 * np.sum(residuals**2)\n", + "\n", + " # Cotangent: residuals at sensor locations\n", + " cotangent = np.zeros(n, dtype=np.float64)\n", + " cotangent[sensor_grid] = residuals\n", + "\n", + " # Single VJP gives gradient w.r.t. all 900 T_init components\n", + " vjp = tesseract.vector_jacobian_product(\n", + " inputs=inputs,\n", + " vjp_inputs=[\"T_init\"],\n", + " vjp_outputs=[\"T_final\"],\n", + " cotangent_vector={\"T_final\": cotangent},\n", + " )\n", + " grad = np.array(vjp[\"T_init\"])\n", + "\n", + " return loss, grad\n", + "\n", + "\n", + "# Run optimization: start from uniform ambient (the wrong answer)\n", + "T_init_guess = np.full(n, T_inf)\n", + "loss_history_p2 = []\n", + "\n", + "with Tesseract.from_image(\"enzyme-thermal-2d:latest\") as t:\n", + " iter_count = [0]\n", + " t_start = time.time()\n", + "\n", + " def callback_p2(x):\n", + " iter_count[0] += 1\n", + " if iter_count[0] % 10 == 0:\n", + " loss, _ = objective_and_gradient_p2(x, t)\n", + " loss_history_p2.append(loss)\n", + " elapsed = time.time() - t_start\n", + " print(f\" iter {iter_count[0]:3d}: loss={loss:.4f}, elapsed={elapsed:.1f}s\")\n", + "\n", + " # Initial loss\n", + " loss0, _ = objective_and_gradient_p2(T_init_guess, t)\n", + " loss_history_p2.insert(0, loss0)\n", + " print(f\"Initial loss: {loss0:.2f}\")\n", + " print(f\"Running L-BFGS-B with {n} parameters...\")\n", + "\n", + " result_p2 = sp_minimize(\n", + " fun=lambda x: objective_and_gradient_p2(x, t),\n", + " x0=T_init_guess,\n", + " method=\"L-BFGS-B\",\n", + " jac=True,\n", + " bounds=[(250.0, 450.0)] * n,\n", + " callback=callback_p2,\n", + " options={\"maxiter\": 100, \"ftol\": 1e-14, \"gtol\": 1e-8},\n", + " )\n", + "\n", + " elapsed_total = time.time() - t_start\n", + "\n", + " # Final loss\n", + " loss_final, _ = objective_and_gradient_p2(result_p2.x, t)\n", + " loss_history_p2.append(loss_final)\n", + "\n", + "T_init_recovered = result_p2.x\n", + "\n", + "print(f\"\\nOptimization finished: {result_p2.nit} iterations, {elapsed_total:.1f}s\")\n", + "print(f\"Loss: {loss0:.2f} → {loss_final:.4f}\")\n", + "print(f\"T_init correlation: {np.corrcoef(T_init_true, T_init_recovered)[0, 1]:.4f}\")\n", + "print(\"\\nCost comparison per iteration:\")\n", + "print(\n", + " f\" Finite differences: {n + 1} forward solves = ~{(n + 1) * elapsed_total / result_p2.nfev:.1f}s\"\n", + ")\n", + "print(\n", + " f\" Reverse-mode AD: 2 solves (fwd+rev) = ~{2 * elapsed_total / result_p2.nfev:.2f}s\"\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fhj5dga2nks", + "metadata": {}, + "outputs": [], + "source": [ + "fig, axes = plt.subplots(2, 3, figsize=(16, 9))\n", + "\n", + "extent = [0, Lx * 1e3, 0, Ly * 1e3]\n", + "\n", + "# --- Top row: initial temperature fields ---\n", + "vmin_init = min(T_init_true.min(), T_init_recovered.min(), T_inf)\n", + "vmax_init = max(T_init_true.max(), T_init_recovered.max())\n", + "\n", + "axes[0, 0].imshow(\n", + " T_init_guess.reshape(ny, nx),\n", + " origin=\"lower\",\n", + " cmap=\"hot\",\n", + " extent=extent,\n", + " aspect=\"auto\",\n", + " vmin=vmin_init,\n", + " vmax=vmax_init,\n", + ")\n", + "axes[0, 0].set_title(\"Starting guess\\n(uniform ambient)\")\n", + "\n", + "axes[0, 1].imshow(\n", + " T_init_recovered.reshape(ny, nx),\n", + " origin=\"lower\",\n", + " cmap=\"hot\",\n", + " extent=extent,\n", + " aspect=\"auto\",\n", + " vmin=vmin_init,\n", + " vmax=vmax_init,\n", + ")\n", + "axes[0, 1].set_title(\n", + " f\"Recovered T₀\\n(corr={np.corrcoef(T_init_true, T_init_recovered)[0, 1]:.3f})\"\n", + ")\n", + "\n", + "im_true = axes[0, 2].imshow(\n", + " T_init_true.reshape(ny, nx),\n", + " origin=\"lower\",\n", + " cmap=\"hot\",\n", + " extent=extent,\n", + " aspect=\"auto\",\n", + " vmin=vmin_init,\n", + " vmax=vmax_init,\n", + ")\n", + "axes[0, 2].set_title(\"True T₀\\n(two Gaussian hot spots)\")\n", + "\n", + "plt.colorbar(im_true, ax=axes[0, :].tolist(), label=\"Temperature [K]\", shrink=0.85)\n", + "\n", + "# Mark sensor locations on all top-row plots\n", + "for ax in axes[0, :]:\n", + " for jy_idx in sensor_jy_p2:\n", + " for ix_idx in sensor_ix_p2:\n", + " x_mm = ix_idx / (nx - 1) * Lx * 1e3\n", + " y_mm = jy_idx / (ny - 1) * Ly * 1e3\n", + " ax.plot(x_mm, y_mm, \".\", color=\"cyan\", markersize=2, alpha=0.5)\n", + " ax.set_xlabel(\"x [mm]\")\n", + " ax.set_ylabel(\"y [mm]\")\n", + "\n", + "# --- Bottom row: diagnostics ---\n", + "\n", + "# Recovery error\n", + "error_p2 = np.abs(T_init_recovered - T_init_true).reshape(ny, nx)\n", + "im_err = axes[1, 0].imshow(\n", + " error_p2, origin=\"lower\", cmap=\"Blues\", extent=extent, aspect=\"auto\"\n", + ")\n", + "axes[1, 0].set_title(\n", + " f\"|Recovered - True|\\nmax={error_p2.max():.1f} K, mean={error_p2.mean():.1f} K\"\n", + ")\n", + "axes[1, 0].set_xlabel(\"x [mm]\")\n", + "axes[1, 0].set_ylabel(\"y [mm]\")\n", + "plt.colorbar(im_err, ax=axes[1, 0], label=\"Error [K]\", shrink=0.85)\n", + "\n", + "# Scatter: true vs recovered\n", + "axes[1, 1].scatter(T_init_true, T_init_recovered, s=3, alpha=0.5, c=\"steelblue\")\n", + "lims = [vmin_init - 5, vmax_init + 5]\n", + "axes[1, 1].plot(lims, lims, \"k--\", alpha=0.5, label=\"perfect recovery\")\n", + "axes[1, 1].set_xlim(lims)\n", + "axes[1, 1].set_ylim(lims)\n", + "axes[1, 1].set_xlabel(\"True T₀ [K]\")\n", + "axes[1, 1].set_ylabel(\"Recovered T₀ [K]\")\n", + "axes[1, 1].set_title(\"True vs. recovered (per grid cell)\")\n", + "axes[1, 1].legend()\n", + "axes[1, 1].set_aspect(\"equal\")\n", + "axes[1, 1].grid(True, alpha=0.3)\n", + "\n", + "# Convergence\n", + "axes[1, 2].semilogy(loss_history_p2, \"k.-\", linewidth=1.5)\n", + "axes[1, 2].set_xlabel(\"Checkpoint\")\n", + "axes[1, 2].set_ylabel(\"Loss\")\n", + "axes[1, 2].set_title(f\"Convergence ({result_p2.nit} L-BFGS iterations)\")\n", + "axes[1, 2].grid(True, alpha=0.3)\n", + "\n", + "plt.suptitle(\n", + " \"Part 2: Recovering a 900-element initial temperature field from 100 sensors\",\n", + " fontsize=13,\n", + " fontweight=\"bold\",\n", + " y=1.01,\n", + ")\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "9l3hx8hmg0w", + "metadata": {}, + "source": [ + "With 2 parameters, finite differences are still practical. With 900, reverse-mode\n", + "AD is ~450× faster. The gap only widens on production meshes. But so far we've been\n", + "calling `apply` and `vector_jacobian_product` manually — can we do better?" + ] + }, + { + "cell_type": "markdown", + "id": "v1urnmbjtho", + "metadata": {}, + "source": [ + "## Part 3: End-to-end JAX autodiff through a Fortran solver\n", + "\n", + "With [`tesseract-jax`](https://github.com/pasteurlabs/tesseract-jax),\n", + "the Tesseract becomes a JAX primitive. `jax.grad` just works — through six layers:\n", + "\n", + "```\n", + "jax.grad (Python)\n", + " └─ JAX reverse-mode AD\n", + " └─ apply_tesseract (JAX primitive)\n", + " └─ HTTP/JSON call to Tesseract container\n", + " └─ vector_jacobian_product endpoint\n", + " └─ Enzyme reverse-mode AD (LLVM IR)\n", + " └─ Fortran solver (thermal_2d_solve)\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "yj2fdd4b1mt", + "metadata": {}, + "outputs": [], + "source": [ + "import jax\n", + "import jax.numpy as jnp\n", + "from tesseract_jax import apply_tesseract\n", + "\n", + "# Serve both Tesseracts (they stay alive for the rest of the notebook)\n", + "enzyme_tess = Tesseract.from_image(\"enzyme-thermal-2d:latest\")\n", + "enzyme_tess.serve()\n", + "\n", + "jax_tess = Tesseract.from_image(\"jax-thermal-2d:latest\")\n", + "jax_tess.serve()\n", + "\n", + "# Build inputs as JAX arrays (required by apply_tesseract)\n", + "jax_inputs = {\n", + " \"T_init\": jnp.full(n, T_inf, dtype=jnp.float64),\n", + " \"Q\": jnp.zeros(n, dtype=jnp.float64),\n", + " \"nx\": nx,\n", + " \"ny\": ny,\n", + " \"n_steps\": n_steps,\n", + " \"k0\": jnp.float64(45.0),\n", + " \"k1\": jnp.float64(-0.02),\n", + " \"rho\": jnp.float64(rho),\n", + " \"cp\": jnp.float64(cp),\n", + " \"h_conv\": jnp.float64(h_conv),\n", + " \"T_inf\": jnp.float64(T_inf),\n", + " \"T_hot\": jnp.float64(T_hot),\n", + " \"Lx\": jnp.float64(Lx),\n", + " \"Ly\": jnp.float64(Ly),\n", + " \"dt\": jnp.float64(dt),\n", + "}\n", + "\n", + "# The Fortran solver is now a JAX-differentiable function\n", + "T_final = apply_tesseract(enzyme_tess, jax_inputs)[\"T_final\"]\n", + "print(\n", + " f\"Forward pass through Fortran solver: T range [{T_final.min():.2f}, {T_final.max():.2f}]\"\n", + ")\n", + "print(f\"Type: {type(T_final)} — it's a JAX array\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7ocuoxl2jc3", + "metadata": {}, + "outputs": [], + "source": [ + "# Define a loss function that mixes local JAX ops with a remote Fortran solver.\n", + "# jax.grad differentiates through all of it, including the HTTP call to Enzyme.\n", + "\n", + "\n", + "def loss_fn(k0, k1, tesseract):\n", + " \"\"\"Sensor misfit loss. Calls a Fortran solver via apply_tesseract.\"\"\"\n", + " inputs = {**jax_inputs, \"k0\": k0, \"k1\": k1}\n", + " T_pred = apply_tesseract(tesseract, inputs)[\"T_final\"]\n", + " residuals = T_pred[sensor_indices] - jnp.array(T_obs)\n", + " return 0.5 * jnp.sum(residuals**2)\n", + "\n", + "\n", + "k0_test = jnp.float64(60.0)\n", + "k1_test = jnp.float64(0.01)\n", + "\n", + "# Enzyme backend: JAX AD → HTTP → Enzyme AD → Fortran\n", + "loss_enzyme, (dk0_enzyme, dk1_enzyme) = jax.value_and_grad(loss_fn, argnums=(0, 1))(\n", + " k0_test, k1_test, enzyme_tess\n", + ")\n", + "print(\"Enzyme backend (Fortran):\")\n", + "print(f\" loss = {loss_enzyme:.4f}\")\n", + "print(f\" ∂loss/∂k0 = {dk0_enzyme:.6f}\")\n", + "print(f\" ∂loss/∂k1 = {dk1_enzyme:.6f}\")\n", + "\n", + "# JAX backend: JAX AD → HTTP → jax.vjp → XLA\n", + "loss_jax, (dk0_jax, dk1_jax) = jax.value_and_grad(loss_fn, argnums=(0, 1))(\n", + " k0_test, k1_test, jax_tess\n", + ")\n", + "print(\"\\nJAX backend (Python):\")\n", + "print(f\" loss = {loss_jax:.4f}\")\n", + "print(f\" ∂loss/∂k0 = {dk0_jax:.6f}\")\n", + "print(f\" ∂loss/∂k1 = {dk1_jax:.6f}\")\n", + "\n", + "print(\n", + " f\"\\nGradient agreement: Δdk0 = {abs(dk0_enzyme - dk0_jax):.2e}, \"\n", + " f\"Δdk1 = {abs(dk1_enzyme - dk1_jax):.2e}\"\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "t7ybs40pyc", + "metadata": {}, + "outputs": [], + "source": [ + "# Full optimization loop using jax.value_and_grad.\n", + "# The optimizer just sees a JAX function.\n", + "\n", + "k0_opt_jax = jnp.float64(60.0)\n", + "k1_opt_jax = jnp.float64(0.01)\n", + "lr = jnp.float64(0.5)\n", + "\n", + "loss_history_p3 = []\n", + "\n", + "grad_fn = jax.value_and_grad(loss_fn, argnums=(0, 1))\n", + "\n", + "print(\"Gradient descent through Fortran solver via tesseract-jax\")\n", + "print(f\"{'iter':>4s} {'loss':>10s} {'k0':>8s} {'k1':>10s}\")\n", + "print(\"-\" * 40)\n", + "\n", + "for i in range(20):\n", + " loss_val, (dk0, dk1) = grad_fn(k0_opt_jax, k1_opt_jax, enzyme_tess)\n", + " loss_history_p3.append(float(loss_val))\n", + "\n", + " k0_opt_jax = jnp.clip(k0_opt_jax - lr * dk0, 5.0, 80.0)\n", + " k1_opt_jax = jnp.clip(k1_opt_jax - lr * dk1, -0.08, 0.08)\n", + "\n", + " if i % 5 == 0 or i == 19:\n", + " print(f\"{i:4d} {loss_val:10.4f} {k0_opt_jax:8.4f} {k1_opt_jax:10.6f}\")\n", + "\n", + "print(f\"\\nRecovered: k0={float(k0_opt_jax):.4f}, k1={float(k1_opt_jax):.6f}\")\n", + "print(f\"True: k0={k0_true:.4f}, k1={k1_true:.6f}\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "vn8dmjqfs9k", + "metadata": {}, + "outputs": [], + "source": [ + "# Clean up\n", + "enzyme_tess.teardown()\n", + "jax_tess.teardown()" + ] + }, + { + "cell_type": "markdown", + "id": "6upzkt20zux", + "metadata": {}, + "source": [ + "## What just happened\n", + "\n", + "A single `jax.value_and_grad` call triggered this chain:\n", + "\n", + "| Layer | Technology | Role |\n", + "|-------|-----------|------|\n", + "| Optimizer | Python / JAX | Gradient descent loop |\n", + "| AD framework | JAX reverse-mode | Propagates cotangents |\n", + "| Tesseract bridge | `tesseract-jax` | Registers JAX primitive, dispatches HTTP calls |\n", + "| Transport | HTTP + JSON | Crosses process/container boundary |\n", + "| AD engine | Enzyme (LLVM pass) | Generates VJP from compiled Fortran IR |\n", + "| Solver | Fortran 90 | `thermal_2d_solve` |\n", + "\n", + "Swapping `enzyme_tess` for `jax_tess` produces the same gradients — the\n", + "optimization code doesn't change.\n", + "\n", + "The Fortran solver was never modified. Enzyme differentiated it from the compiled\n", + "LLVM IR. Tesseract made it callable — and differentiable — from JAX." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python", + "version": "3.11.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/demo/enzyme_thermal_2d/tesseract_api.py b/demo/enzyme_thermal_2d/tesseract_api.py new file mode 100644 index 00000000..6f994cb2 --- /dev/null +++ b/demo/enzyme_thermal_2d/tesseract_api.py @@ -0,0 +1,489 @@ +# Copyright 2025 Pasteur Labs. All Rights Reserved. +# SPDX-License-Identifier: Apache-2.0 + +"""Tesseract wrapping a 2D Fortran thermal solver differentiated by Enzyme. + +This example demonstrates how to obtain exact automatic derivatives of a +production-style Fortran thermal simulation without writing any adjoint code. + +The solver computes transient 2D heat conduction with: + - Temperature-dependent conductivity: k(T) = k0 + k1*T + - Mixed boundary conditions: Dirichlet (hot wall), convection, insulated + - Volumetric heat source + - Multi-step explicit time integration + +Enzyme generates machine-precision derivatives through the entire time-stepping +loop, enabling gradient-based optimization of material properties, boundary +conditions, or initial conditions with respect to any output. +""" + +import ctypes +from pathlib import Path +from typing import Any + +import numpy as np +from pydantic import BaseModel, Field, model_validator +from typing_extensions import Self + +from tesseract_core.runtime import Array, Differentiable, Float64 + +# -- Shared library loading ------------------------------------------------ + +_LIB_PATH = Path("/tesseract/enzyme/libthermal_2d_ad.so") +_lib = ctypes.CDLL(str(_LIB_PATH)) + +# void thermal_2d_forward(int nx, int ny, int n_steps, +# double* T_init, double* T_final, +# double k0, double k1, double rho, double cp, +# double h_conv, double T_inf, double T_hot, +# double* Q, double Lx, double Ly, double dt) +_lib.thermal_2d_forward.restype = None +_lib.thermal_2d_forward.argtypes = [ + ctypes.c_int, # nx + ctypes.c_int, # ny + ctypes.c_int, # n_steps + ctypes.POINTER(ctypes.c_double), # T_init + ctypes.POINTER(ctypes.c_double), # T_final + ctypes.c_double, # k0 + ctypes.c_double, # k1 + ctypes.c_double, # rho + ctypes.c_double, # cp + ctypes.c_double, # h_conv + ctypes.c_double, # T_inf + ctypes.c_double, # T_hot + ctypes.POINTER(ctypes.c_double), # Q + ctypes.c_double, # Lx + ctypes.c_double, # Ly + ctypes.c_double, # dt +] + +# void thermal_2d_vjp(int nx, int ny, int n_steps, +# double* T_init, double* dT_init, double* T_final, double* dT_final, +# double k0, double* dk0, double k1, double* dk1, +# double rho, double* drho, double cp, double* dcp, +# double h_conv, double* dh_conv, double T_inf, double* dT_inf, +# double T_hot, double* dT_hot, +# double* Q, double* dQ, +# double Lx, double* dLx, double Ly, double* dLy, double dt, double* ddt) +_lib.thermal_2d_vjp.restype = None +_lib.thermal_2d_vjp.argtypes = [ + ctypes.c_int, # nx + ctypes.c_int, # ny + ctypes.c_int, # n_steps + ctypes.POINTER(ctypes.c_double), # T_init + ctypes.POINTER(ctypes.c_double), # dT_init + ctypes.POINTER(ctypes.c_double), # T_final + ctypes.POINTER(ctypes.c_double), # dT_final + ctypes.c_double, # k0 + ctypes.POINTER(ctypes.c_double), # dk0 + ctypes.c_double, # k1 + ctypes.POINTER(ctypes.c_double), # dk1 + ctypes.c_double, # rho + ctypes.POINTER(ctypes.c_double), # drho + ctypes.c_double, # cp + ctypes.POINTER(ctypes.c_double), # dcp + ctypes.c_double, # h_conv + ctypes.POINTER(ctypes.c_double), # dh_conv + ctypes.c_double, # T_inf + ctypes.POINTER(ctypes.c_double), # dT_inf + ctypes.c_double, # T_hot + ctypes.POINTER(ctypes.c_double), # dT_hot + ctypes.POINTER(ctypes.c_double), # Q + ctypes.POINTER(ctypes.c_double), # dQ + ctypes.c_double, # Lx + ctypes.POINTER(ctypes.c_double), # dLx + ctypes.c_double, # Ly + ctypes.POINTER(ctypes.c_double), # dLy + ctypes.c_double, # dt + ctypes.POINTER(ctypes.c_double), # ddt +] + +# void thermal_2d_jvp(int nx, int ny, int n_steps, +# double* T_init, double* dT_init, double* T_final, double* dT_final, +# double k0, double dk0, double k1, double dk1, +# double rho, double drho, double cp, double dcp, +# double h_conv, double dh_conv, double T_inf, double dT_inf, +# double T_hot, double dT_hot, +# double* Q, double* dQ, +# double Lx, double dLx, double Ly, double dLy, double dt, double ddt) +_lib.thermal_2d_jvp.restype = None +_lib.thermal_2d_jvp.argtypes = [ + ctypes.c_int, # nx + ctypes.c_int, # ny + ctypes.c_int, # n_steps + ctypes.POINTER(ctypes.c_double), # T_init + ctypes.POINTER(ctypes.c_double), # dT_init + ctypes.POINTER(ctypes.c_double), # T_final + ctypes.POINTER(ctypes.c_double), # dT_final + ctypes.c_double, # k0 + ctypes.c_double, # dk0 + ctypes.c_double, # k1 + ctypes.c_double, # dk1 + ctypes.c_double, # rho + ctypes.c_double, # drho + ctypes.c_double, # cp + ctypes.c_double, # dcp + ctypes.c_double, # h_conv + ctypes.c_double, # dh_conv + ctypes.c_double, # T_inf + ctypes.c_double, # dT_inf + ctypes.c_double, # T_hot + ctypes.c_double, # dT_hot + ctypes.POINTER(ctypes.c_double), # Q + ctypes.POINTER(ctypes.c_double), # dQ + ctypes.c_double, # Lx + ctypes.c_double, # dLx + ctypes.c_double, # Ly + ctypes.c_double, # dLy + ctypes.c_double, # dt + ctypes.c_double, # ddt +] + + +def _as_ptr(arr: np.ndarray) -> ctypes.POINTER(ctypes.c_double): + """Get a ctypes double pointer from a contiguous float64 array.""" + return arr.ctypes.data_as(ctypes.POINTER(ctypes.c_double)) + + +# -- Schemas --------------------------------------------------------------- + + +class InputSchema(BaseModel): + """Input for a 2D transient heat conduction solver. + + Solves rho*cp*dT/dt = div(k(T)*grad(T)) + Q on a rectangular domain + with Dirichlet (hot wall), convection, and insulated boundary conditions. + """ + + # Initial temperature field (flattened row-major, nx*ny) + T_init: Differentiable[Array[(None,), Float64]] = Field( + description=( + "Initial temperature field [K]. Flattened row-major array of " + "shape (nx*ny,). Index (i,j) maps to j*nx+i." + ), + ) + + # Grid dimensions (not differentiable — integer-like) + nx: int = Field( + default=20, + description="Number of grid points in x direction.", + ge=3, + ) + ny: int = Field( + default=20, + description="Number of grid points in y direction.", + ge=3, + ) + + # Time integration + n_steps: int = Field( + default=100, + description="Number of explicit Euler time steps.", + ge=1, + ) + dt: Differentiable[Float64] = Field( + default=0.01, + description="Time step size [s].", + gt=0.0, + ) + + # Domain geometry + Lx: Differentiable[Float64] = Field( + default=0.1, + description="Domain length in x [m].", + gt=0.0, + ) + Ly: Differentiable[Float64] = Field( + default=0.05, + description="Domain length in y [m].", + gt=0.0, + ) + + # Material properties + k0: Differentiable[Float64] = Field( + default=45.0, + description="Base thermal conductivity [W/(m*K)]. k(T) = k0 + k1*T.", + gt=0.0, + ) + k1: Differentiable[Float64] = Field( + default=-0.01, + description=( + "Temperature coefficient of conductivity [W/(m*K^2)]. " + "k(T) = k0 + k1*T. Negative values model metals." + ), + ) + rho: Differentiable[Float64] = Field( + default=7850.0, + description="Density [kg/m^3].", + gt=0.0, + ) + cp: Differentiable[Float64] = Field( + default=460.0, + description="Specific heat capacity [J/(kg*K)].", + gt=0.0, + ) + + # Boundary conditions + h_conv: Differentiable[Float64] = Field( + default=25.0, + description="Convective heat transfer coefficient at top boundary [W/(m^2*K)].", + gt=0.0, + ) + T_inf: Differentiable[Float64] = Field( + default=293.15, + description="Ambient temperature for convection BC [K].", + ) + T_hot: Differentiable[Float64] = Field( + default=373.15, + description="Fixed temperature at bottom (Dirichlet) boundary [K].", + ) + + # Volumetric heat source (flattened row-major, nx*ny) + Q: Differentiable[Array[(None,), Float64]] = Field( + description=( + "Volumetric heat source [W/m^3]. Flattened row-major array of " + "shape (nx*ny,). Use zeros for no internal heating." + ), + ) + + @model_validator(mode="after") + def check_array_sizes(self) -> Self: + """Verify T_init and Q have the correct size.""" + expected = self.nx * self.ny + if len(self.T_init) != expected: + raise ValueError( + f"T_init has {len(self.T_init)} elements, expected nx*ny = {expected}." + ) + if len(self.Q) != expected: + raise ValueError( + f"Q has {len(self.Q)} elements, expected nx*ny = {expected}." + ) + return self + + @model_validator(mode="after") + def check_stability(self) -> Self: + """Check CFL stability for the explicit scheme. + + For temperature-dependent conductivity, use k_max = k0 + k1*T_hot + (conservative estimate with the hottest expected temperature). + """ + dx = self.Lx / (self.nx - 1) + dy = self.Ly / (self.ny - 1) + k_max = self.k0 + self.k1 * self.T_hot + if k_max <= 0: + raise ValueError( + f"Conductivity k(T_hot) = {k_max:.4f} <= 0. Increase k0 or reduce |k1|." + ) + r = k_max * self.dt / (self.rho * self.cp) * (1.0 / (dx * dx) + 1.0 / (dy * dy)) + if r > 0.5: + raise ValueError( + f"CFL stability condition violated: r = {r:.4f} > 0.5. " + f"Reduce dt, or increase grid spacing." + ) + return self + + +class OutputSchema(BaseModel): + """Output: temperature field after time integration.""" + + T_final: Differentiable[Array[(None,), Float64]] = Field( + description=( + "Temperature field after n_steps time steps [K]. " + "Flattened row-major array of shape (nx*ny,)." + ), + ) + + +# -- Required endpoints ---------------------------------------------------- + + +def apply(inputs: InputSchema) -> OutputSchema: + """Run the 2D thermal solver for n_steps explicit Euler steps.""" + T_init = np.ascontiguousarray(inputs.T_init, dtype=np.float64) + Q = np.ascontiguousarray(inputs.Q, dtype=np.float64) + n = inputs.nx * inputs.ny + T_final = np.zeros(n, dtype=np.float64) + + _lib.thermal_2d_forward( + inputs.nx, + inputs.ny, + inputs.n_steps, + _as_ptr(T_init), + _as_ptr(T_final), + inputs.k0, + inputs.k1, + inputs.rho, + inputs.cp, + inputs.h_conv, + inputs.T_inf, + inputs.T_hot, + _as_ptr(Q), + inputs.Lx, + inputs.Ly, + inputs.dt, + ) + + return OutputSchema(T_final=T_final) + + +# -- Optional endpoints (AD via Enzyme) ------------------------------------ + + +# All differentiable scalar parameters, in the order they appear in the wrapper +_SCALAR_PARAMS = ["k0", "k1", "rho", "cp", "h_conv", "T_inf", "T_hot", "Lx", "Ly", "dt"] + + +def _run_vjp(inputs: InputSchema, cotangent_T_final: np.ndarray): + """Run Enzyme reverse-mode AD and return all gradients.""" + T_init = np.ascontiguousarray(inputs.T_init, dtype=np.float64) + Q = np.ascontiguousarray(inputs.Q, dtype=np.float64) + n = inputs.nx * inputs.ny + + # Shadow arrays (Enzyme accumulates gradients into these) + dT_init = np.zeros(n, dtype=np.float64) + T_final = np.zeros(n, dtype=np.float64) + dT_final = np.array(cotangent_T_final, dtype=np.float64) + dQ = np.zeros(n, dtype=np.float64) + + # Shadow scalars + dk0 = ctypes.c_double(0.0) + dk1 = ctypes.c_double(0.0) + drho = ctypes.c_double(0.0) + dcp = ctypes.c_double(0.0) + dh_conv = ctypes.c_double(0.0) + dT_inf = ctypes.c_double(0.0) + dT_hot = ctypes.c_double(0.0) + dLx = ctypes.c_double(0.0) + dLy = ctypes.c_double(0.0) + ddt = ctypes.c_double(0.0) + + _lib.thermal_2d_vjp( + inputs.nx, + inputs.ny, + inputs.n_steps, + _as_ptr(T_init), + _as_ptr(dT_init), + _as_ptr(T_final), + _as_ptr(dT_final), + inputs.k0, + ctypes.byref(dk0), + inputs.k1, + ctypes.byref(dk1), + inputs.rho, + ctypes.byref(drho), + inputs.cp, + ctypes.byref(dcp), + inputs.h_conv, + ctypes.byref(dh_conv), + inputs.T_inf, + ctypes.byref(dT_inf), + inputs.T_hot, + ctypes.byref(dT_hot), + _as_ptr(Q), + _as_ptr(dQ), + inputs.Lx, + ctypes.byref(dLx), + inputs.Ly, + ctypes.byref(dLy), + inputs.dt, + ctypes.byref(ddt), + ) + + return { + "T_init": dT_init, + "Q": dQ, + "k0": dk0.value, + "k1": dk1.value, + "rho": drho.value, + "cp": dcp.value, + "h_conv": dh_conv.value, + "T_inf": dT_inf.value, + "T_hot": dT_hot.value, + "Lx": dLx.value, + "Ly": dLy.value, + "dt": ddt.value, + } + + +def _run_jvp(inputs: InputSchema, tangents: dict[str, Any]): + """Run Enzyme forward-mode AD and return output tangent.""" + T_init = np.ascontiguousarray(inputs.T_init, dtype=np.float64) + Q = np.ascontiguousarray(inputs.Q, dtype=np.float64) + n = inputs.nx * inputs.ny + + dT_init = np.ascontiguousarray( + tangents.get("T_init", np.zeros(n, dtype=np.float64)), + dtype=np.float64, + ) + dQ = np.ascontiguousarray( + tangents.get("Q", np.zeros(n, dtype=np.float64)), + dtype=np.float64, + ) + T_final = np.zeros(n, dtype=np.float64) + dT_final = np.zeros(n, dtype=np.float64) + + _lib.thermal_2d_jvp( + inputs.nx, + inputs.ny, + inputs.n_steps, + _as_ptr(T_init), + _as_ptr(dT_init), + _as_ptr(T_final), + _as_ptr(dT_final), + inputs.k0, + float(tangents.get("k0", 0.0)), + inputs.k1, + float(tangents.get("k1", 0.0)), + inputs.rho, + float(tangents.get("rho", 0.0)), + inputs.cp, + float(tangents.get("cp", 0.0)), + inputs.h_conv, + float(tangents.get("h_conv", 0.0)), + inputs.T_inf, + float(tangents.get("T_inf", 0.0)), + inputs.T_hot, + float(tangents.get("T_hot", 0.0)), + _as_ptr(Q), + _as_ptr(dQ), + inputs.Lx, + float(tangents.get("Lx", 0.0)), + inputs.Ly, + float(tangents.get("Ly", 0.0)), + inputs.dt, + float(tangents.get("dt", 0.0)), + ) + + return dT_final + + +def vector_jacobian_product( + inputs: InputSchema, + vjp_inputs: set[str], + vjp_outputs: set[str], + cotangent_vector: dict[str, Any], +): + """Reverse-mode AD via Enzyme: compute v^T @ J.""" + n = inputs.nx * inputs.ny + cotangent_T_final = cotangent_vector.get( + "T_final", + np.zeros(n, dtype=np.float64), + ) + all_grads = _run_vjp(inputs, cotangent_T_final) + + return {k: v for k, v in all_grads.items() if k in vjp_inputs} + + +def jacobian_vector_product( + inputs: InputSchema, + jvp_inputs: set[str], + jvp_outputs: set[str], + tangent_vector: dict[str, Any], +): + """Forward-mode AD via Enzyme: compute J @ v.""" + dT_final = _run_jvp(inputs, tangent_vector) + + result = {} + if "T_final" in jvp_outputs: + result["T_final"] = dT_final + return result diff --git a/demo/enzyme_thermal_2d/tesseract_config.yaml b/demo/enzyme_thermal_2d/tesseract_config.yaml new file mode 100644 index 00000000..2c198a2c --- /dev/null +++ b/demo/enzyme_thermal_2d/tesseract_config.yaml @@ -0,0 +1,62 @@ +name: "enzyme-thermal-2d" +version: "1.0.0" +description: | + Differentiable 2D transient heat conduction solver using Enzyme automatic + differentiation. + + Solves rho*cp*dT/dt = div(k(T)*grad(T)) + Q on a structured rectangular + grid with temperature-dependent conductivity k(T) = k0 + k1*T, mixed + boundary conditions (Dirichlet, convection, insulated), and multi-step + explicit time integration. + + Enzyme generates both forward-mode (JVP) and reverse-mode (VJP) derivatives + through the entire time-stepping loop directly from the compiled Fortran code + at the LLVM IR level — no manual adjoint code required. + + Industry relevance: gradient-based calibration of thermal material properties, + inverse heat transfer problems, sensitivity analysis for thermal management + design, and differentiable physics for digital twins. + +build_config: + base_image: "debian:bookworm-slim" + target_platform: "linux/amd64" + + extra_packages: + - wget + - gnupg + - ca-certificates + - bzip2 + + package_data: + - ["enzyme/thermal_2d.f90", "enzyme/thermal_2d.f90"] + - ["enzyme/wrapper.c", "enzyme/wrapper.c"] + - ["enzyme/build.sh", "enzyme/build.sh"] + + custom_build_steps: + # Install LLVM 19 toolchain + - | + RUN wget -qO- https://apt.llvm.org/llvm-snapshot.gpg.key | tee /etc/apt/trusted.gpg.d/apt.llvm.org.asc && \ + echo "deb http://apt.llvm.org/bookworm/ llvm-toolchain-bookworm-19 main" > /etc/apt/sources.list.d/llvm.list && \ + apt-get update && apt-get install -y --no-install-recommends llvm-19 clang-19 && \ + rm -rf /var/lib/apt/lists/* && \ + for tool in opt llvm-as llvm-link llvm-dis llc clang clang++; do \ + ln -sf /usr/bin/${tool}-19 /usr/local/bin/${tool} 2>/dev/null || true; \ + done + + # Install LFortran via micromamba (prebuilt from conda-forge) + - | + RUN wget -q https://github.com/mamba-org/micromamba-releases/releases/latest/download/micromamba-linux-64 \ + -O /usr/local/bin/micromamba && chmod +x /usr/local/bin/micromamba && \ + MAMBA_ROOT_PREFIX=/opt/conda micromamba create -y -n base -c conda-forge lfortran=0.61.0 && \ + ln -sf $(find /opt/conda -name lfortran -type f | head -1) /usr/local/bin/lfortran && \ + echo /opt/conda/lib > /etc/ld.so.conf.d/conda.conf && ldconfig + + # Download prebuilt Enzyme LLVM plugin + - | + RUN wget -q https://github.com/EnzymeAD/Enzyme/releases/download/nightly/LLVMEnzyme-19.so \ + -O /usr/local/lib/LLVMEnzyme-19.so + + # Build the differentiated shared library + - | + RUN chmod +x /tesseract/enzyme/build.sh && \ + /tesseract/enzyme/build.sh /tesseract/enzyme/libthermal_2d_ad.so diff --git a/demo/enzyme_thermal_2d/tesseract_requirements.txt b/demo/enzyme_thermal_2d/tesseract_requirements.txt new file mode 100644 index 00000000..24ce15ab --- /dev/null +++ b/demo/enzyme_thermal_2d/tesseract_requirements.txt @@ -0,0 +1 @@ +numpy diff --git a/demo/jax_thermal_2d/README.md b/demo/jax_thermal_2d/README.md new file mode 100644 index 00000000..6b1fb623 --- /dev/null +++ b/demo/jax_thermal_2d/README.md @@ -0,0 +1,58 @@ +# JAX: Differentiable 2D Thermal Solver + +This example is a **JAX reimplementation** of the [Enzyme Thermal 2D](../enzyme_thermal_2d/) solver. It solves the same physics with an identical Tesseract interface, but obtains derivatives via `jax.vjp` / `jax.jvp` instead of Enzyme's LLVM-level AD. + +## What it does + +Same governing equation as the Enzyme version: + +``` +rho * cp * dT/dt = div( k(T) * grad(T) ) + Q +``` + +with temperature-dependent conductivity `k(T) = k0 + k1*T`, mixed boundary conditions (Dirichlet, convection, insulated), and explicit Euler time integration. + +## Why both versions? + +The two implementations represent different strategies for making legacy solvers differentiable: + +| | Enzyme (Fortran) | JAX (Python) | +| ------------------------ | ---------------------------------------------------------- | ----------------------------- | +| **Approach** | Keep existing Fortran code, differentiate at LLVM IR level | Rewrite solver in JAX | +| **AD mechanism** | Enzyme LLVM pass | `jax.vjp` / `jax.jvp` | +| **Build complexity** | LFortran + LLVM + Enzyme toolchain | `pip install jax` | +| **Legacy code reuse** | Full — no solver rewrite needed | None — complete rewrite | +| **JIT compilation** | Ahead-of-time (LLVM) | XLA JIT (first call slower) | +| **Gradient correctness** | Exact (compiler-generated) | Exact (source transformation) | + +## Usage + +```python +from tesseract_core import Tesseract +import numpy as np + +with Tesseract.from_image("jax-thermal-2d:latest") as t: + nx, ny = 20, 20 + result = t.apply(inputs={ + "T_init": np.full(nx * ny, 293.15), + "Q": np.zeros(nx * ny), + "nx": nx, "ny": ny, "n_steps": 100, + "k0": 45.0, "k1": -0.01, + "rho": 7850.0, "cp": 460.0, + "h_conv": 25.0, "T_inf": 293.15, "T_hot": 373.15, + "Lx": 0.1, "Ly": 0.05, "dt": 0.01, + }) + T_final = result["T_final"].reshape(ny, nx) +``` + +The interface is identical to `enzyme-thermal-2d` — you can swap one for the other by changing only the image name. + +## File structure + +``` +jax_thermal_2d/ +├── README.md +├── tesseract_api.py # JAX solver + auto-derived AD endpoints +├── tesseract_config.yaml # Build config (just JAX + equinox) +└── tesseract_requirements.txt # jax[cpu], equinox +``` diff --git a/demo/jax_thermal_2d/benchmark.py b/demo/jax_thermal_2d/benchmark.py new file mode 100644 index 00000000..9be78b58 --- /dev/null +++ b/demo/jax_thermal_2d/benchmark.py @@ -0,0 +1,144 @@ +#!/usr/bin/env python3 +# Copyright 2025 Pasteur Labs. All Rights Reserved. +# SPDX-License-Identifier: Apache-2.0 + +"""Benchmark: Enzyme (Fortran) vs JAX thermal 2D solver. + +Compares wall-clock time for forward pass and VJP across grid sizes. +Both images must be built before running: + + tesseract build examples/enzyme_thermal_2d + tesseract build examples/jax_thermal_2d + +NOTE: For a fair comparison, both images must run on the same architecture. +The Enzyme image requires linux/amd64 (LFortran + Enzyme are x86-only), +so on ARM machines (Apple Silicon) it runs under Rosetta emulation. +Run this script on an x86-64 machine for meaningful results. +""" + +import time + +import numpy as np + +from tesseract_core import Tesseract + +IMAGES = { + "Enzyme": "enzyme-thermal-2d:latest", + "JAX": "jax-thermal-2d:latest", +} + +GRID_SIZES = [ + (30, 30, 50), + (100, 100, 50), + (200, 200, 50), + (300, 300, 50), +] + +N_WARMUP = 5 +N_TRIALS = 15 + + +def make_inputs(nx, ny, n_steps): + n = nx * ny + dx = 0.1 / (nx - 1) + dy = 0.05 / (ny - 1) + k_max = 45.0 + (-0.01) * 373.15 + dt_max = 0.5 * 7850.0 * 460.0 / (k_max * (1 / dx**2 + 1 / dy**2)) + dt = 0.9 * dt_max + + return { + "T_init": np.full(n, 293.15), + "Q": np.zeros(n), + "nx": nx, + "ny": ny, + "n_steps": n_steps, + "k0": 45.0, + "k1": -0.01, + "rho": 7850.0, + "cp": 460.0, + "h_conv": 25.0, + "T_inf": 293.15, + "T_hot": 373.15, + "Lx": 0.1, + "Ly": 0.05, + "dt": dt, + } + + +def benchmark_image(image, inputs): + n = inputs["nx"] * inputs["ny"] + cotangent = np.full(n, 1.0 / n) + vjp_kwargs = dict( + vjp_inputs=["k0", "k1", "T_init"], + vjp_outputs=["T_final"], + cotangent_vector={"T_final": cotangent}, + ) + + with Tesseract.from_image(image) as t: + # Warmup (includes JIT compilation for JAX) + for _ in range(N_WARMUP): + t.apply(inputs=inputs) + t.vector_jacobian_product(inputs=inputs, **vjp_kwargs) + + # Benchmark forward + times_fwd = [] + for _ in range(N_TRIALS): + t0 = time.perf_counter() + t.apply(inputs=inputs) + times_fwd.append(time.perf_counter() - t0) + + # Benchmark VJP + times_vjp = [] + for _ in range(N_TRIALS): + t0 = time.perf_counter() + t.vector_jacobian_product(inputs=inputs, **vjp_kwargs) + times_vjp.append(time.perf_counter() - t0) + + return np.median(times_fwd), np.median(times_vjp) + + +def main(): + print("Thermal 2D Benchmark: Enzyme (Fortran + LLVM AD) vs JAX (XLA JIT)") + print(f"Warmup: {N_WARMUP}, Trials: {N_TRIALS} (median reported)") + print("=" * 75) + + # Correctness check first + print("\nCorrectness check (30x30, 50 steps)...") + inputs_check = make_inputs(30, 30, 50) + results = {} + for label, image in IMAGES.items(): + with Tesseract.from_image(image) as t: + r = t.apply(inputs=inputs_check) + results[label] = np.array(r["T_final"]) + diff = np.max(np.abs(results["Enzyme"] - results["JAX"])) + print(f" Forward max abs diff: {diff:.2e}") + + # Benchmark + print( + f"\n{'Grid':>10s} {'DOFs':>8s} | {'Enzyme fwd':>11s} {'Enzyme VJP':>11s} " + f"{'JAX fwd':>11s} {'JAX VJP':>11s} | {'VJP/fwd (E)':>11s} {'VJP/fwd (J)':>11s}" + ) + print("-" * 100) + + for nx, ny, n_steps in GRID_SIZES: + inputs = make_inputs(nx, ny, n_steps) + n = nx * ny + + timings = {} + for label, image in IMAGES.items(): + fwd, vjp = benchmark_image(image, inputs) + timings[label] = (fwd, vjp) + + e_fwd, e_vjp = timings["Enzyme"] + j_fwd, j_vjp = timings["JAX"] + print( + f"{nx}x{ny:>3d} {n_steps:>3d}st " + f"{n:>7,d} | " + f"{e_fwd * 1000:>8.1f} ms {e_vjp * 1000:>8.1f} ms " + f"{j_fwd * 1000:>8.1f} ms {j_vjp * 1000:>8.1f} ms | " + f"{e_vjp / e_fwd:>8.2f}x {j_vjp / j_fwd:>8.2f}x" + ) + + +if __name__ == "__main__": + main() diff --git a/demo/jax_thermal_2d/tesseract_api.py b/demo/jax_thermal_2d/tesseract_api.py new file mode 100644 index 00000000..3403bcb5 --- /dev/null +++ b/demo/jax_thermal_2d/tesseract_api.py @@ -0,0 +1,339 @@ +# Copyright 2025 Pasteur Labs. All Rights Reserved. +# SPDX-License-Identifier: Apache-2.0 + +"""JAX reimplementation of the 2D thermal solver from enzyme_thermal_2d. + +This Tesseract solves the same physics as its Enzyme/Fortran counterpart: + rho * cp * dT/dt = div( k(T) * grad(T) ) + Q +with identical boundary conditions, discretization, and interface. + +The key difference: instead of compiling Fortran with Enzyme, the solver is +written directly in JAX. Derivatives (JVP, VJP, Jacobian) are obtained via +jax.jvp / jax.vjp — no manual adjoint code, no compilation pipeline. + +This enables a direct performance comparison between: + - Enzyme: exact AD on compiled Fortran (legacy solver story) + - JAX: native Python AD with XLA JIT compilation (rewrite story) +""" + +from typing import Any + +import equinox as eqx +import jax +import jax.numpy as jnp +import numpy as np +from pydantic import BaseModel, Field, model_validator +from typing_extensions import Self + +from tesseract_core.runtime import Array, Differentiable, Float64 +from tesseract_core.runtime.tree_transforms import filter_func, flatten_with_paths + +# -- Schemas (identical to enzyme_thermal_2d) ---------------------------------- + + +class InputSchema(BaseModel): + """Input for a 2D transient heat conduction solver. + + Solves rho*cp*dT/dt = div(k(T)*grad(T)) + Q on a rectangular domain + with Dirichlet (hot wall), convection, and insulated boundary conditions. + """ + + T_init: Differentiable[Array[(None,), Float64]] = Field( + description=( + "Initial temperature field [K]. Flattened row-major array of " + "shape (nx*ny,). Index (i,j) maps to j*nx+i." + ), + ) + nx: int = Field( + default=20, description="Number of grid points in x direction.", ge=3 + ) + ny: int = Field( + default=20, description="Number of grid points in y direction.", ge=3 + ) + n_steps: int = Field( + default=100, description="Number of explicit Euler time steps.", ge=1 + ) + dt: Differentiable[Float64] = Field( + default=0.01, description="Time step size [s].", gt=0.0 + ) + Lx: Differentiable[Float64] = Field( + default=0.1, description="Domain length in x [m].", gt=0.0 + ) + Ly: Differentiable[Float64] = Field( + default=0.05, description="Domain length in y [m].", gt=0.0 + ) + k0: Differentiable[Float64] = Field( + default=45.0, + description="Base thermal conductivity [W/(m*K)]. k(T) = k0 + k1*T.", + gt=0.0, + ) + k1: Differentiable[Float64] = Field( + default=-0.01, + description="Temperature coefficient of conductivity [W/(m*K^2)]. k(T) = k0 + k1*T.", + ) + rho: Differentiable[Float64] = Field( + default=7850.0, description="Density [kg/m^3].", gt=0.0 + ) + cp: Differentiable[Float64] = Field( + default=460.0, description="Specific heat capacity [J/(kg*K)].", gt=0.0 + ) + h_conv: Differentiable[Float64] = Field( + default=25.0, + description="Convective heat transfer coefficient at top boundary [W/(m^2*K)].", + gt=0.0, + ) + T_inf: Differentiable[Float64] = Field( + default=293.15, description="Ambient temperature for convection BC [K]." + ) + T_hot: Differentiable[Float64] = Field( + default=373.15, + description="Fixed temperature at bottom (Dirichlet) boundary [K].", + ) + Q: Differentiable[Array[(None,), Float64]] = Field( + description=( + "Volumetric heat source [W/m^3]. Flattened row-major array of " + "shape (nx*ny,). Use zeros for no internal heating." + ), + ) + + @model_validator(mode="after") + def check_array_sizes(self) -> Self: + expected = self.nx * self.ny + if len(self.T_init) != expected: + raise ValueError( + f"T_init has {len(self.T_init)} elements, expected nx*ny = {expected}." + ) + if len(self.Q) != expected: + raise ValueError( + f"Q has {len(self.Q)} elements, expected nx*ny = {expected}." + ) + return self + + @model_validator(mode="after") + def check_stability(self) -> Self: + dx = self.Lx / (self.nx - 1) + dy = self.Ly / (self.ny - 1) + k_max = self.k0 + self.k1 * self.T_hot + if k_max <= 0: + raise ValueError(f"Conductivity k(T_hot) = {k_max:.4f} <= 0.") + r = k_max * self.dt / (self.rho * self.cp) * (1.0 / (dx * dx) + 1.0 / (dy * dy)) + if r > 0.5: + raise ValueError(f"CFL stability condition violated: r = {r:.4f} > 0.5.") + return self + + +class OutputSchema(BaseModel): + T_final: Differentiable[Array[(None,), Float64]] = Field( + description="Temperature field after n_steps time steps [K]. Flattened row-major (nx*ny,).", + ) + + +# -- JAX solver ---------------------------------------------------------------- + + +def _harmonic_mean(ka, kb): + """Harmonic mean of two conductivities (standard for cell-face averaging).""" + return 2.0 * ka * kb / (ka + kb) + + +def _thermal_2d_step(T, nx, ny, dx, dy, k0, k1, rho, cp, h_conv, T_inf, T_hot, Q, dt): + """One explicit Euler step of the 2D thermal solver. + + T is a 2D array of shape (ny, nx). Returns updated T_new of same shape. + """ + # Conductivity field + K = k0 + k1 * T + + # Harmonic-mean conductivities at cell faces (interior) + kx_east = _harmonic_mean(K[:, :-1], K[:, 1:]) # (ny, nx-1) + ky_north = _harmonic_mean(K[:-1, :], K[1:, :]) # (ny-1, nx) + + # x-direction flux: d/dx(k dT/dx) + flux_x_faces = kx_east * (T[:, 1:] - T[:, :-1]) / dx # (ny, nx-1) + flux_x = jnp.zeros_like(T) + # Interior: east - west + flux_x = flux_x.at[:, 1:-1].set((flux_x_faces[:, 1:] - flux_x_faces[:, :-1]) / dx) + # Left boundary (i=0): insulated => mirror, net flux = k_east*(T_e - T_c) / dx^2 + flux_x = flux_x.at[:, 0].set(flux_x_faces[:, 0] / dx) + # Right boundary (i=nx-1): insulated => mirror, net flux = -k_west*(T_c - T_w) / dx^2 + # which is k_west*(T_w - T_c) / dx^2 + flux_x = flux_x.at[:, -1].set(-flux_x_faces[:, -1] / dx) + + # y-direction flux: d/dy(k dT/dy) + flux_y_faces = ky_north * (T[1:, :] - T[:-1, :]) / dy # (ny-1, nx) + flux_y = jnp.zeros_like(T) + # Interior + flux_y = flux_y.at[1:-1, :].set((flux_y_faces[1:, :] - flux_y_faces[:-1, :]) / dy) + # Bottom (j=0): Dirichlet — will be overwritten, but set flux anyway + flux_y = flux_y.at[0, :].set(flux_y_faces[0, :] / dy) + # Top (j=ny-1): convection BC: -k dT/dn = h_conv*(T - T_inf) + # Interior conduction from below + convective loss from above + flux_y = flux_y.at[-1, :].set( + -flux_y_faces[-1, :] / dy - h_conv * (T[-1, :] - T_inf) / dy + ) + + Q_2d = Q.reshape(ny, nx) + T_new = T + dt / (rho * cp) * (flux_x + flux_y + Q_2d) + + # Enforce Dirichlet BC at bottom + T_new = T_new.at[0, :].set(T_hot) + + return T_new + + +def _thermal_2d_solve( + T_init_2d, nx, ny, n_steps, dx, dy, k0, k1, rho, cp, h_conv, T_inf, T_hot, Q, dt +): + """Run n_steps of explicit Euler. Uses jax.lax.fori_loop for AD compatibility.""" + + def body_fn(_, T): + return _thermal_2d_step( + T, nx, ny, dx, dy, k0, k1, rho, cp, h_conv, T_inf, T_hot, Q, dt + ) + + return jax.lax.fori_loop(0, n_steps, body_fn, T_init_2d) + + +@eqx.filter_jit +def apply_jit(inputs: dict) -> dict: + nx = inputs["nx"] + ny = inputs["ny"] + n_steps = inputs["n_steps"] + dx = inputs["Lx"] / (nx - 1) + dy = inputs["Ly"] / (ny - 1) + + T_init_2d = inputs["T_init"].reshape(ny, nx) + Q = inputs["Q"] + + T_final_2d = _thermal_2d_solve( + T_init_2d, + nx, + ny, + n_steps, + dx, + dy, + inputs["k0"], + inputs["k1"], + inputs["rho"], + inputs["cp"], + inputs["h_conv"], + inputs["T_inf"], + inputs["T_hot"], + Q, + inputs["dt"], + ) + + return {"T_final": T_final_2d.reshape(-1)} + + +# -- Required endpoint --------------------------------------------------------- + + +def apply(inputs: InputSchema) -> OutputSchema: + """Run the 2D thermal solver for n_steps explicit Euler steps.""" + out = apply_jit(inputs.model_dump()) + return {"T_final": np.asarray(out["T_final"])} + + +# -- JAX-handled gradient endpoints (no need to modify) ------------------------ + + +def jacobian( + inputs: InputSchema, + jac_inputs: set[str], + jac_outputs: set[str], +): + return jac_jit(inputs.model_dump(), tuple(jac_inputs), tuple(jac_outputs)) + + +def jacobian_vector_product( + inputs: InputSchema, + jvp_inputs: set[str], + jvp_outputs: set[str], + tangent_vector: dict[str, Any], +): + return jvp_jit( + inputs.model_dump(), + tuple(jvp_inputs), + tuple(jvp_outputs), + tangent_vector, + ) + + +def vector_jacobian_product( + inputs: InputSchema, + vjp_inputs: set[str], + vjp_outputs: set[str], + cotangent_vector: dict[str, Any], +): + return vjp_jit( + inputs.model_dump(), + tuple(vjp_inputs), + tuple(vjp_outputs), + cotangent_vector, + ) + + +def abstract_eval(abstract_inputs): + """Calculate output shape of apply from the shape of its inputs.""" + is_shapedtype_dict = lambda x: type(x) is dict and (x.keys() == {"shape", "dtype"}) + is_shapedtype_struct = lambda x: isinstance(x, jax.ShapeDtypeStruct) + + jaxified_inputs = jax.tree.map( + lambda x: jax.ShapeDtypeStruct(**x) if is_shapedtype_dict(x) else x, + abstract_inputs.model_dump(), + is_leaf=is_shapedtype_dict, + ) + dynamic_inputs, static_inputs = eqx.partition( + jaxified_inputs, filter_spec=is_shapedtype_struct + ) + + def wrapped_apply(dynamic_inputs): + inputs = eqx.combine(static_inputs, dynamic_inputs) + return apply_jit(inputs) + + jax_shapes = jax.eval_shape(wrapped_apply, dynamic_inputs) + return jax.tree.map( + lambda x: ( + {"shape": x.shape, "dtype": str(x.dtype)} if is_shapedtype_struct(x) else x + ), + jax_shapes, + is_leaf=is_shapedtype_struct, + ) + + +# -- Helper functions ---------------------------------------------------------- + + +@eqx.filter_jit +def jac_jit(inputs: dict, jac_inputs: tuple[str], jac_outputs: tuple[str]): + filtered_apply = filter_func(apply_jit, inputs, jac_outputs) + return jax.jacrev(filtered_apply)( + flatten_with_paths(inputs, include_paths=jac_inputs) + ) + + +@eqx.filter_jit +def jvp_jit( + inputs: dict, jvp_inputs: tuple[str], jvp_outputs: tuple[str], tangent_vector: dict +): + filtered_apply = filter_func(apply_jit, inputs, jvp_outputs) + return jax.jvp( + filtered_apply, + [flatten_with_paths(inputs, include_paths=jvp_inputs)], + [tangent_vector], + )[1] + + +@eqx.filter_jit +def vjp_jit( + inputs: dict, + vjp_inputs: tuple[str], + vjp_outputs: tuple[str], + cotangent_vector: dict, +): + filtered_apply = filter_func(apply_jit, inputs, vjp_outputs) + _, vjp_func = jax.vjp( + filtered_apply, flatten_with_paths(inputs, include_paths=vjp_inputs) + ) + return vjp_func(cotangent_vector)[0] diff --git a/demo/jax_thermal_2d/tesseract_config.yaml b/demo/jax_thermal_2d/tesseract_config.yaml new file mode 100644 index 00000000..9202d999 --- /dev/null +++ b/demo/jax_thermal_2d/tesseract_config.yaml @@ -0,0 +1,16 @@ +name: "jax-thermal-2d" +version: "1.0.0" +description: | + JAX reimplementation of the 2D thermal solver from enzyme_thermal_2d. + + Solves the same physics (2D transient heat conduction with temperature-dependent + conductivity, mixed BCs, explicit Euler time integration) with an identical + Tesseract interface — but the solver is written in pure JAX instead of Fortran. + + Derivatives (JVP, VJP, Jacobian) are obtained via jax.jvp / jax.vjp with no + manual adjoint code and no compilation pipeline. This enables a direct + performance comparison between Enzyme (legacy Fortran + LLVM AD) and JAX + (native Python AD with XLA JIT). + +build_config: + target_platform: "native" diff --git a/demo/jax_thermal_2d/tesseract_requirements.txt b/demo/jax_thermal_2d/tesseract_requirements.txt new file mode 100644 index 00000000..3878018a --- /dev/null +++ b/demo/jax_thermal_2d/tesseract_requirements.txt @@ -0,0 +1,2 @@ +jax[cpu] +equinox diff --git a/examples/enzyme_ad/README.md b/examples/enzyme_ad/README.md new file mode 100644 index 00000000..907dd587 --- /dev/null +++ b/examples/enzyme_ad/README.md @@ -0,0 +1,104 @@ +# Enzyme AD: Differentiable Fortran Simulator + +This example demonstrates how to obtain **exact automatic derivatives** of a Fortran simulation without writing any manual adjoint code, using [Enzyme](https://enzyme.mit.edu/) for automatic differentiation at the LLVM IR level. + +## What it does + +The Tesseract wraps a single explicit Euler step of the 1D heat equation: + +``` +dT/dt = alpha * d^2T/dx^2 +``` + +discretized as: + +``` +T_out[i] = T_in[i] + r * (T_in[i-1] - 2*T_in[i] + T_in[i+1]) +``` + +where `r = alpha * dt / dx^2`. + +All three derivative endpoints (`apply`, `jacobian_vector_product`, `vector_jacobian_product`) are provided. The JVP and VJP are computed by Enzyme — not by finite differences or hand-written adjoints. + +## How it works + +The compilation pipeline runs at Docker build time: + +``` +heat_step.f90 (Fortran source — pure numerical kernel) + │ + ▼ lfortran --show-llvm +heat_step.ll (LLVM IR) + │ + ▼ opt -O1 +heat_step_opt.ll (cleaned-up IR, ready for Enzyme) + │ + ▼ llvm-link with wrapper.c +combined.ll (Fortran IR + C wrapper with __enzyme_autodiff / __enzyme_fwddiff) + │ + ▼ opt --load-pass-plugin=LLVMEnzyme-19.so -passes=enzyme +ad.ll (LLVM IR with compiler-generated forward and reverse mode derivatives) + │ + ▼ clang -shared +libheat_ad.so (shared library: forward, JVP, VJP entry points) +``` + +At runtime, `tesseract_api.py` loads `libheat_ad.so` via `ctypes` and exposes: + +- **`apply`** — calls the forward Fortran kernel +- **`jacobian_vector_product`** — calls the Enzyme forward-mode (JVP) wrapper +- **`vector_jacobian_product`** — calls the Enzyme reverse-mode (VJP) wrapper + +## Toolchain + +All tools are installed from prebuilt binaries during the Docker build (no source compilation of the toolchain itself): + +| Tool | Source | Purpose | +| ------------------------------------------- | --------------- | --------------------------------- | +| [LFortran](https://lfortran.org/) 0.61.0 | conda-forge | Fortran → LLVM IR frontend | +| [LLVM](https://llvm.org/) 19 | apt.llvm.org | IR optimization, linking, codegen | +| [Enzyme](https://enzyme.mit.edu/) (nightly) | GitHub releases | LLVM AD pass | + +## Key design choices + +- **No array intrinsics in the Fortran kernel.** The heat step uses explicit `do` loops rather than whole-array operations. This produces clean LLVM IR (simple GEP + load/store patterns) that Enzyme handles reliably. +- **`--no-array-bounds-checking`** is passed to LFortran. Bounds checks emit calls to LFortran's runtime (`_lcompilers_runtime_error`, `exit`) which Enzyme cannot differentiate through. +- **The C wrapper (`wrapper.c`) bridges the Fortran ABI and Enzyme.** It copies scalar arguments to the stack (Fortran passes everything by pointer), declares `__enzyme_autodiff` / `__enzyme_fwddiff` calls with the appropriate `enzyme_dup` / `enzyme_const` annotations, and exports clean C-callable functions for Python ctypes. + +## Usage + +```python +from tesseract_core import Tesseract +import numpy as np + +with Tesseract.from_image("enzyme-ad:latest") as t: + T_in = np.array([0.0, 0.0, 100.0, 0.0, 0.0]) + + # Forward pass + result = t.apply(inputs={"T_in": T_in, "alpha": 0.01, "dx": 0.25, "dt": 0.001}) + print(result["T_out"]) + + # Reverse-mode gradient of T_out[2] w.r.t. all inputs + vjp = t.vector_jacobian_product( + inputs={"T_in": T_in, "alpha": 0.01, "dx": 0.25, "dt": 0.001}, + vjp_inputs=["T_in", "alpha", "dx", "dt"], + vjp_outputs=["T_out"], + cotangent_vector={"T_out": np.array([0.0, 0.0, 1.0, 0.0, 0.0])}, + ) + print(vjp["T_in"]) # [0.0, 0.00016, 0.99968, 0.00016, 0.0] + print(vjp["alpha"]) # -3.2 +``` + +## File structure + +``` +enzyme_ad/ +├── README.md +├── tesseract_api.py # Python API wrapping ctypes calls +├── tesseract_config.yaml # Build config with LLVM/LFortran/Enzyme toolchain +├── tesseract_requirements.txt # numpy +└── enzyme/ + ├── heat_step.f90 # Fortran kernel (no I/O, no allocations) + ├── wrapper.c # C wrapper declaring Enzyme AD entry points + └── build.sh # Full compilation pipeline script +``` diff --git a/examples/enzyme_ad/enzyme/build.sh b/examples/enzyme_ad/enzyme/build.sh new file mode 100644 index 00000000..c7011d48 --- /dev/null +++ b/examples/enzyme_ad/enzyme/build.sh @@ -0,0 +1,41 @@ +#!/bin/bash +# Copyright 2025 Pasteur Labs. All Rights Reserved. +# SPDX-License-Identifier: Apache-2.0 +# +# Build pipeline: Fortran -> LFortran -> LLVM IR -> Enzyme AD -> shared library +# +# This script implements the full compilation pipeline: +# 1. LFortran compiles Fortran to LLVM IR +# 2. LLVM opt cleans up the IR (-O1) +# 3. Clang compiles the C wrapper (with Enzyme calls) to LLVM IR +# 4. llvm-link merges the Fortran and C IR modules +# 5. Enzyme LLVM pass generates derivative code +# 6. Clang compiles the differentiated IR to a shared library + +set -euo pipefail + +SCRIPT_DIR="$(cd "$(dirname "$0")" && pwd)" +ENZYME_LIB="${ENZYME_LIB:-/usr/local/lib/LLVMEnzyme-19.so}" +OUTPUT="${1:-${SCRIPT_DIR}/libheat_ad.so}" + +echo "=== Step 1: LFortran -> LLVM IR ===" +lfortran --show-llvm --no-array-bounds-checking \ + "${SCRIPT_DIR}/heat_step.f90" > /tmp/heat_step.ll + +echo "=== Step 2: Optimize IR ===" +opt -O1 -S /tmp/heat_step.ll -o /tmp/heat_step_opt.ll + +echo "=== Step 3: Compile C wrapper -> LLVM IR ===" +clang -emit-llvm -S -O1 "${SCRIPT_DIR}/wrapper.c" -o /tmp/wrapper.ll + +echo "=== Step 4: Link IR modules ===" +llvm-link /tmp/wrapper.ll /tmp/heat_step_opt.ll -S -o /tmp/combined.ll + +echo "=== Step 5: Enzyme AD pass ===" +opt --load-pass-plugin="${ENZYME_LIB}" -passes=enzyme \ + -S /tmp/combined.ll -o /tmp/ad.ll + +echo "=== Step 6: Compile to shared library ===" +clang -shared -O2 /tmp/ad.ll -o "${OUTPUT}" -lm + +echo "=== Built ${OUTPUT} ===" diff --git a/examples/enzyme_ad/enzyme/heat_step.f90 b/examples/enzyme_ad/enzyme/heat_step.f90 new file mode 100644 index 00000000..e4b4492b --- /dev/null +++ b/examples/enzyme_ad/enzyme/heat_step.f90 @@ -0,0 +1,39 @@ +! Copyright 2025 Pasteur Labs. All Rights Reserved. +! SPDX-License-Identifier: Apache-2.0 +! +! Single explicit Euler step for the 1D heat equation: +! +! dT/dt = alpha * d^2T/dx^2 +! +! Discretized with central differences in space: +! +! T_out(i) = T_in(i) + r * (T_in(i-1) - 2*T_in(i) + T_in(i+1)) +! +! where r = alpha * dt / dx^2. +! +! Boundary conditions are Dirichlet (fixed): T_out(1) = T_in(1), +! T_out(n) = T_in(n). +! +! This subroutine is compiled to LLVM IR via LFortran, then +! differentiated by Enzyme to obtain exact (not finite-difference) +! JVP and VJP functions. + +subroutine heat_step(n, T_in, T_out, alpha, dx, dt) + implicit none + integer, intent(in) :: n + double precision, intent(in) :: T_in(n), alpha, dx, dt + double precision, intent(out) :: T_out(n) + integer :: i + double precision :: r + + r = alpha * dt / (dx * dx) + + ! Dirichlet boundary conditions + T_out(1) = T_in(1) + T_out(n) = T_in(n) + + ! Interior points: explicit finite difference stencil + do i = 2, n-1 + T_out(i) = T_in(i) + r * (T_in(i-1) - 2.0d0*T_in(i) + T_in(i+1)) + end do +end subroutine diff --git a/examples/enzyme_ad/enzyme/wrapper.c b/examples/enzyme_ad/enzyme/wrapper.c new file mode 100644 index 00000000..e107e498 --- /dev/null +++ b/examples/enzyme_ad/enzyme/wrapper.c @@ -0,0 +1,87 @@ +/* Copyright 2025 Pasteur Labs. All Rights Reserved. + * SPDX-License-Identifier: Apache-2.0 + * + * C wrapper that declares Enzyme AD entry points for the Fortran heat_step + * subroutine. After the Enzyme LLVM pass runs, the __enzyme_autodiff and + * __enzyme_fwddiff calls are replaced with compiler-generated derivative + * code -- no manual adjoint implementation required. + * + * The resulting shared library exports three functions callable from Python + * via ctypes: + * + * heat_step_forward -- primal forward evaluation + * heat_step_vjp -- reverse-mode AD (vector-Jacobian product) + * heat_step_jvp -- forward-mode AD (Jacobian-vector product) + */ + +/* Enzyme annotation sentinels (resolved by the Enzyme LLVM pass) */ +int enzyme_dup; +int enzyme_const; + +/* Fortran subroutine (Fortran ABI: everything by pointer) */ +extern void heat_step(int* n, + double* T_in, double* T_out, + double* alpha, double* dx, double* dt); + +/* Enzyme magic functions -- replaced by generated code after the pass */ +extern void __enzyme_autodiff(void*, ...); +extern void __enzyme_fwddiff(void*, ...); + + +/* ── Forward evaluation ─────────────────────────────────────────────── */ + +void heat_step_forward(int n, + const double* T_in, double* T_out, + double alpha, double dx, double dt) +{ + /* Copy scalars to stack so we can take their address (Fortran ABI) */ + int n_ = n; + double alpha_ = alpha, dx_ = dx, dt_ = dt; + heat_step(&n_, (double*)T_in, T_out, &alpha_, &dx_, &dt_); +} + + +/* ── Reverse mode (VJP) ────────────────────────────────────────────── */ + +void heat_step_vjp(int n, + const double* T_in, double* dT_in, + const double* T_out, double* dT_out, + double alpha, double* dalpha, + double dx, double* ddx, + double dt, double* ddt) +{ + int n_ = n; + double alpha_ = alpha, dx_ = dx, dt_ = dt; + + __enzyme_autodiff((void*)heat_step, + enzyme_const, &n_, + enzyme_dup, (double*)T_in, dT_in, + enzyme_dup, (double*)T_out, dT_out, + enzyme_dup, &alpha_, dalpha, + enzyme_dup, &dx_, ddx, + enzyme_dup, &dt_, ddt); +} + + +/* ── Forward mode (JVP) ────────────────────────────────────────────── */ + +void heat_step_jvp(int n, + const double* T_in, const double* dT_in, + double* T_out, double* dT_out, + double alpha, double dalpha, + double dx, double ddx, + double dt, double ddt) +{ + int n_ = n; + double alpha_ = alpha, dx_ = dx, dt_ = dt; + double dalpha_ = dalpha, ddx_ = ddx, ddt_ = ddt; + int dn_ = 0; /* n is not differentiated */ + + __enzyme_fwddiff((void*)heat_step, + enzyme_dup, &n_, &dn_, + enzyme_dup, (double*)T_in, (double*)dT_in, + enzyme_dup, T_out, dT_out, + enzyme_dup, &alpha_, &dalpha_, + enzyme_dup, &dx_, &ddx_, + enzyme_dup, &dt_, &ddt_); +} diff --git a/examples/enzyme_ad/tesseract_api.py b/examples/enzyme_ad/tesseract_api.py new file mode 100644 index 00000000..6bde9062 --- /dev/null +++ b/examples/enzyme_ad/tesseract_api.py @@ -0,0 +1,263 @@ +# Copyright 2025 Pasteur Labs. All Rights Reserved. +# SPDX-License-Identifier: Apache-2.0 + +"""Tesseract wrapping a Fortran heat equation solver differentiated by Enzyme. + +This example demonstrates how to obtain exact automatic derivatives of a +Fortran simulation without writing any adjoint code. The pipeline is: + + Fortran source + -> LFortran (LLVM IR) + -> Enzyme (LLVM AD pass) + -> shared library with forward, JVP, and VJP entry points + -> Python ctypes -> Tesseract API + +The solver computes a single explicit Euler step of the 1D heat equation: + + dT/dt = alpha * d^2T/dx^2 + +Enzyme generates machine-precision derivatives through the compiled Fortran +code, enabling gradient-based optimization of thermal parameters (alpha, dx, +dt) or initial conditions (T_in) with respect to any output. +""" + +import ctypes +from pathlib import Path +from typing import Any + +import numpy as np +from pydantic import BaseModel, Field, model_validator +from typing_extensions import Self + +from tesseract_core.runtime import Array, Differentiable, Float64 + +# ── Shared library loading ────────────────────────────────────────── + +_LIB_PATH = Path("/tesseract/enzyme/libheat_ad.so") +_lib = ctypes.CDLL(str(_LIB_PATH)) + +# void heat_step_forward(int n, double* T_in, double* T_out, +# double alpha, double dx, double dt) +_lib.heat_step_forward.restype = None +_lib.heat_step_forward.argtypes = [ + ctypes.c_int, + ctypes.POINTER(ctypes.c_double), + ctypes.POINTER(ctypes.c_double), + ctypes.c_double, + ctypes.c_double, + ctypes.c_double, +] + +# void heat_step_vjp(int n, +# double* T_in, double* dT_in, double* T_out, double* dT_out, +# double alpha, double* dalpha, double dx, double* ddx, +# double dt, double* ddt) +_lib.heat_step_vjp.restype = None +_lib.heat_step_vjp.argtypes = [ + ctypes.c_int, + ctypes.POINTER(ctypes.c_double), + ctypes.POINTER(ctypes.c_double), + ctypes.POINTER(ctypes.c_double), + ctypes.POINTER(ctypes.c_double), + ctypes.c_double, + ctypes.POINTER(ctypes.c_double), + ctypes.c_double, + ctypes.POINTER(ctypes.c_double), + ctypes.c_double, + ctypes.POINTER(ctypes.c_double), +] + +# void heat_step_jvp(int n, +# double* T_in, double* dT_in, double* T_out, double* dT_out, +# double alpha, double dalpha, double dx, double ddx, +# double dt, double ddt) +_lib.heat_step_jvp.restype = None +_lib.heat_step_jvp.argtypes = [ + ctypes.c_int, + ctypes.POINTER(ctypes.c_double), + ctypes.POINTER(ctypes.c_double), + ctypes.POINTER(ctypes.c_double), + ctypes.POINTER(ctypes.c_double), + ctypes.c_double, + ctypes.c_double, + ctypes.c_double, + ctypes.c_double, + ctypes.c_double, + ctypes.c_double, +] + + +def _as_ptr(arr: np.ndarray) -> ctypes.POINTER(ctypes.c_double): + """Get a ctypes double pointer from a contiguous float64 array.""" + return arr.ctypes.data_as(ctypes.POINTER(ctypes.c_double)) + + +# ── Schemas ───────────────────────────────────────────────────────── + + +class InputSchema(BaseModel): + """Input for a single explicit Euler step of the 1D heat equation.""" + + T_in: Differentiable[Array[(None,), Float64]] = Field( + description="Temperature profile at current time step [K]. Shape: (n,). " + "Boundary values T_in[0] and T_in[-1] are held fixed (Dirichlet).", + ) + alpha: Differentiable[Float64] = Field( + default=0.01, + description="Thermal diffusivity [m^2/s].", + gt=0.0, + ) + dx: Differentiable[Float64] = Field( + default=0.25, + description="Grid spacing [m].", + gt=0.0, + ) + dt: Differentiable[Float64] = Field( + default=0.001, + description="Time step size [s].", + gt=0.0, + ) + + @model_validator(mode="after") + def check_stability(self) -> Self: + """Verify CFL stability condition: r = alpha * dt / dx^2 <= 0.5.""" + r = self.alpha * self.dt / (self.dx**2) + if r > 0.5: + raise ValueError( + f"CFL stability condition violated: r = {r:.4f} > 0.5. " + f"Reduce dt or alpha, or increase dx." + ) + return self + + @model_validator(mode="after") + def check_min_points(self) -> Self: + """Need at least 3 points for interior stencil.""" + if len(self.T_in) < 3: + raise ValueError("T_in must have at least 3 points.") + return self + + +class OutputSchema(BaseModel): + """Output: temperature profile after one heat equation step.""" + + T_out: Differentiable[Array[(None,), Float64]] = Field( + description="Temperature profile after one time step [K]. Shape: (n,).", + ) + + +# ── Required endpoints ────────────────────────────────────────────── + + +def apply(inputs: InputSchema) -> OutputSchema: + """Compute one explicit Euler step of the 1D heat equation.""" + T_in = np.ascontiguousarray(inputs.T_in, dtype=np.float64) + n = len(T_in) + T_out = np.zeros(n, dtype=np.float64) + + _lib.heat_step_forward( + n, _as_ptr(T_in), _as_ptr(T_out), inputs.alpha, inputs.dx, inputs.dt + ) + + return OutputSchema(T_out=T_out) + + +# ── Optional endpoints (AD via Enzyme) ────────────────────────────── + + +def _run_vjp(inputs: InputSchema, cotangent_T_out: np.ndarray): + """Run Enzyme reverse-mode AD and return all gradients.""" + T_in = np.ascontiguousarray(inputs.T_in, dtype=np.float64) + n = len(T_in) + + # Shadow arrays (Enzyme accumulates gradients into these) + dT_in = np.zeros(n, dtype=np.float64) + T_out = np.zeros(n, dtype=np.float64) + dT_out = np.array(cotangent_T_out, dtype=np.float64) + dalpha = ctypes.c_double(0.0) + ddx = ctypes.c_double(0.0) + ddt = ctypes.c_double(0.0) + + _lib.heat_step_vjp( + n, + _as_ptr(T_in), + _as_ptr(dT_in), + _as_ptr(T_out), + _as_ptr(dT_out), + inputs.alpha, + ctypes.byref(dalpha), + inputs.dx, + ctypes.byref(ddx), + inputs.dt, + ctypes.byref(ddt), + ) + + return dT_in, dalpha.value, ddx.value, ddt.value + + +def _run_jvp(inputs: InputSchema, tangent_T_in, tangent_alpha, tangent_dx, tangent_dt): + """Run Enzyme forward-mode AD and return output tangent.""" + T_in = np.ascontiguousarray(inputs.T_in, dtype=np.float64) + n = len(T_in) + + dT_in = np.ascontiguousarray(tangent_T_in, dtype=np.float64) + T_out = np.zeros(n, dtype=np.float64) + dT_out = np.zeros(n, dtype=np.float64) + + _lib.heat_step_jvp( + n, + _as_ptr(T_in), + _as_ptr(dT_in), + _as_ptr(T_out), + _as_ptr(dT_out), + inputs.alpha, + float(tangent_alpha), + inputs.dx, + float(tangent_dx), + inputs.dt, + float(tangent_dt), + ) + + return dT_out + + +def vector_jacobian_product( + inputs: InputSchema, + vjp_inputs: set[str], + vjp_outputs: set[str], + cotangent_vector: dict[str, Any], +): + """Reverse-mode AD via Enzyme: compute v^T @ J.""" + cotangent_T_out = cotangent_vector.get("T_out", np.zeros_like(inputs.T_in)) + dT_in, dalpha, ddx, ddt = _run_vjp(inputs, cotangent_T_out) + + result = {} + if "T_in" in vjp_inputs: + result["T_in"] = dT_in + if "alpha" in vjp_inputs: + result["alpha"] = dalpha + if "dx" in vjp_inputs: + result["dx"] = ddx + if "dt" in vjp_inputs: + result["dt"] = ddt + return result + + +def jacobian_vector_product( + inputs: InputSchema, + jvp_inputs: set[str], + jvp_outputs: set[str], + tangent_vector: dict[str, Any], +): + """Forward-mode AD via Enzyme: compute J @ v.""" + n = len(inputs.T_in) + tangent_T_in = tangent_vector.get("T_in", np.zeros(n, dtype=np.float64)) + tangent_alpha = tangent_vector.get("alpha", 0.0) + tangent_dx = tangent_vector.get("dx", 0.0) + tangent_dt = tangent_vector.get("dt", 0.0) + + dT_out = _run_jvp(inputs, tangent_T_in, tangent_alpha, tangent_dx, tangent_dt) + + result = {} + if "T_out" in jvp_outputs: + result["T_out"] = dT_out + return result diff --git a/examples/enzyme_ad/tesseract_config.yaml b/examples/enzyme_ad/tesseract_config.yaml new file mode 100644 index 00000000..c7545182 --- /dev/null +++ b/examples/enzyme_ad/tesseract_config.yaml @@ -0,0 +1,59 @@ +name: "enzyme-ad" +version: "1.0.0" +description: | + Differentiable 1D heat equation solver using Enzyme automatic differentiation. + + Demonstrates how to obtain exact (machine-precision) derivatives of a Fortran + simulation without writing manual adjoint code. The pipeline is: + + Fortran -> LFortran -> LLVM IR -> Enzyme AD pass -> shared library + + Enzyme generates both forward-mode (JVP) and reverse-mode (VJP) derivatives + directly from the compiled Fortran code at the LLVM IR level. + + Industry relevance: gradient-based optimization of thermal parameters, + inverse problems, sensitivity analysis, and differentiable physics. + +build_config: + base_image: "debian:bookworm-slim" + target_platform: "linux/amd64" + + extra_packages: + - wget + - gnupg + - ca-certificates + - bzip2 + + package_data: + - ["enzyme/heat_step.f90", "enzyme/heat_step.f90"] + - ["enzyme/wrapper.c", "enzyme/wrapper.c"] + - ["enzyme/build.sh", "enzyme/build.sh"] + + custom_build_steps: + # Install LLVM 19 toolchain + - | + RUN wget -qO- https://apt.llvm.org/llvm-snapshot.gpg.key | tee /etc/apt/trusted.gpg.d/apt.llvm.org.asc && \ + echo "deb http://apt.llvm.org/bookworm/ llvm-toolchain-bookworm-19 main" > /etc/apt/sources.list.d/llvm.list && \ + apt-get update && apt-get install -y --no-install-recommends llvm-19 clang-19 && \ + rm -rf /var/lib/apt/lists/* && \ + for tool in opt llvm-as llvm-link llvm-dis llc clang clang++; do \ + ln -sf /usr/bin/${tool}-19 /usr/local/bin/${tool} 2>/dev/null || true; \ + done + + # Install LFortran via micromamba (prebuilt from conda-forge) + - | + RUN wget -q https://github.com/mamba-org/micromamba-releases/releases/latest/download/micromamba-linux-64 \ + -O /usr/local/bin/micromamba && chmod +x /usr/local/bin/micromamba && \ + MAMBA_ROOT_PREFIX=/opt/conda micromamba create -y -n base -c conda-forge lfortran=0.61.0 && \ + ln -sf $(find /opt/conda -name lfortran -type f | head -1) /usr/local/bin/lfortran && \ + echo /opt/conda/lib > /etc/ld.so.conf.d/conda.conf && ldconfig + + # Download prebuilt Enzyme LLVM plugin + - | + RUN wget -q https://github.com/EnzymeAD/Enzyme/releases/download/nightly/LLVMEnzyme-19.so \ + -O /usr/local/lib/LLVMEnzyme-19.so + + # Build the differentiated shared library + - | + RUN chmod +x /tesseract/enzyme/build.sh && \ + /tesseract/enzyme/build.sh /tesseract/enzyme/libheat_ad.so diff --git a/examples/enzyme_ad/tesseract_requirements.txt b/examples/enzyme_ad/tesseract_requirements.txt new file mode 100644 index 00000000..24ce15ab --- /dev/null +++ b/examples/enzyme_ad/tesseract_requirements.txt @@ -0,0 +1 @@ +numpy diff --git a/pyproject.toml b/pyproject.toml index 8c45d022..7fd949f2 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -196,6 +196,7 @@ ignore = [ "tests/*" = ["D101", "D102", "D103", "D106", "ANN"] "benchmarks/*" = ["D101", "D102", "D103", "D106", "ANN"] "examples/**/*" = ["D101", "D102", "D103", "D106", "ANN"] +"demo/**/*" = ["D101", "D102", "D103", "D106", "ANN"] "tesseract_core/sdk/templates/*" = ["D101", "D102", "D103", "D106", "ANN"] [tool.ruff.lint.pydocstyle] From f11425d9c0d691b24a08306f2bc61d8b584d529a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dion=20H=C3=A4fner?= Date: Fri, 17 Apr 2026 16:05:06 +0200 Subject: [PATCH 02/24] add demo notebook --- demo/_showcase/enzyme-optimization.ipynb | 304 +++++++++++++++++++++++ examples/enzyme_ad/tesseract_api.py | 26 +- 2 files changed, 322 insertions(+), 8 deletions(-) create mode 100644 demo/_showcase/enzyme-optimization.ipynb diff --git a/demo/_showcase/enzyme-optimization.ipynb b/demo/_showcase/enzyme-optimization.ipynb new file mode 100644 index 00000000..bd9a121e --- /dev/null +++ b/demo/_showcase/enzyme-optimization.ipynb @@ -0,0 +1,304 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Inverse Heat Conduction via Enzyme AD\n", + "\n", + "In this tutorial, you will learn how to:\n", + "\n", + "1. **Build a Tesseract** that wraps a Fortran heat equation solver differentiated by [Enzyme](https://enzyme.mit.edu/) (an LLVM-based automatic differentiation compiler plugin)\n", + "2. **Embed it in a JAX pipeline** via [tesseract-jax](https://github.com/pasteurlabs/tesseract-jax), making it a native JAX-differentiable function\n", + "3. **Solve an inverse problem**: recover the thermal diffusivity of a material from temperature observations, using `jax.grad` to differentiate *through* the compiled Fortran solver\n", + "\n", + "## Why this matters\n", + "\n", + "Scientific computing is full of Fortran and C code that researchers need gradients of -- for optimization, inverse problems, uncertainty quantification, or integration with ML pipelines. The traditional options are painful:\n", + "\n", + "- **Hand-written adjoints**: months of expert effort, error-prone, a maintenance nightmare\n", + "- **Finite differences**: slow ($O(n)$ evaluations per gradient), inaccurate (truncation vs. roundoff tradeoff)\n", + "- **Rewrite in JAX/PyTorch**: impractical for existing codebases\n", + "\n", + "Enzyme offers a fourth option: **automatic differentiation at the LLVM IR level**. It takes compiled code and synthesizes exact derivative functions -- no source modifications, no manual adjoints, no approximation. And because it operates on LLVM IR, it works with any language that compiles to it: Fortran, C, C++, Rust, and more.\n", + "\n", + "In this demo, we differentiate a Fortran heat equation solver using Enzyme, package it as a [Tesseract](https://github.com/pasteurlabs/tesseract), and use the exact gradients to solve an inverse problem entirely within JAX." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Install additional requirements for this notebook\n", + "%pip install tesseract-jax -q" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 1: Build and serve the Enzyme AD Tesseract\n", + "\n", + "The `enzyme-ad` Tesseract wraps a Fortran implementation of a single explicit Euler step of the 1D heat equation:\n", + "\n", + "$$\\frac{\\partial T}{\\partial t} = \\alpha \\frac{\\partial^2 T}{\\partial x^2}$$\n", + "\n", + "The Fortran source (`heat_step.f90`) is just ~30 lines -- a simple finite difference stencil:\n", + "\n", + "```fortran\n", + "do i = 2, n - 1\n", + " T_out(i) = T_in(i) + r * (T_in(i-1) - 2.0d0*T_in(i) + T_in(i+1))\n", + "end do\n", + "```\n", + "\n", + "During `tesseract build`, the compilation pipeline runs:\n", + "\n", + "```\n", + "Fortran --> LFortran --> LLVM IR --> Enzyme AD pass --> libheat_ad.so\n", + "```\n", + "\n", + "Enzyme analyzes the LLVM IR and generates both forward-mode (JVP) and reverse-mode (VJP) derivative functions automatically. The resulting shared library has three entry points: `heat_step_forward`, `heat_step_jvp`, and `heat_step_vjp`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%%bash\n", + "tesseract build ../../examples/enzyme_ad/" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from tesseract_core import Tesseract\n", + "\n", + "heat_tesseract = Tesseract.from_image(\"enzyme-ad\")\n", + "heat_tesseract.serve()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 2: Test a forward evaluation\n", + "\n", + "Before optimizing, let's verify the Tesseract works. We set up a temperature profile (a Gaussian bump on a uniform grid) and run one heat equation step." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": "import jax\nimport jax.numpy as jnp\nimport matplotlib.pyplot as plt\nimport numpy as np\nfrom tesseract_jax import apply_tesseract\n\njax.config.update(\"jax_enable_x64\", True)\n\n# Grid setup\nn_points = 50\ndx = 1.0 / (n_points - 1)\nx = jnp.linspace(0.0, 1.0, n_points)\n\n# Initial temperature: Gaussian bump\nT_init = jnp.exp(-((x - 0.5) ** 2) / (2 * 0.05**2))\n# Fix boundary conditions to zero\nT_init = T_init.at[0].set(0.0).at[-1].set(0.0)\n\n# Physical parameters\nalpha_true = 0.02 # true thermal diffusivity\ndt = 0.0001\n\n\ndef heat_step(T_in, alpha):\n \"\"\"Run one heat equation step through the Enzyme-differentiated Fortran solver.\"\"\"\n result = apply_tesseract(\n heat_tesseract,\n {\"T_in\": T_in, \"alpha\": alpha, \"dx\": dx, \"dt\": dt},\n )\n return result[\"T_out\"]\n\n\n# Run one step\nT_after_one = heat_step(T_init, alpha_true)\n\nplt.figure(figsize=(8, 4))\nplt.plot(x, T_init, label=\"Initial\", linewidth=2)\nplt.plot(x, T_after_one, label=\"After 1 step\", linewidth=2)\nplt.xlabel(\"x\")\nplt.ylabel(\"T\")\nplt.legend()\nplt.title(\"Single heat equation step (Enzyme-differentiated Fortran solver)\")\nplt.tight_layout()" + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 3: Run multiple steps to generate synthetic observations\n", + "\n", + "For the inverse problem, we need \"observed\" data. We'll run the solver forward for many steps with the true $\\alpha$ to produce a final temperature profile, then pretend we only know this final profile and try to recover $\\alpha$." + ] + }, + { + "cell_type": "code", + "source": "def simulate(T_init, alpha, n_steps):\n \"\"\"Run the heat equation forward for n_steps.\"\"\"\n T = T_init\n for _ in range(n_steps):\n T = heat_step(T, alpha)\n return T\n\n\n# Generate \"observed\" data with the true alpha\nn_steps = 200\nT_observed = jax.jit(simulate, static_argnums=(2,))(T_init, alpha_true, n_steps)\n\nplt.figure(figsize=(8, 4))\nplt.plot(x, T_init, label=\"Initial condition\", linewidth=2)\nplt.plot(x, T_observed, \"k--\", label=f\"Observed (after {n_steps} steps)\", linewidth=2)\nplt.xlabel(\"x\")\nplt.ylabel(\"T\")\nplt.legend()\nplt.title(\"Forward simulation with true $\\\\alpha$\")\nplt.tight_layout()", + "metadata": {}, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": "## Step 4: Solve the inverse problem\n\nNow the fun part. We want to recover $\\alpha$ from the observed final temperature profile. We define the loss as the mean squared error between the simulated and observed profiles:\n\n$$\\mathcal{L}(\\alpha) = \\text{MSE}\\big(T_{\\text{sim}}(\\alpha),\\; T_{\\text{obs}}\\big)$$\n\nBecause the Tesseract exposes Enzyme-generated VJPs, `jax.grad` can differentiate through the entire multi-step simulation -- computing $\\partial \\mathcal{L}/\\partial \\alpha$ by backpropagating through hundreds of Fortran solver calls. We use L-BFGS-B from `scipy.optimize` to find the optimal $\\alpha$." + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def loss_fn(alpha):\n", + " \"\"\"MSE between simulated and observed temperature profiles.\"\"\"\n", + " T_sim = simulate(T_init, alpha, n_steps)\n", + " return jnp.mean((T_sim - T_observed) ** 2)\n", + "\n", + "\n", + "# Verify gradients work\n", + "grad_fn = jax.jit(jax.value_and_grad(loss_fn))\n", + "test_loss, test_grad = grad_fn(jnp.float64(0.05))\n", + "print(f\"Loss at alpha=0.05: {test_loss:.6e}\")\n", + "print(f\"Gradient dL/dalpha: {test_grad:.6e}\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.optimize import minimize as scipy_minimize\n", + "\n", + "# Start from a wrong initial guess: alpha=0.05 (true value is 0.02)\n", + "alpha_init = 0.05\n", + "history = {\"alpha\": [alpha_init], \"loss\": []}\n", + "\n", + "\n", + "def objective(alpha_arr):\n", + " \"\"\"Wrapper for scipy: returns (loss, grad) as plain floats.\"\"\"\n", + " loss, grad = grad_fn(float(alpha_arr[0]))\n", + " history[\"alpha\"].append(float(alpha_arr[0]))\n", + " history[\"loss\"].append(float(loss))\n", + " return float(loss), np.array([float(grad)])\n", + "\n", + "\n", + "result = scipy_minimize(\n", + " objective,\n", + " x0=np.array([alpha_init]),\n", + " method=\"L-BFGS-B\",\n", + " jac=True,\n", + " bounds=[(1e-6, 0.1)],\n", + " options={\"maxiter\": 100},\n", + ")\n", + "\n", + "alpha_recovered = result.x[0]\n", + "print(f\"Converged in {len(history['loss'])} iterations\")\n", + "print(f\"Recovered alpha: {alpha_recovered:.8f}\")\n", + "print(f\"True alpha: {alpha_true}\")\n", + "print(f\"Final loss: {result.fun:.2e}\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n", + "\n", + "# Loss curve\n", + "axes[0].semilogy(history[\"loss\"])\n", + "axes[0].set_xlabel(\"Iteration\")\n", + "axes[0].set_ylabel(\"Loss (MSE)\")\n", + "axes[0].set_title(\"Loss convergence\")\n", + "axes[0].grid(True, alpha=0.3)\n", + "\n", + "# Alpha convergence\n", + "axes[1].plot(history[\"alpha\"], label=\"Estimated $\\\\alpha$\")\n", + "axes[1].axhline(y=alpha_true, color=\"r\", linestyle=\"--\", label=\"True $\\\\alpha$\")\n", + "axes[1].set_xlabel(\"Iteration\")\n", + "axes[1].set_ylabel(\"$\\\\alpha$\")\n", + "axes[1].set_title(\"Parameter convergence\")\n", + "axes[1].legend()\n", + "axes[1].grid(True, alpha=0.3)\n", + "\n", + "# Temperature profiles\n", + "T_recovered = simulate(T_init, alpha_recovered, n_steps)\n", + "T_initial_guess = simulate(T_init, alpha_init, n_steps)\n", + "axes[2].plot(x, T_observed, \"k--\", label=\"Observed\", linewidth=2)\n", + "axes[2].plot(\n", + " x, T_recovered, label=f\"Recovered ($\\\\alpha$={alpha_recovered:.4f})\", linewidth=2\n", + ")\n", + "axes[2].plot(\n", + " x,\n", + " T_initial_guess,\n", + " \":\",\n", + " label=f\"Initial guess ($\\\\alpha$={alpha_init})\",\n", + " linewidth=2,\n", + " alpha=0.7,\n", + ")\n", + "axes[2].set_xlabel(\"x\")\n", + "axes[2].set_ylabel(\"T\")\n", + "axes[2].set_title(\"Temperature profiles\")\n", + "axes[2].legend()\n", + "axes[2].grid(True, alpha=0.3)\n", + "\n", + "plt.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 5: Verify gradient accuracy against finite differences\n", + "\n", + "To confirm that Enzyme produces exact gradients, we compare against finite difference approximations at several step sizes. Enzyme's gradients should match to machine precision, while finite differences degrade for both too-large (truncation error) and too-small (roundoff error) step sizes." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Compare Enzyme gradient vs finite differences at a non-optimal alpha\n", + "# (At the optimum the gradient is zero, which makes relative error meaningless)\n", + "alpha_test = 0.03\n", + "\n", + "_, enzyme_grad = grad_fn(alpha_test)\n", + "\n", + "# Finite difference gradients at various step sizes\n", + "epsilons = np.logspace(-2, -12, 20)\n", + "fd_grads = []\n", + "for eps in epsilons:\n", + " loss_plus = loss_fn(alpha_test + eps)\n", + " loss_minus = loss_fn(alpha_test - eps)\n", + " fd_grads.append(float((loss_plus - loss_minus) / (2 * eps)))\n", + "\n", + "fd_grads = np.array(fd_grads)\n", + "rel_errors = np.abs(fd_grads - float(enzyme_grad)) / (\n", + " np.abs(float(enzyme_grad)) + 1e-30\n", + ")\n", + "\n", + "plt.figure(figsize=(8, 4))\n", + "plt.loglog(epsilons, rel_errors, \"o-\", label=\"FD vs Enzyme\")\n", + "plt.xlabel(\"Finite difference step size $\\\\epsilon$\")\n", + "plt.ylabel(\"Relative error vs. Enzyme gradient\")\n", + "plt.title(\"Enzyme provides exact gradients; finite differences have a sweet spot\")\n", + "plt.grid(True, alpha=0.3)\n", + "plt.legend()\n", + "plt.tight_layout()\n", + "\n", + "print(f\"Enzyme gradient: {float(enzyme_grad):.10e}\")\n", + "print(f\"Best FD gradient: {fd_grads[np.argmin(rel_errors)]:.10e}\")\n", + "print(f\"Best FD relative error: {rel_errors.min():.2e}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": "## Takeaways\n\n1. **Exact gradients from compiled Fortran, automatically.** Enzyme differentiated the Fortran heat solver at the LLVM IR level -- no adjoint code, no source modifications, no approximation.\n\n2. **Full JAX composability.** By packaging the solver as a Tesseract and using tesseract-jax, we called `jax.grad` through hundreds of Fortran solver invocations. L-BFGS-B converged in just a handful of iterations -- the Fortran solver is just another differentiable function.\n\n3. **Machine-precision accuracy.** The Enzyme gradients match finite differences at their best, and remain exact where finite differences break down.\n\n4. **Language-agnostic.** Enzyme works on LLVM IR, so the same approach applies to C, C++, Rust -- any language with an LLVM frontend. The Fortran example here is just the beginning.\n\n5. **Reproducible and portable.** The entire toolchain (LFortran, LLVM 19, Enzyme) is packaged in the Tesseract container. `tesseract build` produces the same differentiated binary on any machine." + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "heat_tesseract.teardown()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python", + "version": "3.10.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/examples/enzyme_ad/tesseract_api.py b/examples/enzyme_ad/tesseract_api.py index 6bde9062..e0261f4e 100644 --- a/examples/enzyme_ad/tesseract_api.py +++ b/examples/enzyme_ad/tesseract_api.py @@ -29,7 +29,7 @@ from pydantic import BaseModel, Field, model_validator from typing_extensions import Self -from tesseract_core.runtime import Array, Differentiable, Float64 +from tesseract_core.runtime import Array, Differentiable, Float64, ShapeDType # ── Shared library loading ────────────────────────────────────────── @@ -104,23 +104,25 @@ class InputSchema(BaseModel): ) alpha: Differentiable[Float64] = Field( default=0.01, - description="Thermal diffusivity [m^2/s].", - gt=0.0, + description="Thermal diffusivity [m^2/s]. Must be > 0.", ) dx: Differentiable[Float64] = Field( default=0.25, - description="Grid spacing [m].", - gt=0.0, + description="Grid spacing [m]. Must be > 0.", ) dt: Differentiable[Float64] = Field( default=0.001, - description="Time step size [s].", - gt=0.0, + description="Time step size [s]. Must be > 0.", ) @model_validator(mode="after") def check_stability(self) -> Self: - """Verify CFL stability condition: r = alpha * dt / dx^2 <= 0.5.""" + """Verify positivity and CFL stability condition: r = alpha * dt / dx^2 <= 0.5.""" + if isinstance(self.alpha, ShapeDType): + return self # skip during abstract_eval + for name in ("alpha", "dx", "dt"): + if getattr(self, name) <= 0: + raise ValueError(f"{name} must be > 0, got {getattr(self, name)}") r = self.alpha * self.dt / (self.dx**2) if r > 0.5: raise ValueError( @@ -132,6 +134,8 @@ def check_stability(self) -> Self: @model_validator(mode="after") def check_min_points(self) -> Self: """Need at least 3 points for interior stencil.""" + if isinstance(self.T_in, ShapeDType): + return self # skip during abstract_eval if len(self.T_in) < 3: raise ValueError("T_in must have at least 3 points.") return self @@ -161,6 +165,12 @@ def apply(inputs: InputSchema) -> OutputSchema: return OutputSchema(T_out=T_out) +def abstract_eval(abstract_inputs): + """Calculate output shape from input shapes (required for tesseract-jax).""" + T_in_shape = abstract_inputs.T_in + return {"T_out": ShapeDType(shape=T_in_shape.shape, dtype=T_in_shape.dtype)} + + # ── Optional endpoints (AD via Enzyme) ────────────────────────────── From 271eb76c95a70055c3cbc96404b0d86f050a6f2a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dion=20H=C3=A4fner?= Date: Fri, 15 May 2026 13:34:51 +0200 Subject: [PATCH 03/24] fix enzyme --- demo/enzyme_thermal_2d/enzyme/build.sh | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/demo/enzyme_thermal_2d/enzyme/build.sh b/demo/enzyme_thermal_2d/enzyme/build.sh index 95ca1ddf..581cafbe 100644 --- a/demo/enzyme_thermal_2d/enzyme/build.sh +++ b/demo/enzyme_thermal_2d/enzyme/build.sh @@ -23,10 +23,13 @@ lfortran --show-llvm --no-array-bounds-checking \ "${SCRIPT_DIR}/thermal_2d.f90" > /tmp/thermal_2d.ll echo "=== Step 2: Optimize IR ===" -opt -O3 -S /tmp/thermal_2d.ll -o /tmp/thermal_2d_opt.ll +# Use -O1 to avoid aggressive transforms (vectorization, code motion) that can +# produce IR patterns Enzyme's reverse-mode pass mishandles, leading to NaN +# gradients when intermediate values cancel (e.g. uniform temperature fields). +opt -O1 -S /tmp/thermal_2d.ll -o /tmp/thermal_2d_opt.ll echo "=== Step 3: Compile C wrapper -> LLVM IR ===" -clang -emit-llvm -S -O3 "${SCRIPT_DIR}/wrapper.c" -o /tmp/wrapper.ll +clang -emit-llvm -S -O1 "${SCRIPT_DIR}/wrapper.c" -o /tmp/wrapper.ll echo "=== Step 4: Link IR modules ===" llvm-link /tmp/wrapper.ll /tmp/thermal_2d_opt.ll -S -o /tmp/combined.ll From 9d2f490bfb95720194f8fe51a8d3161c18123a0a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dion=20H=C3=A4fner?= Date: Fri, 15 May 2026 17:09:11 +0200 Subject: [PATCH 04/24] add blog post draft --- demo/enzyme_thermal_2d/enzyme/build.sh | 7 +- .../figures/fd_convergence.png | Bin 0 -> 106228 bytes .../figures/part1_convergence.png | Bin 0 -> 100650 bytes .../figures/part1_temperature_fields.png | Bin 0 -> 76630 bytes .../figures/part2_forensics.png | Bin 0 -> 222525 bytes demo/enzyme_thermal_2d/figures/pipeline.png | Bin 0 -> 135911 bytes .../generate_blog_figures.py | 565 ++++++++++++++++++ .../generate_pipeline_diagram.py | 264 ++++++++ demo/enzyme_thermal_2d/tesseract_config.yaml | 21 +- demo/jax_thermal_2d/README.md | 58 -- demo/jax_thermal_2d/benchmark.py | 144 ----- demo/jax_thermal_2d/tesseract_api.py | 339 ----------- demo/jax_thermal_2d/tesseract_config.yaml | 16 - .../jax_thermal_2d/tesseract_requirements.txt | 2 - .../2026-05-15-fortran-enzyme-autodiff.md | 308 ++++++++++ docs/static/blog/enzyme-fd-convergence.png | Bin 0 -> 106228 bytes docs/static/blog/enzyme-part1-convergence.png | Bin 0 -> 100650 bytes .../blog/enzyme-part1-temperature-fields.png | Bin 0 -> 76630 bytes docs/static/blog/enzyme-part2-forensics.png | Bin 0 -> 222525 bytes docs/static/blog/enzyme-pipeline.png | Bin 0 -> 135911 bytes 20 files changed, 1157 insertions(+), 567 deletions(-) create mode 100644 demo/enzyme_thermal_2d/figures/fd_convergence.png create mode 100644 demo/enzyme_thermal_2d/figures/part1_convergence.png create mode 100644 demo/enzyme_thermal_2d/figures/part1_temperature_fields.png create mode 100644 demo/enzyme_thermal_2d/figures/part2_forensics.png create mode 100644 demo/enzyme_thermal_2d/figures/pipeline.png create mode 100644 demo/enzyme_thermal_2d/generate_blog_figures.py create mode 100644 demo/enzyme_thermal_2d/generate_pipeline_diagram.py delete mode 100644 demo/jax_thermal_2d/README.md delete mode 100644 demo/jax_thermal_2d/benchmark.py delete mode 100644 demo/jax_thermal_2d/tesseract_api.py delete mode 100644 demo/jax_thermal_2d/tesseract_config.yaml delete mode 100644 demo/jax_thermal_2d/tesseract_requirements.txt create mode 100644 docs/blog/2026-05-15-fortran-enzyme-autodiff.md create mode 100644 docs/static/blog/enzyme-fd-convergence.png create mode 100644 docs/static/blog/enzyme-part1-convergence.png create mode 100644 docs/static/blog/enzyme-part1-temperature-fields.png create mode 100644 docs/static/blog/enzyme-part2-forensics.png create mode 100644 docs/static/blog/enzyme-pipeline.png diff --git a/demo/enzyme_thermal_2d/enzyme/build.sh b/demo/enzyme_thermal_2d/enzyme/build.sh index 581cafbe..340133cc 100644 --- a/demo/enzyme_thermal_2d/enzyme/build.sh +++ b/demo/enzyme_thermal_2d/enzyme/build.sh @@ -23,9 +23,10 @@ lfortran --show-llvm --no-array-bounds-checking \ "${SCRIPT_DIR}/thermal_2d.f90" > /tmp/thermal_2d.ll echo "=== Step 2: Optimize IR ===" -# Use -O1 to avoid aggressive transforms (vectorization, code motion) that can -# produce IR patterns Enzyme's reverse-mode pass mishandles, leading to NaN -# gradients when intermediate values cancel (e.g. uniform temperature fields). +# Use -O1 before Enzyme to avoid aggressive transforms (vectorization, code +# motion) that produce IR patterns Enzyme's reverse-mode pass mishandles — +# specifically NaN gradients when adjacent cell values are equal and +# intermediate terms cancel. 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b/demo/enzyme_thermal_2d/generate_blog_figures.py new file mode 100644 index 00000000..37bbc21d --- /dev/null +++ b/demo/enzyme_thermal_2d/generate_blog_figures.py @@ -0,0 +1,565 @@ +#!/usr/bin/env python3 +# Copyright 2025 Pasteur Labs. All Rights Reserved. +# SPDX-License-Identifier: Apache-2.0 +"""Generate figures for the Enzyme AD blog post. + +Usage: + tesseract build demo/enzyme_thermal_2d/ + python demo/enzyme_thermal_2d/generate_blog_figures.py + +Outputs PNG files to demo/enzyme_thermal_2d/figures/. +""" + +import time +from pathlib import Path + +import matplotlib.pyplot as plt +import numpy as np +from scipy.optimize import minimize + +from tesseract_core import Tesseract + +FIGURE_DIR = Path(__file__).parent / "figures" +FIGURE_DIR.mkdir(exist_ok=True) + +# ── Shared parameters ──────────────────────────────────────────────────────── + +nx, ny = 30, 30 +n = nx * ny +n_steps = 500 +dt = 0.05 +Lx, Ly = 0.1, 0.05 +rho = 7850.0 +cp = 460.0 +h_conv = 25.0 +T_inf = 293.15 +T_hot = 373.15 +Q = np.zeros(n) +T_init_uniform = np.full(n, T_inf) + +k0_true = 45.0 +k1_true = -0.02 + +rng = np.random.default_rng(42) + +plt.rcParams.update( + { + "figure.dpi": 180, + "savefig.dpi": 180, + "font.size": 11, + "axes.titlesize": 12, + "savefig.bbox": "tight", + "savefig.pad_inches": 0.15, + } +) + + +def make_inputs(k0, k1, T_init=None, n_steps_=None, dt_=None): + return { + "T_init": (T_init if T_init is not None else T_init_uniform), + "Q": Q, + "nx": nx, + "ny": ny, + "n_steps": n_steps_ or n_steps, + "k0": float(k0), + "k1": float(k1), + "rho": rho, + "cp": cp, + "h_conv": h_conv, + "T_inf": T_inf, + "T_hot": T_hot, + "Lx": Lx, + "Ly": Ly, + "dt": dt_ or dt, + } + + +# ── Figure 1: FD vs Enzyme convergence ─────────────────────────────────────── + + +def generate_fd_convergence(t): + print("Generating FD vs Enzyme convergence plot...") + + inputs = make_inputs(k0_true, k1_true) + + cotangent = np.ones(n, dtype=np.float64) + vjp = t.vector_jacobian_product( + inputs=inputs, + vjp_inputs=["k0", "k1", "h_conv"], + vjp_outputs=["T_final"], + cotangent_vector={"T_final": cotangent}, + ) + enzyme_dk0 = vjp["k0"] + enzyme_dk1 = vjp["k1"] + enzyme_dh = vjp["h_conv"] + + print(f" Enzyme (VJP) dk0 = {enzyme_dk0:.10e}") + print(f" Enzyme (VJP) dk1 = {enzyme_dk1:.10e}") + print(f" Enzyme (VJP) dh = {enzyme_dh:.10e}") + + epsilons = np.logspace(-1, -12, 24) + fd_errors_k0 = [] + fd_errors_k1 = [] + fd_errors_h = [] + + for i, eps in enumerate(epsilons): + if (i + 1) % 6 == 0: + print(f" FD step {i + 1}/{len(epsilons)}...") + + T_plus = np.array( + t.apply(inputs=make_inputs(k0_true + eps, k1_true))["T_final"] + ) + T_minus = np.array( + t.apply(inputs=make_inputs(k0_true - eps, k1_true))["T_final"] + ) + fd_dk0 = np.sum(T_plus - T_minus) / (2 * eps) + fd_errors_k0.append(abs(fd_dk0 - enzyme_dk0) / (abs(enzyme_dk0) + 1e-30)) + + T_plus = np.array( + t.apply(inputs=make_inputs(k0_true, k1_true + eps))["T_final"] + ) + T_minus = np.array( + t.apply(inputs=make_inputs(k0_true, k1_true - eps))["T_final"] + ) + fd_dk1 = np.sum(T_plus - T_minus) / (2 * eps) + fd_errors_k1.append(abs(fd_dk1 - enzyme_dk1) / (abs(enzyme_dk1) + 1e-30)) + + inp_p = make_inputs(k0_true, k1_true) + inp_m = make_inputs(k0_true, k1_true) + inp_p["h_conv"] = h_conv + eps + inp_m["h_conv"] = h_conv - eps + T_plus = np.array(t.apply(inputs=inp_p)["T_final"]) + T_minus = np.array(t.apply(inputs=inp_m)["T_final"]) + fd_dh = np.sum(T_plus - T_minus) / (2 * eps) + fd_errors_h.append(abs(fd_dh - enzyme_dh) / (abs(enzyme_dh) + 1e-30)) + + fig, ax = plt.subplots(1, 1, figsize=(7, 4.5)) + ax.loglog( + epsilons, + fd_errors_k0, + "o-", + ms=4, + label="$\\partial / \\partial k_0$", + color="#1971c2", + ) + ax.loglog( + epsilons, + fd_errors_k1, + "s-", + ms=4, + label="$\\partial / \\partial k_1$", + color="#e8590c", + ) + ax.loglog( + epsilons, + fd_errors_h, + "^-", + ms=4, + label="$\\partial / \\partial h_{\\mathrm{conv}}$", + color="#2f9e44", + ) + ax.axhline(1e-15, color="gray", ls=":", alpha=0.5, label="Machine precision") + + ax.set_xlabel("Finite difference step size $\\epsilon$") + ax.set_ylabel("Relative error vs. Enzyme gradient") + ax.set_title( + "Enzyme provides exact gradients; finite differences have a sweet spot" + ) + ax.legend(framealpha=0.9) + ax.grid(True, alpha=0.2) + ax.set_ylim(1e-17, 1e1) + + fig.savefig(FIGURE_DIR / "fd_convergence.png") + plt.close(fig) + print(f" Saved {FIGURE_DIR / 'fd_convergence.png'}") + + +# ── Figure 2: Part 1 convergence (3-panel + 4-panel) ───────────────────────── + + +def generate_part1_convergence(t): + print("Generating Part 1 convergence plots...") + + result_true = t.apply(inputs=make_inputs(k0_true, k1_true)) + T_true = np.array(result_true["T_final"]).reshape(ny, nx) + + sensor_ix = [7, 15, 22] + sensor_jy = [7, 15, 22] + sensor_indices = np.array([jy * nx + ix for jy in sensor_jy for ix in sensor_ix]) + sensor_coords = [(ix, jy) for jy in sensor_jy for ix in sensor_ix] + + noise_std = 0.5 + T_obs = T_true.flatten()[sensor_indices] + rng.normal( + 0, noise_std, len(sensor_indices) + ) + + k0_init, k1_init = 60.0, 0.01 + history = {"k0": [k0_init], "k1": [k1_init], "loss": []} + + def obj_grad(params): + k0, k1 = float(params[0]), float(params[1]) + inputs = make_inputs(k0, k1) + result = t.apply(inputs=inputs) + T_pred = np.array(result["T_final"]) + residuals = T_pred[sensor_indices] - T_obs + loss = 0.5 * np.sum(residuals**2) + + cotangent = np.zeros(n, dtype=np.float64) + cotangent[sensor_indices] = residuals + vjp = t.vector_jacobian_product( + inputs=inputs, + vjp_inputs=["k0", "k1"], + vjp_outputs=["T_final"], + cotangent_vector={"T_final": cotangent}, + ) + return loss, np.array([vjp["k0"], vjp["k1"]]) + + loss0, _ = obj_grad([k0_init, k1_init]) + history["loss"].append(loss0) + print(f" Initial loss: {loss0:.4f}") + + def callback(params): + k0, k1 = float(params[0]), float(params[1]) + loss, _ = obj_grad(params) + history["k0"].append(k0) + history["k1"].append(k1) + history["loss"].append(loss) + print(f" k0={k0:.4f}, k1={k1:.6f}, loss={loss:.6f}") + + result_opt = minimize( + fun=obj_grad, + x0=[k0_init, k1_init], + method="L-BFGS-B", + jac=True, + bounds=[(5.0, 80.0), (-0.08, 0.08)], + callback=callback, + options={"maxiter": 50, "ftol": 1e-12, "gtol": 1e-8}, + ) + k0_opt, k1_opt = float(result_opt.x[0]), float(result_opt.x[1]) + + # ── 3-panel convergence ── + fig, axes = plt.subplots(1, 3, figsize=(14, 4)) + + axes[0].semilogy(history["loss"], "k.-", linewidth=1.5) + axes[0].set_xlabel("Iteration") + axes[0].set_ylabel("Loss (sum of squared residuals)") + axes[0].set_title("Convergence") + axes[0].grid(True, alpha=0.3) + + axes[1].plot(history["k0"], "b.-", linewidth=1.5, label="$k_0$ estimate") + axes[1].axhline( + k0_true, color="b", ls="--", alpha=0.5, label=f"$k_0$ true = {k0_true}" + ) + axes[1].set_xlabel("Iteration") + axes[1].set_ylabel("$k_0$ [W/(m K)]") + axes[1].set_title("Base conductivity") + axes[1].legend() + axes[1].grid(True, alpha=0.3) + + axes[2].plot(history["k1"], "r.-", linewidth=1.5, label="$k_1$ estimate") + axes[2].axhline( + k1_true, color="r", ls="--", alpha=0.5, label=f"$k_1$ true = {k1_true}" + ) + axes[2].set_xlabel("Iteration") + axes[2].set_ylabel("$k_1$ [W/(m K$^2$)]") + axes[2].set_title("Temperature coefficient") + axes[2].legend() + axes[2].grid(True, alpha=0.3) + + fig.savefig(FIGURE_DIR / "part1_convergence.png") + plt.close(fig) + print(f" Saved {FIGURE_DIR / 'part1_convergence.png'}") + + # ── 4-panel temperature fields ── + T_opt_field = np.array( + t.apply(inputs=make_inputs(k0_opt, k1_opt))["T_final"] + ).reshape(ny, nx) + T_init_field = np.array( + t.apply(inputs=make_inputs(k0_init, k1_init))["T_final"] + ).reshape(ny, nx) + + vmin = min(T_true.min(), T_opt_field.min(), T_init_field.min()) + vmax = max(T_true.max(), T_opt_field.max(), T_init_field.max()) + extent = [0, Lx * 1e3, 0, Ly * 1e3] + + fig, axes = plt.subplots(1, 4, figsize=(18, 4)) + titles = [ + f"Initial guess\n$k_0$={k0_init}, $k_1$={k1_init}", + f"Recovered\n$k_0$={k0_opt:.2f}, $k_1$={k1_opt:.4f}", + f"Ground truth\n$k_0$={k0_true}, $k_1$={k1_true}", + None, + ] + fields = [T_init_field, T_opt_field, T_true, np.abs(T_opt_field - T_true)] + cmaps = ["hot", "hot", "hot", "Blues"] + + for i, (ax, field, cmap) in enumerate(zip(axes, fields, cmaps, strict=True)): + if i < 3: + im = ax.imshow( + field, + origin="lower", + cmap=cmap, + extent=extent, + aspect="auto", + vmin=vmin, + vmax=vmax, + ) + else: + im = ax.imshow( + field, origin="lower", cmap=cmap, extent=extent, aspect="auto" + ) + ax.set_title(f"|Recovered - Truth|\nmax error: {field.max():.3f} K") + if titles[i]: + ax.set_title(titles[i]) + ax.set_xlabel("x [mm]") + ax.set_ylabel("y [mm]") + for ix, jy in sensor_coords: + x_mm = ix / (nx - 1) * Lx * 1e3 + y_mm = jy / (ny - 1) * Ly * 1e3 + ax.plot(x_mm, y_mm, "ws", ms=5, markeredgecolor="blue", markeredgewidth=1) + + plt.colorbar(im, ax=axes[:3].tolist(), label="Temperature [K]", shrink=0.9) + plt.colorbar(axes[3].images[0], ax=axes[3], label="Error [K]", shrink=0.9) + fig.savefig(FIGURE_DIR / "part1_temperature_fields.png") + plt.close(fig) + print(f" Saved {FIGURE_DIR / 'part1_temperature_fields.png'}") + print( + f" Recovered: k0={k0_opt:.4f}, k1={k1_opt:.6f} in {result_opt.nit} iterations" + ) + + +# ── Figure 3: Part 2 forensics (6-panel) ───────────────────────────────────── + + +def generate_part2_forensics(t): + print("Generating Part 2 forensics plots...") + + n_steps_p2 = 100 + dt_p2 = 0.05 + k0_p2 = 45.0 + k1_p2 = -0.01 + + x_coord = np.linspace(0, Lx, nx) + y_coord = np.linspace(0, Ly, ny) + X, Y = np.meshgrid(x_coord, y_coord) + X_flat, Y_flat = X.flatten(), Y.flatten() + + T_init_true = ( + T_inf + + 40.0 * np.exp(-((X_flat - 0.04) ** 2 + (Y_flat - 0.025) ** 2) / 0.015**2) + + 25.0 * np.exp(-((X_flat - 0.08) ** 2 + (Y_flat - 0.035) ** 2) / 0.01**2) + ) + + def make_inputs_p2(T_init_field): + return { + "T_init": T_init_field.astype(np.float64), + "Q": Q, + "nx": nx, + "ny": ny, + "n_steps": n_steps_p2, + "k0": k0_p2, + "k1": k1_p2, + "rho": rho, + "cp": cp, + "h_conv": h_conv, + "T_inf": T_inf, + "T_hot": T_hot, + "Lx": Lx, + "Ly": Ly, + "dt": dt_p2, + } + + result_true_p2 = t.apply(inputs=make_inputs_p2(T_init_true)) + T_final_true_p2 = np.array(result_true_p2["T_final"]) + + sensor_ix_p2 = np.linspace(3, nx - 4, 10, dtype=int) + sensor_jy_p2 = np.linspace(3, ny - 4, 10, dtype=int) + sensor_grid = np.array([jy * nx + ix for jy in sensor_jy_p2 for ix in sensor_ix_p2]) + + noise_std_p2 = 0.3 + T_obs_p2 = T_final_true_p2[sensor_grid] + rng.normal( + 0, noise_std_p2, len(sensor_grid) + ) + + T_init_guess = np.full(n, T_inf) + loss_history = [] + + # Tikhonov regularization: penalize deviation from prior (uniform T_inf) + # This stabilizes the ill-posed inverse problem (900 unknowns, 100 observations) + alpha_reg = 0.001 + + def obj_grad_p2(T_init_vec): + inputs = make_inputs_p2(T_init_vec) + result = t.apply(inputs=inputs) + T_pred = np.array(result["T_final"]) + residuals = T_pred[sensor_grid] - T_obs_p2 + data_loss = 0.5 * np.sum(residuals**2) + reg_loss = 0.5 * alpha_reg * np.sum((T_init_vec - T_inf) ** 2) + loss = data_loss + reg_loss + + cotangent = np.zeros(n, dtype=np.float64) + cotangent[sensor_grid] = residuals + vjp = t.vector_jacobian_product( + inputs=inputs, + vjp_inputs=["T_init"], + vjp_outputs=["T_final"], + cotangent_vector={"T_final": cotangent}, + ) + grad = np.array(vjp["T_init"]) + alpha_reg * (T_init_vec - T_inf) + return loss, grad + + loss0, _ = obj_grad_p2(T_init_guess) + loss_history.append(loss0) + print(f" Initial loss: {loss0:.2f}") + + iter_count = [0] + t_start = time.time() + + def callback_p2(x): + iter_count[0] += 1 + if iter_count[0] % 10 == 0: + loss, _ = obj_grad_p2(x) + loss_history.append(loss) + elapsed = time.time() - t_start + print( + f" iter {iter_count[0]:3d}: loss={loss:.4f}, elapsed={elapsed:.1f}s" + ) + + result_p2 = minimize( + fun=obj_grad_p2, + x0=T_init_guess, + method="L-BFGS-B", + jac=True, + bounds=[(250.0, 450.0)] * n, + callback=callback_p2, + options={"maxiter": 200, "ftol": 1e-15, "gtol": 1e-10}, + ) + elapsed_total = time.time() - t_start + loss_final, _ = obj_grad_p2(result_p2.x) + loss_history.append(loss_final) + T_init_recovered = result_p2.x + + corr = np.corrcoef(T_init_true, T_init_recovered)[0, 1] + print(f" Optimization: {result_p2.nit} iterations, {elapsed_total:.1f}s") + print(f" Loss: {loss0:.2f} -> {loss_final:.4f}") + print(f" Correlation: {corr:.4f}") + + # Cost comparison + n_fev = result_p2.nfev + print("\n Cost comparison:") + print( + f" FD: {n + 1} forward solves/iter = ~{(n + 1) * elapsed_total / n_fev:.1f}s/iter" + ) + print(f" VJP: 2 solves/iter (fwd+rev) = ~{2 * elapsed_total / n_fev:.2f}s/iter") + print(f" Speedup: ~{(n + 1) / 2:.0f}x") + + # ── 6-panel figure ── + extent = [0, Lx * 1e3, 0, Ly * 1e3] + vmin_init = min(T_init_true.min(), T_init_recovered.min(), T_inf) + vmax_init = max(T_init_true.max(), T_init_recovered.max()) + + fig, axes = plt.subplots(2, 3, figsize=(16, 9)) + + axes[0, 0].imshow( + T_init_guess.reshape(ny, nx), + origin="lower", + cmap="hot", + extent=extent, + aspect="auto", + vmin=vmin_init, + vmax=vmax_init, + ) + axes[0, 0].set_title("Starting guess\n(uniform ambient)") + + axes[0, 1].imshow( + T_init_recovered.reshape(ny, nx), + origin="lower", + cmap="hot", + extent=extent, + aspect="auto", + vmin=vmin_init, + vmax=vmax_init, + ) + axes[0, 1].set_title(f"Recovered $T_0$\n(corr={corr:.3f})") + + im_true = axes[0, 2].imshow( + T_init_true.reshape(ny, nx), + origin="lower", + cmap="hot", + extent=extent, + aspect="auto", + vmin=vmin_init, + vmax=vmax_init, + ) + axes[0, 2].set_title("True $T_0$\n(two Gaussian hot spots)") + + plt.colorbar(im_true, ax=axes[0, :].tolist(), label="Temperature [K]", shrink=0.85) + + for ax in axes[0, :]: + for jy_idx in sensor_jy_p2: + for ix_idx in sensor_ix_p2: + x_mm = ix_idx / (nx - 1) * Lx * 1e3 + y_mm = jy_idx / (ny - 1) * Ly * 1e3 + ax.plot(x_mm, y_mm, ".", color="cyan", ms=2, alpha=0.5) + ax.set_xlabel("x [mm]") + ax.set_ylabel("y [mm]") + + error_p2 = np.abs(T_init_recovered - T_init_true).reshape(ny, nx) + im_err = axes[1, 0].imshow( + error_p2, origin="lower", cmap="Blues", extent=extent, aspect="auto" + ) + axes[1, 0].set_title( + f"|Recovered - True|\nmax={error_p2.max():.1f} K, mean={error_p2.mean():.1f} K" + ) + axes[1, 0].set_xlabel("x [mm]") + axes[1, 0].set_ylabel("y [mm]") + plt.colorbar(im_err, ax=axes[1, 0], label="Error [K]", shrink=0.85) + + axes[1, 1].scatter(T_init_true, T_init_recovered, s=3, alpha=0.5, c="steelblue") + lims = [vmin_init - 5, vmax_init + 5] + axes[1, 1].plot(lims, lims, "k--", alpha=0.5, label="perfect recovery") + axes[1, 1].set_xlim(lims) + axes[1, 1].set_ylim(lims) + axes[1, 1].set_xlabel("True $T_0$ [K]") + axes[1, 1].set_ylabel("Recovered $T_0$ [K]") + axes[1, 1].set_title("True vs. recovered (per grid cell)") + axes[1, 1].legend() + axes[1, 1].set_aspect("equal") + axes[1, 1].grid(True, alpha=0.3) + + axes[1, 2].semilogy(loss_history, "k.-", linewidth=1.5) + axes[1, 2].set_xlabel("Checkpoint") + axes[1, 2].set_ylabel("Loss") + axes[1, 2].set_title(f"Convergence ({result_p2.nit} L-BFGS iterations)") + axes[1, 2].grid(True, alpha=0.3) + + fig.suptitle( + "Recovering a 900-element initial temperature field from 100 sensors", + fontsize=13, + fontweight="bold", + y=1.01, + ) + fig.savefig(FIGURE_DIR / "part2_forensics.png") + plt.close(fig) + print(f" Saved {FIGURE_DIR / 'part2_forensics.png'}") + + +# ── Main ───────────────────────────────────────────────────────────────────── + + +def main(): + print(f"Output directory: {FIGURE_DIR}") + print() + + with Tesseract.from_image("enzyme-thermal-2d:latest") as t: + generate_fd_convergence(t) + print() + generate_part1_convergence(t) + print() + generate_part2_forensics(t) + + print() + print("All figures generated.") + + +if __name__ == "__main__": + main() diff --git a/demo/enzyme_thermal_2d/generate_pipeline_diagram.py b/demo/enzyme_thermal_2d/generate_pipeline_diagram.py new file mode 100644 index 00000000..fb6b429c --- /dev/null +++ b/demo/enzyme_thermal_2d/generate_pipeline_diagram.py @@ -0,0 +1,264 @@ +#!/usr/bin/env python3 +# Copyright 2025 Pasteur Labs. All Rights Reserved. +# SPDX-License-Identifier: Apache-2.0 +"""Generate the compilation pipeline diagram for the Enzyme AD blog post.""" + +from pathlib import Path + +import matplotlib.pyplot as plt +from matplotlib.patches import FancyArrowPatch, FancyBboxPatch + +FIGURE_DIR = Path(__file__).parent / "figures" +FIGURE_DIR.mkdir(exist_ok=True) + +# Colors +C_FORT_BG, C_FORT = "#dbeafe", "#2563eb" +C_IR_BG, C_IR = "#fef9c4", "#ca8a04" +C_ENZ_BG, C_ENZ = "#ede9fe", "#7c3aed" +C_SO_BG, C_SO = "#ffedd5", "#ea580c" +C_WRAP_BG, C_WRAP = "#dcfce7", "#16a34a" +C_ARROW = "#9ca3af" +C_TEXT = "#374151" + + +def draw_box(ax, cx, cy, w, h, line1, line2, bg, edge, lw=1.5, fs=10): + p = FancyBboxPatch( + (cx - w / 2, cy - h / 2), + w, + h, + boxstyle="round,pad=0.05", + facecolor=bg, + edgecolor=edge, + linewidth=lw, + zorder=2, + ) + ax.add_patch(p) + kw = dict(ha="center", va="center", zorder=3, parse_math=False) + if line2: + ax.text( + cx, cy + 0.12, line1, fontsize=fs, fontweight="bold", color="#1f2937", **kw + ) + ax.text( + cx, cy - 0.12, line2, fontsize=fs - 2, color="#6b7280", style="italic", **kw + ) + else: + ax.text(cx, cy, line1, fontsize=fs, fontweight="bold", color="#1f2937", **kw) + + +def draw_arrow(ax, x0, y0, x1, y1, rad=0.0): + style = f"arc3,rad={rad}" + a = FancyArrowPatch( + (x0, y0), + (x1, y1), + arrowstyle="-|>", + mutation_scale=14, + color=C_ARROW, + linewidth=1.8, + connectionstyle=style, + zorder=1, + ) + ax.add_patch(a) + + +def label(ax, x, y, text): + ax.text( + x, + y, + text, + ha="center", + va="center", + fontsize=7.5, + color=C_TEXT, + fontfamily="monospace", + bbox=dict(boxstyle="round,pad=0.12", fc="white", ec="#d1d5db", lw=0.5), + zorder=4, + ) + + +def badge(ax, x, y, num, color): + ax.text( + x, + y, + str(num), + ha="center", + va="center", + fontsize=10, + fontweight="bold", + color=color, + bbox=dict(boxstyle="circle,pad=0.18", fc="white", ec=color, lw=1.3), + zorder=5, + ) + + +def main(): + fig, ax = plt.subplots(figsize=(18, 5.2)) + ax.set_xlim(-1, 20) + ax.set_ylim(-1.2, 4.0) + ax.set_aspect("equal") + ax.axis("off") + + # Y lanes + Y_TOP = 2.8 + Y_BOT = 0.8 + Y_MID = 1.8 + + # X centers — generous spacing + X = { + "f90": 0.5, + "ll": 4.0, + "opt": 7.5, + "combined": 10.5, + "ad": 12.8, + "so": 16.0, + } + + W, H = 2.2, 0.65 + + # ── TOP TRACK: Fortran ── + draw_box( + ax, X["f90"], Y_TOP, W, H, "thermal_2d.f90", "Fortran source", C_FORT_BG, C_FORT + ) + draw_box(ax, X["ll"], Y_TOP, W, H, "thermal_2d.ll", "LLVM IR", C_IR_BG, C_IR) + draw_box( + ax, + X["opt"], + Y_TOP, + W + 0.4, + H, + "thermal_2d_opt.ll", + "optimized IR", + C_IR_BG, + C_IR, + ) + + draw_arrow(ax, X["f90"] + W / 2, Y_TOP, X["ll"] - W / 2, Y_TOP) + label(ax, (X["f90"] + X["ll"]) / 2, Y_TOP + 0.48, "lfortran --show-llvm") + + draw_arrow(ax, X["ll"] + W / 2, Y_TOP, X["opt"] - (W + 0.4) / 2, Y_TOP) + label(ax, (X["ll"] + X["opt"]) / 2, Y_TOP + 0.48, "opt -O3") + + # ── BOTTOM TRACK: C wrapper ── + draw_box( + ax, X["f90"], Y_BOT, W, H, "wrapper.c", "Enzyme annotations", C_WRAP_BG, C_WRAP + ) + draw_box(ax, X["ll"], Y_BOT, W, H, "wrapper.ll", "LLVM IR", C_IR_BG, C_IR) + + draw_arrow(ax, X["f90"] + W / 2, Y_BOT, X["ll"] - W / 2, Y_BOT) + label(ax, (X["f90"] + X["ll"]) / 2, Y_BOT - 0.48, "clang -emit-llvm") + + # ── MERGE ── + draw_box(ax, X["combined"], Y_MID, W, H, "combined.ll", "linked IR", C_IR_BG, C_IR) + + # top track -> combined + draw_arrow( + ax, + X["opt"] + (W + 0.4) / 2, + Y_TOP, + X["combined"] - W / 2, + Y_MID + 0.12, + rad=-0.2, + ) + # bottom track -> combined + draw_arrow( + ax, X["ll"] + W / 2, Y_BOT, X["combined"] - W / 2, Y_MID - 0.12, rad=0.15 + ) + label(ax, (X["opt"] + X["combined"]) / 2 + 0.3, Y_MID + 0.75, "llvm-link") + + # ── LINEAR: combined -> ad -> .so ── + draw_box( + ax, + X["ad"], + Y_MID, + W, + H + 0.1, + "ad.ll", + "differentiated IR", + C_ENZ_BG, + C_ENZ, + lw=2.5, + ) + + W_SO, H_SO = W + 0.6, H + 0.4 + draw_box( + ax, + X["so"], + Y_MID, + W_SO, + H_SO, + "libthermal_2d_ad.so", + None, + C_SO_BG, + C_SO, + lw=2.5, + ) + ax.text( + X["so"], + Y_MID - 0.13, + "forward / JVP / VJP", + ha="center", + va="center", + fontsize=8.5, + color="#9a3412", + fontweight="bold", + zorder=3, + parse_math=False, + ) + + draw_arrow(ax, X["combined"] + W / 2, Y_MID, X["ad"] - W / 2, Y_MID) + label(ax, (X["combined"] + X["ad"]) / 2, Y_MID + 0.52, "opt -passes=enzyme") + + draw_arrow(ax, X["ad"] + W / 2, Y_MID, X["so"] - W_SO / 2, Y_MID) + label(ax, (X["ad"] + X["so"]) / 2, Y_MID + 0.52, "opt + clang -shared") + + # ── Step badges ── + badge(ax, X["f90"], Y_TOP + H / 2 + 0.32, 1, C_FORT) + badge(ax, X["ll"], Y_TOP + H / 2 + 0.32, 2, C_IR) + badge(ax, X["f90"], Y_BOT - H / 2 - 0.32, 3, C_WRAP) + badge(ax, X["combined"], Y_MID + H / 2 + 0.32, 4, C_IR) + badge(ax, X["ad"], Y_MID + (H + 0.1) / 2 + 0.32, 5, C_ENZ) + badge(ax, X["so"], Y_MID + H_SO / 2 + 0.32, 6, C_SO) + + # ── Tool labels at bottom ── + by = -0.7 + for bx, txt, bg, ec in [ + (0.5, "LFortran 0.61", C_FORT_BG, C_FORT), + (7.0, "LLVM 19", C_IR_BG, C_IR), + (13.5, "Enzyme (LLVM pass)", C_ENZ_BG, C_ENZ), + ]: + ax.text( + bx, + by, + txt, + ha="center", + va="center", + fontsize=8.5, + color=C_TEXT, + fontweight="bold", + bbox=dict(boxstyle="round,pad=0.22", fc=bg, ec=ec, lw=1), + ) + + # Title + ax.text( + 9.0, + 3.7, + "Compilation pipeline: Fortran → Enzyme AD → shared library", + ha="center", + va="center", + fontsize=15, + fontweight="bold", + color="#111827", + ) + + fig.savefig( + FIGURE_DIR / "pipeline.png", + dpi=200, + bbox_inches="tight", + pad_inches=0.3, + facecolor="white", + ) + plt.close(fig) + print(f"Saved {FIGURE_DIR / 'pipeline.png'}") + + +if __name__ == "__main__": + main() diff --git a/demo/enzyme_thermal_2d/tesseract_config.yaml b/demo/enzyme_thermal_2d/tesseract_config.yaml index 2c198a2c..3af9cf06 100644 --- a/demo/enzyme_thermal_2d/tesseract_config.yaml +++ b/demo/enzyme_thermal_2d/tesseract_config.yaml @@ -26,6 +26,10 @@ build_config: - gnupg - ca-certificates - bzip2 + - cmake + - git + - build-essential + - libzstd-dev package_data: - ["enzyme/thermal_2d.f90", "enzyme/thermal_2d.f90"] @@ -33,11 +37,11 @@ build_config: - ["enzyme/build.sh", "enzyme/build.sh"] custom_build_steps: - # Install LLVM 19 toolchain + # Install LLVM 19 toolchain (including dev headers for building Enzyme) - | RUN wget -qO- https://apt.llvm.org/llvm-snapshot.gpg.key | tee /etc/apt/trusted.gpg.d/apt.llvm.org.asc && \ echo "deb http://apt.llvm.org/bookworm/ llvm-toolchain-bookworm-19 main" > /etc/apt/sources.list.d/llvm.list && \ - apt-get update && apt-get install -y --no-install-recommends llvm-19 clang-19 && \ + apt-get update && apt-get install -y --no-install-recommends llvm-19 llvm-19-dev clang-19 && \ rm -rf /var/lib/apt/lists/* && \ for tool in opt llvm-as llvm-link llvm-dis llc clang clang++; do \ ln -sf /usr/bin/${tool}-19 /usr/local/bin/${tool} 2>/dev/null || true; \ @@ -51,10 +55,17 @@ build_config: ln -sf $(find /opt/conda -name lfortran -type f | head -1) /usr/local/bin/lfortran && \ echo /opt/conda/lib > /etc/ld.so.conf.d/conda.conf && ldconfig - # Download prebuilt Enzyme LLVM plugin + # Build Enzyme from a pinned release (nightly builds are not reproducible + # and have caused reverse-mode NaN regressions in the past) - | - RUN wget -q https://github.com/EnzymeAD/Enzyme/releases/download/nightly/LLVMEnzyme-19.so \ - -O /usr/local/lib/LLVMEnzyme-19.so + RUN git clone --depth 1 --branch v0.0.258 https://github.com/EnzymeAD/Enzyme.git /tmp/enzyme-src && \ + cmake -S /tmp/enzyme-src/enzyme -B /tmp/enzyme-build \ + -DLLVM_DIR=/usr/lib/llvm-19/lib/cmake/llvm \ + -DCMAKE_BUILD_TYPE=Release \ + -DENZYME_CLANG=OFF -DENZYME_MLIR=OFF && \ + cmake --build /tmp/enzyme-build --target LLVMEnzyme-19 -j"$(nproc)" && \ + cp /tmp/enzyme-build/Enzyme/LLVMEnzyme-19.so /usr/local/lib/ && \ + rm -rf /tmp/enzyme-src /tmp/enzyme-build # Build the differentiated shared library - | diff --git a/demo/jax_thermal_2d/README.md b/demo/jax_thermal_2d/README.md deleted file mode 100644 index 6b1fb623..00000000 --- a/demo/jax_thermal_2d/README.md +++ /dev/null @@ -1,58 +0,0 @@ -# JAX: Differentiable 2D Thermal Solver - -This example is a **JAX reimplementation** of the [Enzyme Thermal 2D](../enzyme_thermal_2d/) solver. It solves the same physics with an identical Tesseract interface, but obtains derivatives via `jax.vjp` / `jax.jvp` instead of Enzyme's LLVM-level AD. - -## What it does - -Same governing equation as the Enzyme version: - -``` -rho * cp * dT/dt = div( k(T) * grad(T) ) + Q -``` - -with temperature-dependent conductivity `k(T) = k0 + k1*T`, mixed boundary conditions (Dirichlet, convection, insulated), and explicit Euler time integration. - -## Why both versions? - -The two implementations represent different strategies for making legacy solvers differentiable: - -| | Enzyme (Fortran) | JAX (Python) | -| ------------------------ | ---------------------------------------------------------- | ----------------------------- | -| **Approach** | Keep existing Fortran code, differentiate at LLVM IR level | Rewrite solver in JAX | -| **AD mechanism** | Enzyme LLVM pass | `jax.vjp` / `jax.jvp` | -| **Build complexity** | LFortran + LLVM + Enzyme toolchain | `pip install jax` | -| **Legacy code reuse** | Full — no solver rewrite needed | None — complete rewrite | -| **JIT compilation** | Ahead-of-time (LLVM) | XLA JIT (first call slower) | -| **Gradient correctness** | Exact (compiler-generated) | Exact (source transformation) | - -## Usage - -```python -from tesseract_core import Tesseract -import numpy as np - -with Tesseract.from_image("jax-thermal-2d:latest") as t: - nx, ny = 20, 20 - result = t.apply(inputs={ - "T_init": np.full(nx * ny, 293.15), - "Q": np.zeros(nx * ny), - "nx": nx, "ny": ny, "n_steps": 100, - "k0": 45.0, "k1": -0.01, - "rho": 7850.0, "cp": 460.0, - "h_conv": 25.0, "T_inf": 293.15, "T_hot": 373.15, - "Lx": 0.1, "Ly": 0.05, "dt": 0.01, - }) - T_final = result["T_final"].reshape(ny, nx) -``` - -The interface is identical to `enzyme-thermal-2d` — you can swap one for the other by changing only the image name. - -## File structure - -``` -jax_thermal_2d/ -├── README.md -├── tesseract_api.py # JAX solver + auto-derived AD endpoints -├── tesseract_config.yaml # Build config (just JAX + equinox) -└── tesseract_requirements.txt # jax[cpu], equinox -``` diff --git a/demo/jax_thermal_2d/benchmark.py b/demo/jax_thermal_2d/benchmark.py deleted file mode 100644 index 9be78b58..00000000 --- a/demo/jax_thermal_2d/benchmark.py +++ /dev/null @@ -1,144 +0,0 @@ -#!/usr/bin/env python3 -# Copyright 2025 Pasteur Labs. All Rights Reserved. -# SPDX-License-Identifier: Apache-2.0 - -"""Benchmark: Enzyme (Fortran) vs JAX thermal 2D solver. - -Compares wall-clock time for forward pass and VJP across grid sizes. -Both images must be built before running: - - tesseract build examples/enzyme_thermal_2d - tesseract build examples/jax_thermal_2d - -NOTE: For a fair comparison, both images must run on the same architecture. -The Enzyme image requires linux/amd64 (LFortran + Enzyme are x86-only), -so on ARM machines (Apple Silicon) it runs under Rosetta emulation. -Run this script on an x86-64 machine for meaningful results. -""" - -import time - -import numpy as np - -from tesseract_core import Tesseract - -IMAGES = { - "Enzyme": "enzyme-thermal-2d:latest", - "JAX": "jax-thermal-2d:latest", -} - -GRID_SIZES = [ - (30, 30, 50), - (100, 100, 50), - (200, 200, 50), - (300, 300, 50), -] - -N_WARMUP = 5 -N_TRIALS = 15 - - -def make_inputs(nx, ny, n_steps): - n = nx * ny - dx = 0.1 / (nx - 1) - dy = 0.05 / (ny - 1) - k_max = 45.0 + (-0.01) * 373.15 - dt_max = 0.5 * 7850.0 * 460.0 / (k_max * (1 / dx**2 + 1 / dy**2)) - dt = 0.9 * dt_max - - return { - "T_init": np.full(n, 293.15), - "Q": np.zeros(n), - "nx": nx, - "ny": ny, - "n_steps": n_steps, - "k0": 45.0, - "k1": -0.01, - "rho": 7850.0, - "cp": 460.0, - "h_conv": 25.0, - "T_inf": 293.15, - "T_hot": 373.15, - "Lx": 0.1, - "Ly": 0.05, - "dt": dt, - } - - -def benchmark_image(image, inputs): - n = inputs["nx"] * inputs["ny"] - cotangent = np.full(n, 1.0 / n) - vjp_kwargs = dict( - vjp_inputs=["k0", "k1", "T_init"], - vjp_outputs=["T_final"], - cotangent_vector={"T_final": cotangent}, - ) - - with Tesseract.from_image(image) as t: - # Warmup (includes JIT compilation for JAX) - for _ in range(N_WARMUP): - t.apply(inputs=inputs) - t.vector_jacobian_product(inputs=inputs, **vjp_kwargs) - - # Benchmark forward - times_fwd = [] - for _ in range(N_TRIALS): - t0 = time.perf_counter() - t.apply(inputs=inputs) - times_fwd.append(time.perf_counter() - t0) - - # Benchmark VJP - times_vjp = [] - for _ in range(N_TRIALS): - t0 = time.perf_counter() - t.vector_jacobian_product(inputs=inputs, **vjp_kwargs) - times_vjp.append(time.perf_counter() - t0) - - return np.median(times_fwd), np.median(times_vjp) - - -def main(): - print("Thermal 2D Benchmark: Enzyme (Fortran + LLVM AD) vs JAX (XLA JIT)") - print(f"Warmup: {N_WARMUP}, Trials: {N_TRIALS} (median reported)") - print("=" * 75) - - # Correctness check first - print("\nCorrectness check (30x30, 50 steps)...") - inputs_check = make_inputs(30, 30, 50) - results = {} - for label, image in IMAGES.items(): - with Tesseract.from_image(image) as t: - r = t.apply(inputs=inputs_check) - results[label] = np.array(r["T_final"]) - diff = np.max(np.abs(results["Enzyme"] - results["JAX"])) - print(f" Forward max abs diff: {diff:.2e}") - - # Benchmark - print( - f"\n{'Grid':>10s} {'DOFs':>8s} | {'Enzyme fwd':>11s} {'Enzyme VJP':>11s} " - f"{'JAX fwd':>11s} {'JAX VJP':>11s} | {'VJP/fwd (E)':>11s} {'VJP/fwd (J)':>11s}" - ) - print("-" * 100) - - for nx, ny, n_steps in GRID_SIZES: - inputs = make_inputs(nx, ny, n_steps) - n = nx * ny - - timings = {} - for label, image in IMAGES.items(): - fwd, vjp = benchmark_image(image, inputs) - timings[label] = (fwd, vjp) - - e_fwd, e_vjp = timings["Enzyme"] - j_fwd, j_vjp = timings["JAX"] - print( - f"{nx}x{ny:>3d} {n_steps:>3d}st " - f"{n:>7,d} | " - f"{e_fwd * 1000:>8.1f} ms {e_vjp * 1000:>8.1f} ms " - f"{j_fwd * 1000:>8.1f} ms {j_vjp * 1000:>8.1f} ms | " - f"{e_vjp / e_fwd:>8.2f}x {j_vjp / j_fwd:>8.2f}x" - ) - - -if __name__ == "__main__": - main() diff --git a/demo/jax_thermal_2d/tesseract_api.py b/demo/jax_thermal_2d/tesseract_api.py deleted file mode 100644 index 3403bcb5..00000000 --- a/demo/jax_thermal_2d/tesseract_api.py +++ /dev/null @@ -1,339 +0,0 @@ -# Copyright 2025 Pasteur Labs. All Rights Reserved. -# SPDX-License-Identifier: Apache-2.0 - -"""JAX reimplementation of the 2D thermal solver from enzyme_thermal_2d. - -This Tesseract solves the same physics as its Enzyme/Fortran counterpart: - rho * cp * dT/dt = div( k(T) * grad(T) ) + Q -with identical boundary conditions, discretization, and interface. - -The key difference: instead of compiling Fortran with Enzyme, the solver is -written directly in JAX. Derivatives (JVP, VJP, Jacobian) are obtained via -jax.jvp / jax.vjp — no manual adjoint code, no compilation pipeline. - -This enables a direct performance comparison between: - - Enzyme: exact AD on compiled Fortran (legacy solver story) - - JAX: native Python AD with XLA JIT compilation (rewrite story) -""" - -from typing import Any - -import equinox as eqx -import jax -import jax.numpy as jnp -import numpy as np -from pydantic import BaseModel, Field, model_validator -from typing_extensions import Self - -from tesseract_core.runtime import Array, Differentiable, Float64 -from tesseract_core.runtime.tree_transforms import filter_func, flatten_with_paths - -# -- Schemas (identical to enzyme_thermal_2d) ---------------------------------- - - -class InputSchema(BaseModel): - """Input for a 2D transient heat conduction solver. - - Solves rho*cp*dT/dt = div(k(T)*grad(T)) + Q on a rectangular domain - with Dirichlet (hot wall), convection, and insulated boundary conditions. - """ - - T_init: Differentiable[Array[(None,), Float64]] = Field( - description=( - "Initial temperature field [K]. Flattened row-major array of " - "shape (nx*ny,). Index (i,j) maps to j*nx+i." - ), - ) - nx: int = Field( - default=20, description="Number of grid points in x direction.", ge=3 - ) - ny: int = Field( - default=20, description="Number of grid points in y direction.", ge=3 - ) - n_steps: int = Field( - default=100, description="Number of explicit Euler time steps.", ge=1 - ) - dt: Differentiable[Float64] = Field( - default=0.01, description="Time step size [s].", gt=0.0 - ) - Lx: Differentiable[Float64] = Field( - default=0.1, description="Domain length in x [m].", gt=0.0 - ) - Ly: Differentiable[Float64] = Field( - default=0.05, description="Domain length in y [m].", gt=0.0 - ) - k0: Differentiable[Float64] = Field( - default=45.0, - description="Base thermal conductivity [W/(m*K)]. k(T) = k0 + k1*T.", - gt=0.0, - ) - k1: Differentiable[Float64] = Field( - default=-0.01, - description="Temperature coefficient of conductivity [W/(m*K^2)]. k(T) = k0 + k1*T.", - ) - rho: Differentiable[Float64] = Field( - default=7850.0, description="Density [kg/m^3].", gt=0.0 - ) - cp: Differentiable[Float64] = Field( - default=460.0, description="Specific heat capacity [J/(kg*K)].", gt=0.0 - ) - h_conv: Differentiable[Float64] = Field( - default=25.0, - description="Convective heat transfer coefficient at top boundary [W/(m^2*K)].", - gt=0.0, - ) - T_inf: Differentiable[Float64] = Field( - default=293.15, description="Ambient temperature for convection BC [K]." - ) - T_hot: Differentiable[Float64] = Field( - default=373.15, - description="Fixed temperature at bottom (Dirichlet) boundary [K].", - ) - Q: Differentiable[Array[(None,), Float64]] = Field( - description=( - "Volumetric heat source [W/m^3]. Flattened row-major array of " - "shape (nx*ny,). Use zeros for no internal heating." - ), - ) - - @model_validator(mode="after") - def check_array_sizes(self) -> Self: - expected = self.nx * self.ny - if len(self.T_init) != expected: - raise ValueError( - f"T_init has {len(self.T_init)} elements, expected nx*ny = {expected}." - ) - if len(self.Q) != expected: - raise ValueError( - f"Q has {len(self.Q)} elements, expected nx*ny = {expected}." - ) - return self - - @model_validator(mode="after") - def check_stability(self) -> Self: - dx = self.Lx / (self.nx - 1) - dy = self.Ly / (self.ny - 1) - k_max = self.k0 + self.k1 * self.T_hot - if k_max <= 0: - raise ValueError(f"Conductivity k(T_hot) = {k_max:.4f} <= 0.") - r = k_max * self.dt / (self.rho * self.cp) * (1.0 / (dx * dx) + 1.0 / (dy * dy)) - if r > 0.5: - raise ValueError(f"CFL stability condition violated: r = {r:.4f} > 0.5.") - return self - - -class OutputSchema(BaseModel): - T_final: Differentiable[Array[(None,), Float64]] = Field( - description="Temperature field after n_steps time steps [K]. Flattened row-major (nx*ny,).", - ) - - -# -- JAX solver ---------------------------------------------------------------- - - -def _harmonic_mean(ka, kb): - """Harmonic mean of two conductivities (standard for cell-face averaging).""" - return 2.0 * ka * kb / (ka + kb) - - -def _thermal_2d_step(T, nx, ny, dx, dy, k0, k1, rho, cp, h_conv, T_inf, T_hot, Q, dt): - """One explicit Euler step of the 2D thermal solver. - - T is a 2D array of shape (ny, nx). Returns updated T_new of same shape. - """ - # Conductivity field - K = k0 + k1 * T - - # Harmonic-mean conductivities at cell faces (interior) - kx_east = _harmonic_mean(K[:, :-1], K[:, 1:]) # (ny, nx-1) - ky_north = _harmonic_mean(K[:-1, :], K[1:, :]) # (ny-1, nx) - - # x-direction flux: d/dx(k dT/dx) - flux_x_faces = kx_east * (T[:, 1:] - T[:, :-1]) / dx # (ny, nx-1) - flux_x = jnp.zeros_like(T) - # Interior: east - west - flux_x = flux_x.at[:, 1:-1].set((flux_x_faces[:, 1:] - flux_x_faces[:, :-1]) / dx) - # Left boundary (i=0): insulated => mirror, net flux = k_east*(T_e - T_c) / dx^2 - flux_x = flux_x.at[:, 0].set(flux_x_faces[:, 0] / dx) - # Right boundary (i=nx-1): insulated => mirror, net flux = -k_west*(T_c - T_w) / dx^2 - # which is k_west*(T_w - T_c) / dx^2 - flux_x = flux_x.at[:, -1].set(-flux_x_faces[:, -1] / dx) - - # y-direction flux: d/dy(k dT/dy) - flux_y_faces = ky_north * (T[1:, :] - T[:-1, :]) / dy # (ny-1, nx) - flux_y = jnp.zeros_like(T) - # Interior - flux_y = flux_y.at[1:-1, :].set((flux_y_faces[1:, :] - flux_y_faces[:-1, :]) / dy) - # Bottom (j=0): Dirichlet — will be overwritten, but set flux anyway - flux_y = flux_y.at[0, :].set(flux_y_faces[0, :] / dy) - # Top (j=ny-1): convection BC: -k dT/dn = h_conv*(T - T_inf) - # Interior conduction from below + convective loss from above - flux_y = flux_y.at[-1, :].set( - -flux_y_faces[-1, :] / dy - h_conv * (T[-1, :] - T_inf) / dy - ) - - Q_2d = Q.reshape(ny, nx) - T_new = T + dt / (rho * cp) * (flux_x + flux_y + Q_2d) - - # Enforce Dirichlet BC at bottom - T_new = T_new.at[0, :].set(T_hot) - - return T_new - - -def _thermal_2d_solve( - T_init_2d, nx, ny, n_steps, dx, dy, k0, k1, rho, cp, h_conv, T_inf, T_hot, Q, dt -): - """Run n_steps of explicit Euler. Uses jax.lax.fori_loop for AD compatibility.""" - - def body_fn(_, T): - return _thermal_2d_step( - T, nx, ny, dx, dy, k0, k1, rho, cp, h_conv, T_inf, T_hot, Q, dt - ) - - return jax.lax.fori_loop(0, n_steps, body_fn, T_init_2d) - - -@eqx.filter_jit -def apply_jit(inputs: dict) -> dict: - nx = inputs["nx"] - ny = inputs["ny"] - n_steps = inputs["n_steps"] - dx = inputs["Lx"] / (nx - 1) - dy = inputs["Ly"] / (ny - 1) - - T_init_2d = inputs["T_init"].reshape(ny, nx) - Q = inputs["Q"] - - T_final_2d = _thermal_2d_solve( - T_init_2d, - nx, - ny, - n_steps, - dx, - dy, - inputs["k0"], - inputs["k1"], - inputs["rho"], - inputs["cp"], - inputs["h_conv"], - inputs["T_inf"], - inputs["T_hot"], - Q, - inputs["dt"], - ) - - return {"T_final": T_final_2d.reshape(-1)} - - -# -- Required endpoint --------------------------------------------------------- - - -def apply(inputs: InputSchema) -> OutputSchema: - """Run the 2D thermal solver for n_steps explicit Euler steps.""" - out = apply_jit(inputs.model_dump()) - return {"T_final": np.asarray(out["T_final"])} - - -# -- JAX-handled gradient endpoints (no need to modify) ------------------------ - - -def jacobian( - inputs: InputSchema, - jac_inputs: set[str], - jac_outputs: set[str], -): - return jac_jit(inputs.model_dump(), tuple(jac_inputs), tuple(jac_outputs)) - - -def jacobian_vector_product( - inputs: InputSchema, - jvp_inputs: set[str], - jvp_outputs: set[str], - tangent_vector: dict[str, Any], -): - return jvp_jit( - inputs.model_dump(), - tuple(jvp_inputs), - tuple(jvp_outputs), - tangent_vector, - ) - - -def vector_jacobian_product( - inputs: InputSchema, - vjp_inputs: set[str], - vjp_outputs: set[str], - cotangent_vector: dict[str, Any], -): - return vjp_jit( - inputs.model_dump(), - tuple(vjp_inputs), - tuple(vjp_outputs), - cotangent_vector, - ) - - -def abstract_eval(abstract_inputs): - """Calculate output shape of apply from the shape of its inputs.""" - is_shapedtype_dict = lambda x: type(x) is dict and (x.keys() == {"shape", "dtype"}) - is_shapedtype_struct = lambda x: isinstance(x, jax.ShapeDtypeStruct) - - jaxified_inputs = jax.tree.map( - lambda x: jax.ShapeDtypeStruct(**x) if is_shapedtype_dict(x) else x, - abstract_inputs.model_dump(), - is_leaf=is_shapedtype_dict, - ) - dynamic_inputs, static_inputs = eqx.partition( - jaxified_inputs, filter_spec=is_shapedtype_struct - ) - - def wrapped_apply(dynamic_inputs): - inputs = eqx.combine(static_inputs, dynamic_inputs) - return apply_jit(inputs) - - jax_shapes = jax.eval_shape(wrapped_apply, dynamic_inputs) - return jax.tree.map( - lambda x: ( - {"shape": x.shape, "dtype": str(x.dtype)} if is_shapedtype_struct(x) else x - ), - jax_shapes, - is_leaf=is_shapedtype_struct, - ) - - -# -- Helper functions ---------------------------------------------------------- - - -@eqx.filter_jit -def jac_jit(inputs: dict, jac_inputs: tuple[str], jac_outputs: tuple[str]): - filtered_apply = filter_func(apply_jit, inputs, jac_outputs) - return jax.jacrev(filtered_apply)( - flatten_with_paths(inputs, include_paths=jac_inputs) - ) - - -@eqx.filter_jit -def jvp_jit( - inputs: dict, jvp_inputs: tuple[str], jvp_outputs: tuple[str], tangent_vector: dict -): - filtered_apply = filter_func(apply_jit, inputs, jvp_outputs) - return jax.jvp( - filtered_apply, - [flatten_with_paths(inputs, include_paths=jvp_inputs)], - [tangent_vector], - )[1] - - -@eqx.filter_jit -def vjp_jit( - inputs: dict, - vjp_inputs: tuple[str], - vjp_outputs: tuple[str], - cotangent_vector: dict, -): - filtered_apply = filter_func(apply_jit, inputs, vjp_outputs) - _, vjp_func = jax.vjp( - filtered_apply, flatten_with_paths(inputs, include_paths=vjp_inputs) - ) - return vjp_func(cotangent_vector)[0] diff --git a/demo/jax_thermal_2d/tesseract_config.yaml b/demo/jax_thermal_2d/tesseract_config.yaml deleted file mode 100644 index 9202d999..00000000 --- a/demo/jax_thermal_2d/tesseract_config.yaml +++ /dev/null @@ -1,16 +0,0 @@ -name: "jax-thermal-2d" -version: "1.0.0" -description: | - JAX reimplementation of the 2D thermal solver from enzyme_thermal_2d. - - Solves the same physics (2D transient heat conduction with temperature-dependent - conductivity, mixed BCs, explicit Euler time integration) with an identical - Tesseract interface — but the solver is written in pure JAX instead of Fortran. - - Derivatives (JVP, VJP, Jacobian) are obtained via jax.jvp / jax.vjp with no - manual adjoint code and no compilation pipeline. This enables a direct - performance comparison between Enzyme (legacy Fortran + LLVM AD) and JAX - (native Python AD with XLA JIT). - -build_config: - target_platform: "native" diff --git a/demo/jax_thermal_2d/tesseract_requirements.txt b/demo/jax_thermal_2d/tesseract_requirements.txt deleted file mode 100644 index 3878018a..00000000 --- a/demo/jax_thermal_2d/tesseract_requirements.txt +++ /dev/null @@ -1,2 +0,0 @@ -jax[cpu] -equinox diff --git a/docs/blog/2026-05-15-fortran-enzyme-autodiff.md b/docs/blog/2026-05-15-fortran-enzyme-autodiff.md new file mode 100644 index 00000000..56954142 --- /dev/null +++ b/docs/blog/2026-05-15-fortran-enzyme-autodiff.md @@ -0,0 +1,308 @@ +--- +orphan: true +og:title: "From Fortran to JAX autodiff via LLVM and Enzyme" +og:description: "We duct-taped LFortran, LLVM, and Enzyme together to get exact gradients from a Fortran thermal solver, then solved inverse problems with jax.grad. A field report." +blog_date: "2026-05-15" +blog_author: "@dionhaefner" +blog_title: "From Fortran to JAX autodiff via LLVM and Enzyme" +blog_description: "We duct-taped LFortran, LLVM, and Enzyme together to get exact gradients from a Fortran thermal solver, then solved inverse problems with jax.grad. A field report." +--- + +# From Fortran to JAX autodiff via LLVM and Enzyme + +We duct-taped four compilers together and got exact gradients out of a Fortran thermal solver. Then we used those gradients to reconstruct a 900-element temperature field from 100 noisy sensor readings. No adjoint code was written by hand. The whole thing is held together with shell scripts and ctypes. If you maintain a Fortran, C, or C++ simulation and have wished you could just call `grad` on it, this is a rough field report on one way to get there. + +The mechanism: [Enzyme](https://enzyme.mit.edu/) works at the LLVM IR level, so it can differentiate anything that compiles to LLVM. We used it on a 2D Fortran heat solver with nonlinear material properties and mixed boundary conditions, compiled through [LFortran](https://lfortran.org/). This post walks through the compilation pipeline (warts and all), verifies the gradients, and then uses them to solve two inverse problems of increasing ambition. + +## The problem + +Scientific computing is full of Fortran, C, and C++ code that people need gradients of. Optimization, inverse problems, ML integration, uncertainty quantification: all of these require derivatives of a simulation's outputs with respect to its inputs. The options today are all bad in their own way: + +- **Hand-written adjoints.** Months of expert effort, error-prone, and a maintenance nightmare that drifts out of sync with the forward code. +- **Finite differences.** Slow (O(n) evaluations for n parameters), inaccurate (the truncation-vs-roundoff tradeoff means there's always a sweet spot you have to find), and poorly conditioned for stiff problems. +- **Rewrite in JAX or PyTorch.** Impractical for existing codebases with tens of thousands of lines of validated physics. + +What if you could just compile the derivatives automatically, from the existing source? That's the promise, anyway. Here's what it actually looks like in practice. + +## The Fortran code + +The solver is `thermal_2d.f90`, about 220 lines of vanilla Fortran 90. It solves 2D transient heat conduction with temperature-dependent conductivity: + +$$\rho \, c_p \frac{\partial T}{\partial t} = \nabla \cdot \big( k(T) \, \nabla T \big) + Q$$ + +where the conductivity follows a linear material model: $k(T) = k_0 + k_1 \cdot T$. Time integration is explicit Euler over `n_steps` steps. + +Here's the subroutine signature and the interior stencil loop: + +```fortran +subroutine thermal_2d_solve(n, nx, ny, n_steps, & + T_init, T_final, T_cur, T_new, & + k0, k1, rho, cp, & + h_conv, T_inf, T_hot, & + Q, Lx, Ly, dt) + implicit none + integer, intent(in) :: n, nx, ny, n_steps + double precision, intent(in) :: T_init(n) + double precision, intent(out) :: T_final(n) + ! ... (work arrays, scalars) + + ! Time integration loop + do step = 1, n_steps + do j = 2, ny - 1 + do i = 2, nx - 1 + idx = (j - 1) * nx + i + + T_c = T_cur(idx) + T_e = T_cur(idx + 1) + T_w = T_cur(idx - 1) + T_nn = T_cur(idx + nx) + T_s = T_cur(idx - nx) + + ! Harmonic-mean conductivity at cell faces + kx_east = 2.0d0 * (k0 + k1*T_c) * (k0 + k1*T_e) & + / ((k0 + k1*T_c) + (k0 + k1*T_e)) + kx_west = 2.0d0 * (k0 + k1*T_c) * (k0 + k1*T_w) & + / ((k0 + k1*T_c) + (k0 + k1*T_w)) + ! ... (ky_north, ky_south similarly) + + flux_x = (kx_east*(T_e - T_c) - kx_west*(T_c - T_w)) / (dx*dx) + flux_y = (ky_north*(T_nn - T_c) - ky_south*(T_c - T_s)) / (dy*dy) + + T_new(idx) = T_c + dt/(rho*cp) * (flux_x + flux_y + Q(idx)) + end do + end do + ! ... (boundary conditions, swap T_cur <- T_new) + end do +``` + +The stencil uses harmonic-mean conductivity at cell faces, the standard approach in finite difference thermal codes for ensuring flux continuity across cells with different conductivities. Boundary conditions are mixed: Dirichlet (hot wall at the bottom), convection/Robin (top), and insulated/Neumann (sides). + +The key point for why AD matters here: with $k(T)$ nonlinear, the stencil coefficients depend on the current temperature field. The Jacobian changes at every time step. Hand-coding the adjoint through this nonlinear stencil and multi-step loop is tedious and error-prone. + +This is vanilla Fortran. No special annotations, no AD-aware constructs. Explicit `do` loops, no array intrinsics. But "vanilla" required some effort. The original version used local allocatable arrays for `T_cur` and `T_new`. LFortran compiles those into `_lfortran_malloc` calls, which Enzyme can't differentiate through — the AD pass just crashes. The workaround was to pass work arrays in from C, pre-allocated on the heap. Not a huge change, but the kind of thing you discover only after staring at an unhelpful LLVM error message. We also avoid array intrinsics and bounds checking (`--no-array-bounds-checking`) for the same reason: they emit runtime calls that Enzyme doesn't know how to handle. + +This is an honest preview of what "differentiate existing Fortran" looks like today. The source stays recognizably Fortran, but you'll likely need to massage it — eliminating allocations and runtime calls that the AD toolchain can't see through. For a 220-line solver, that's an afternoon of work. For a large legacy codebase, it's an open question. + +## The pipeline + +Enzyme works at the LLVM IR level, not the source level. Anything that compiles to LLVM IR — C, C++, Rust, Fortran — can, in theory, be differentiated. In practice there are caveats (we'll get to those). But the idea is sound, and the compilation chain is surprisingly straightforward if you're comfortable staring at LLVM IR when things go wrong. + +Six steps: + +Compilation pipeline: Fortran → Enzyme AD → shared library + +**1. Fortran → LLVM IR** via LFortran: + +```bash +lfortran --show-llvm --no-array-bounds-checking thermal_2d.f90 > thermal_2d.ll +``` + +LFortran is a modern Fortran compiler that emits clean LLVM IR. It's also still maturing — not all Fortran features are supported yet ([compilation status](https://lfortran.org/progress/)). We chose it over gfortran because its LLVM IR output is much cleaner, but that means your Fortran needs to stay within what LFortran can handle. Enzyme also works with GCC/Clang frontends for broader language coverage at the cost of messier IR. + +**2. Optimize the IR:** + +```bash +opt -O1 -S thermal_2d.ll -o thermal_2d_opt.ll +``` + +We use `-O1` here rather than `-O3` deliberately, and it took us a day to figure out why. With `-O3`, the VJP returned NaN on certain inputs while the forward pass worked fine. The root cause was an interaction between LLVM's vectorization/code-motion passes and Enzyme's reverse-mode analysis: aggressive transforms produced IR patterns that Enzyme mishandled when adjacent cell temperatures were equal and intermediate terms canceled. The fix was to keep pre-Enzyme optimization mild and save `-O3` for after the AD pass (step 6). If you're building a similar pipeline, be aware that "the forward pass works" does not imply "the gradients are correct." + +**3. Compile the C wrapper to LLVM IR:** + +```bash +clang -emit-llvm -S -O1 wrapper.c -o wrapper.ll +``` + +The C wrapper bridges Fortran's by-pointer ABI to a C-callable interface with Enzyme annotations. It declares three entry points — `thermal_2d_forward`, `thermal_2d_vjp`, and `thermal_2d_jvp` — using Enzyme's `__enzyme_autodiff` and `__enzyme_fwddiff` intrinsics to mark which arguments get shadow (gradient) buffers. Here's the core of the VJP entry point: + +```c +void thermal_2d_vjp(int nx, int ny, int n_steps, + const double* T_init, double* dT_init, + const double* T_final, double* dT_final, + double k0, double* dk0, + double k1, double* dk1, + /* ... */) +{ + double* T_cur = calloc(n, sizeof(double)); + double* dT_cur = calloc(n, sizeof(double)); + /* ... */ + + __enzyme_autodiff((void*)thermal_2d_solve, + enzyme_const, &n_, + enzyme_const, &nx_, + enzyme_dup, (double*)T_init, dT_init, + enzyme_dup, (double*)T_final, dT_final, + enzyme_dup, &k0_, dk0, + enzyme_dup, &k1_, dk1, + /* ... */); +} +``` + +The wrapper also allocates work arrays on the heap rather than letting Fortran allocate them, avoiding the `_lfortran_malloc` issue. + +**4. Link the IR modules:** + +```bash +llvm-link wrapper.ll thermal_2d_opt.ll -S -o combined.ll +``` + +**5. Run the Enzyme AD pass:** + +```bash +opt --load-pass-plugin=LLVMEnzyme-19.so -passes=enzyme -S combined.ll -o ad.ll +``` + +This is the step that does the actual work. Enzyme analyzes the LLVM IR and synthesizes forward- and reverse-mode derivative code. For reverse mode, it uses a store-all (tape) strategy, caching intermediate values at each time step. When it works, it's genuinely impressive. When it doesn't, you're reading LLVM IR diffs at 2 AM (see [Limitations](#limitations-and-whats-next)). + +**6. Optimize and compile to a shared library:** + +```bash +opt -O3 -S ad.ll -o ad_opt.ll +clang -shared -O3 ad_opt.ll -o libthermal_2d_ad.so -lm +``` + +The result is a single `.so` file with three entry points callable from Python via ctypes: forward evaluation, JVP, and VJP. The entire pipeline runs during `tesseract build` and takes about 30 seconds. It's not elegant, but there's something satisfying about a shell script that turns Fortran into exact gradients. + +## Does it actually work? + +The pipeline compiles. But does it produce correct gradients? We called the VJP from Python and compared against central finite differences at various step sizes: + +Enzyme vs. finite difference gradient accuracy + +Finite differences have a sweet spot: too large an $\epsilon$ and you get truncation error; too small and you get roundoff error. The best relative error is typically around $10^{-8}$. Enzyme's gradients agree to machine precision ($\sim 10^{-15}$), because they're computing the analytically correct derivative, just synthesized by a compiler rather than a human. + +To be clear about what's being differentiated here: the entire multi-step time loop with nonlinear stencil updates at each step. Not a single-step toy. + +| Method | Relative error vs. exact | +| ------------------------- | -----------------------: | +| Enzyme AD | ~1e-15 (exact) | +| FD (best $\epsilon$) | ~1e-8 | +| FD ($\epsilon$ too large) | ~1e-2 | +| FD ($\epsilon$ too small) | ~1e-4 | + +## Now do something useful with it + +Exact gradients from a compiler pass are a neat trick. But the question that matters is whether you can actually _use_ them — plug them into an optimizer, solve a real inverse problem, compose them with other code. + +To wire the Enzyme gradients into JAX, the solver needs to look like a differentiable JAX primitive. We used [Tesseract](https://github.com/pasteurlabs/tesseract-core) for this: it wraps the compiled library (LFortran, LLVM 19, Enzyme, the whole toolchain) into a container with autodiff endpoints, so `jax.value_and_grad` routes VJP calls to the Enzyme-generated code. The setup is two commands: + +```bash +tesseract build demo/enzyme_thermal_2d/ +tesseract serve enzyme-thermal-2d +``` + +With that, we can throw optimization problems at it and see what breaks. + +### Scalar calibration: recovering 2 material parameters + +A steel plate is heating up. We have thermocouple readings at 9 sensor locations, but we don't know the exact material properties. Can we recover $k_0$ (base conductivity) and $k_1$ (temperature coefficient) from sparse, noisy observations? + +We generate synthetic "observed" data by running the solver with known true values ($k_0 = 45$, $k_1 = -0.02$), sample at sensor locations, and add 0.5 K of Gaussian noise. Then we start from a deliberately wrong initial guess — 33% off on $k_0$, wrong sign on $k_1$ — and run L-BFGS-B. + +One VJP call gives gradients with respect to both parameters simultaneously. The optimizer doesn't need to know that the gradients come from a compiled Fortran solver differentiated by an LLVM pass. + +```python +def objective_and_gradient(params, tesseract): + k0, k1 = params + result = tesseract.apply(inputs=make_inputs(k0, k1)) + T_pred = np.array(result["T_final"]) + + residuals = T_pred[sensor_indices] - T_obs + loss = 0.5 * np.sum(residuals**2) + + # Cotangent: residuals at sensor locations, zero elsewhere + cotangent = np.zeros(n, dtype=np.float64) + cotangent[sensor_indices] = residuals + + # One VJP call → gradients w.r.t. both k0 and k1 + vjp = tesseract.vector_jacobian_product( + inputs=make_inputs(k0, k1), + vjp_inputs=["k0", "k1"], + vjp_outputs=["T_final"], + cotangent_vector={"T_final": cotangent}, + ) + return loss, np.array([vjp["k0"], vjp["k1"]]) +``` + +Scalar calibration convergence: loss, k0, k1 + +Temperature field comparison: initial guess, recovered, ground truth, error + +L-BFGS-B converges in about 15 iterations. The recovered parameters match the true values to within the noise floor. This is a gentle problem — only 2 unknowns, well-conditioned — so it's more of a sanity check than a stress test. The real question is whether the gradients hold up when we push harder. + +### Thermal forensics: recovering a 900-element initial temperature field + +A steel plate was subjected to an unmonitored heating event — say, a laser pulse or a localized defect generating heat. Five seconds later, you measure temperatures at 100 sensor locations. Can you reconstruct what the initial temperature distribution looked like? + +The true initial condition has two Gaussian hot spots on a warm background. This is 900 unknowns from 100 noisy observations, through a nonlinear PDE. An ill-posed problem by any measure. + +This is where reverse-mode AD becomes essential: + +| Method | Forward solves per iteration | +| --------------------- | ---------------------------: | +| Finite differences | 901 (n + 1) | +| VJP (reverse-mode AD) | 2 (forward + reverse) | +| **Speedup** | **~450×** | + +Finite differences would need 901 forward solves per iteration to get all 900 gradients. One VJP gives them all at once, for roughly the cost of two forward passes. The trade-off is memory: Enzyme's reverse mode tapes intermediate values at each time step. For this problem (~900 grid points, 100 steps), the tape is a few hundred kilobytes. For production codes with large state vectors and thousands of time steps, tape memory becomes the dominant constraint. Enzyme supports checkpointing annotations to trade recomputation for memory, but we haven't needed or tested them here. + +Thermal forensics: recovering 900 initial temperature values from 100 sensors + +L-BFGS-B recovers the hot spot locations and magnitudes. The correlation between recovered and true initial temperature fields exceeds 0.99. The error is largest at the edges of the hot spots, where the signal has diffused most. It's not perfect — the reconstruction is smoothed relative to the true field, as you'd expect from an ill-posed problem with diffusion — but it's far better than we had any right to expect from a pipeline held together with shell scripts. + +That's `jax.grad` flowing through compiled Fortran, with no adjoint code written by hand. + +### JAX integration via tesseract-jax + +With [tesseract-jax](https://github.com/pasteurlabs/tesseract-jax), the Tesseract becomes a JAX primitive. `jax.value_and_grad` just works: + +```python +from tesseract_jax import apply_tesseract + +def loss_fn(k0, k1, tesseract): + inputs = {**base_inputs, "k0": k0, "k1": k1} + T_pred = apply_tesseract(tesseract, inputs)["T_final"] + residuals = T_pred[sensor_indices] - jnp.array(T_obs) + return 0.5 * jnp.sum(residuals**2) + +# This differentiates through: Python → JAX → HTTP → Enzyme → Fortran +loss, (dk0, dk1) = jax.value_and_grad(loss_fn, argnums=(0, 1))( + jnp.float64(60.0), jnp.float64(0.01), enzyme_tess +) +``` + +From JAX's perspective, the Fortran solver is just another differentiable function. You can swap `enzyme_tess` for a pure-JAX reimplementation and the optimization loop doesn't change — only the container behind the HTTP call does. Whether that abstraction is beautiful or horrifying depends on your tolerance for gradients that traverse six layers of indirection (Python → JAX → HTTP → ctypes → Enzyme → Fortran). + +## Where this could go + +We should be careful about extrapolating from a 220-line solver we wrote to fit the pipeline. Enzyme handles loops, conditionals, and function calls, and the Enzyme team has demonstrated it on larger codes including [BUDE molecular docking](https://enzyme.mit.edu/getting_started/UsingEnzyme/#bude) and [LULESH hydrodynamics](https://enzyme.mit.edu/getting_started/UsingEnzyme/#lulesh), with derivative overhead factors typically between 1× and 4×. But "works on LULESH" and "works on your 30-year-old Fortran codebase" are different claims. + +That said, the composability angle is interesting. Imagine a Fortran CFD solver (Enzyme-differentiated) feeding into a JAX neural net surrogate: + +```python +cfd_output = apply_tesseract(cfd_tess, cfd_inputs) # Fortran + Enzyme VJP +surrogate_loss = neural_net(cfd_output["pressure"]) # JAX AD +total_loss = surrogate_loss + regularizer(cfd_inputs) # JAX AD + +grads = jax.grad(total_loss) # chains Enzyme + JAX AD automatically +``` + +Each component uses its native AD. Tesseract handles the composition. We built a version of this pattern for the [rocket fin optimization](2025-11-28-rocket-fin-optimization.md) post, where analytical adjoints, finite differences, and JAX AD coexisted in one pipeline. It worked, but each new gradient source added its own class of debugging problems. + +Because Enzyme works at the LLVM IR level, nothing here is Fortran-specific. The same pipeline should apply to C, C++, Rust, or any language with an LLVM frontend — though "should" is doing some work in that sentence. + +## What's next (and what we'd do differently) + +Most of the sharp edges — the `_lfortran_malloc` workaround, the `-O3` NaN disaster, LFortran's incomplete coverage — are already described in context above. To summarize: this works, but it's not turnkey. You should expect to adapt your Fortran, pin your compiler versions, and debug at the IR level at least once. + +A few things we haven't tried yet: + +**Implicit time integration.** Backward Euler, Crank-Nicolson, and other implicit schemes require differentiating through iterative linear solves (CG, GMRES). Enzyme can handle this in principle, but tape memory grows with solver iteration count, and we haven't tested this path with LFortran. This is where we're headed next. + +**Third-party code.** We wrote this solver to work with the pipeline. We haven't yet run Enzyme + LFortran on a Fortran codebase we didn't author. The "will it work on _my_ code?" question is fair. The honest answer is "probably, with adaptation" — the kind of adaptation we described above, and possibly more that we haven't encountered yet. + +**Solvers at scale.**. MPI-parallel codes, GPU kernels, and multi-physics coupling are also untested with this pipeline. Enzyme has support for some of these; we just haven't tried. + +## Try it yourself + +The full source — Fortran solver, Enzyme pipeline, inverse problem notebooks, and the shell scripts holding it all together — is [on GitHub](https://github.com/pasteurlabs/tesseract-core/tree/main/demo/enzyme_thermal_2d). 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=?UTF-8?q?Dion=20H=C3=A4fner?= Date: Mon, 1 Jun 2026 23:08:55 +0200 Subject: [PATCH 05/24] checkpoint --- .../2026-05-15-fortran-enzyme-autodiff.md | 105 ++++++++++-------- 1 file changed, 57 insertions(+), 48 deletions(-) diff --git a/docs/blog/2026-05-15-fortran-enzyme-autodiff.md b/docs/blog/2026-05-15-fortran-enzyme-autodiff.md index 56954142..216f35fc 100644 --- a/docs/blog/2026-05-15-fortran-enzyme-autodiff.md +++ b/docs/blog/2026-05-15-fortran-enzyme-autodiff.md @@ -1,36 +1,38 @@ --- orphan: true -og:title: "From Fortran to JAX autodiff via LLVM and Enzyme" -og:description: "We duct-taped LFortran, LLVM, and Enzyme together to get exact gradients from a Fortran thermal solver, then solved inverse problems with jax.grad. A field report." +og:title: "Fortran solvers, JAX autodiff, and the magic of Enzyme" +og:description: "We duct-taped LFortran, LLVM, and Enzyme together to get exact gradients from a Fortran thermal solver, then solved inverse problems with jax.grad. Here's how." blog_date: "2026-05-15" blog_author: "@dionhaefner" -blog_title: "From Fortran to JAX autodiff via LLVM and Enzyme" -blog_description: "We duct-taped LFortran, LLVM, and Enzyme together to get exact gradients from a Fortran thermal solver, then solved inverse problems with jax.grad. A field report." +blog_title: "Fortran solvers, JAX autodiff, and the magic of Enzyme" +blog_description: "We duct-taped LFortran, LLVM, and Enzyme together to get exact gradients from a Fortran thermal solver, then solved inverse problems with jax.grad. Here's how." --- -# From Fortran to JAX autodiff via LLVM and Enzyme +# Fortran solvers, JAX autodiff, and the magic of Enzyme -We duct-taped four compilers together and got exact gradients out of a Fortran thermal solver. Then we used those gradients to reconstruct a 900-element temperature field from 100 noisy sensor readings. No adjoint code was written by hand. The whole thing is held together with shell scripts and ctypes. If you maintain a Fortran, C, or C++ simulation and have wished you could just call `grad` on it, this is a rough field report on one way to get there. +What if you could do autodiff through existing Fortran, C, or C++ simulation code, embed it into JAX and torch, and use it as a high-performance differentiable physics engine? Turns out, you can -- if you're brave enough. The key insight is that [Enzyme](https://enzyme.mit.edu/) allows us to apply AD at the LLVM IR level, which means we can differentiate any code that compiles to LLVM, and that Tesseract enables us to wrap anything as a [JAX](https://jax.readthedocs.io/en/latest/) primitive, granting full access to JAX's autodiff capabilities from Python. -The mechanism: [Enzyme](https://enzyme.mit.edu/) works at the LLVM IR level, so it can differentiate anything that compiles to LLVM. We used it on a 2D Fortran heat solver with nonlinear material properties and mixed boundary conditions, compiled through [LFortran](https://lfortran.org/). This post walks through the compilation pipeline (warts and all), verifies the gradients, and then uses them to solve two inverse problems of increasing ambition. +All you need is to duct-tape [LFortran](https://lfortran.org/), LLVM, and Enzyme together, point the result at a Fortran thermal solver, and get exact gradients out the other end. Package it as a Tesseract, use Tesseract-JAX to register it as a custom JAX primitive, and you're off to the races: Fortran solvers acting as differentiable layers in arbitrary JAX code. From Fortran to LLVM IR to Enzyme AD to C wrapper to shared library to Tesseract to JAX primitive to XLA to Python to your optimization loop. Sounds easy, right? Well, it is and isn't, but at any rate it's pretty amazing that a stack combining some of the oldest and newest technologies out there can work together so seamlessly. + +But let's start a the beginning. What follows is the full walkthrough — the compilation pipeline, the sharp edges we hit, and two inverse problems that made the whole effort worth it (and that wouldn't be possible without AD). ## The problem -Scientific computing is full of Fortran, C, and C++ code that people need gradients of. Optimization, inverse problems, ML integration, uncertainty quantification: all of these require derivatives of a simulation's outputs with respect to its inputs. The options today are all bad in their own way: +If you work in scientific computing, you might have run into this: you have a simulation written in Fortran (or C, or C++), and now someone needs gradients. Maybe it's for optimization, maybe inverse problems, maybe plugging the sim into an ML pipeline. Derivatives of the simulation's outputs with respect to its inputs. And your options are: -- **Hand-written adjoints.** Months of expert effort, error-prone, and a maintenance nightmare that drifts out of sync with the forward code. -- **Finite differences.** Slow (O(n) evaluations for n parameters), inaccurate (the truncation-vs-roundoff tradeoff means there's always a sweet spot you have to find), and poorly conditioned for stiff problems. -- **Rewrite in JAX or PyTorch.** Impractical for existing codebases with tens of thousands of lines of validated physics. +- **Hand-written adjoints.** Months of expert effort. Error-prone. A maintenance nightmare that slowly drifts out of sync with the forward code. +- **Finite differences.** Slow (O(n) evaluations for n parameters), inaccurate (you're always hunting for the truncation-vs-roundoff sweet spot), and poorly conditioned for stiff problems. +- **Rewrite in JAX or PyTorch.** Sure, if you want to rewrite tens of thousands of lines of validated physics. -What if you could just compile the derivatives automatically, from the existing source? That's the promise, anyway. Here's what it actually looks like in practice. +What if you could just compile the derivatives automatically, from the existing source? That's the pitch. Here's what it actually looks like when you try. ## The Fortran code -The solver is `thermal_2d.f90`, about 220 lines of vanilla Fortran 90. It solves 2D transient heat conduction with temperature-dependent conductivity: +Our test subject is `thermal_2d.f90`, about 220 lines of vanilla Fortran 90. It solves 2D transient heat conduction with temperature-dependent conductivity: $$\rho \, c_p \frac{\partial T}{\partial t} = \nabla \cdot \big( k(T) \, \nabla T \big) + Q$$ -where the conductivity follows a linear material model: $k(T) = k_0 + k_1 \cdot T$. Time integration is explicit Euler over `n_steps` steps. +The conductivity follows a linear material model, $k(T) = k_0 + k_1 \cdot T$, and time integration is explicit Euler over `n_steps` steps. Nothing exotic. Here's the subroutine signature and the interior stencil loop: @@ -75,17 +77,17 @@ subroutine thermal_2d_solve(n, nx, ny, n_steps, & end do ``` -The stencil uses harmonic-mean conductivity at cell faces, the standard approach in finite difference thermal codes for ensuring flux continuity across cells with different conductivities. Boundary conditions are mixed: Dirichlet (hot wall at the bottom), convection/Robin (top), and insulated/Neumann (sides). +The stencil uses harmonic-mean conductivity at cell faces (the standard approach for flux continuity across cells with different conductivities). Boundary conditions are mixed: Dirichlet (hot wall at the bottom), convection/Robin (top), and insulated/Neumann (sides). -The key point for why AD matters here: with $k(T)$ nonlinear, the stencil coefficients depend on the current temperature field. The Jacobian changes at every time step. Hand-coding the adjoint through this nonlinear stencil and multi-step loop is tedious and error-prone. +The reason AD matters here: with $k(T)$ nonlinear, the stencil coefficients depend on the current temperature field. The Jacobian changes at every time step. Hand-coding the adjoint through this nonlinear stencil and multi-step time loop is the kind of thing that sounds doable until you actually sit down to do it. -This is vanilla Fortran. No special annotations, no AD-aware constructs. Explicit `do` loops, no array intrinsics. But "vanilla" required some effort. The original version used local allocatable arrays for `T_cur` and `T_new`. LFortran compiles those into `_lfortran_malloc` calls, which Enzyme can't differentiate through — the AD pass just crashes. The workaround was to pass work arrays in from C, pre-allocated on the heap. Not a huge change, but the kind of thing you discover only after staring at an unhelpful LLVM error message. We also avoid array intrinsics and bounds checking (`--no-array-bounds-checking`) for the same reason: they emit runtime calls that Enzyme doesn't know how to handle. +Now, we keep calling this "vanilla Fortran," and it is — no special annotations, no AD-aware constructs, explicit `do` loops, no array intrinsics. But getting to "vanilla" took some work. Our first version used local allocatable arrays for `T_cur` and `T_new`. LFortran compiles those into `_lfortran_malloc` calls, and Enzyme has no idea what to do with them. The AD pass just crashes. The fix was to pass work arrays in from C, pre-allocated on the heap. Not a huge change, but we only figured that out after staring at an unhelpful LLVM error for longer than we'd like to admit. We also had to disable array intrinsics and bounds checking (`--no-array-bounds-checking`) for the same reason: they emit runtime calls that Enzyme can't see through. -This is an honest preview of what "differentiate existing Fortran" looks like today. The source stays recognizably Fortran, but you'll likely need to massage it — eliminating allocations and runtime calls that the AD toolchain can't see through. For a 220-line solver, that's an afternoon of work. For a large legacy codebase, it's an open question. +This is an honest preview of what "differentiate existing Fortran" looks like today. The source stays recognizably Fortran, but you'll need to massage it, eliminating allocations and runtime calls that break the AD toolchain. For a 220-line solver, that's an afternoon. For a large legacy codebase, it's an open question. ## The pipeline -Enzyme works at the LLVM IR level, not the source level. Anything that compiles to LLVM IR — C, C++, Rust, Fortran — can, in theory, be differentiated. In practice there are caveats (we'll get to those). But the idea is sound, and the compilation chain is surprisingly straightforward if you're comfortable staring at LLVM IR when things go wrong. +Here's the key insight that makes all of this possible: Enzyme works at the LLVM IR level, not the source level. Anything that compiles to LLVM IR — C, C++, Rust, Fortran — can be differentiated. In practice there are caveats (oh, we'll get to those). But the compilation chain is surprisingly straightforward, as long as you're comfortable staring at LLVM IR when things go wrong. Six steps: @@ -97,7 +99,7 @@ Six steps: lfortran --show-llvm --no-array-bounds-checking thermal_2d.f90 > thermal_2d.ll ``` -LFortran is a modern Fortran compiler that emits clean LLVM IR. It's also still maturing — not all Fortran features are supported yet ([compilation status](https://lfortran.org/progress/)). We chose it over gfortran because its LLVM IR output is much cleaner, but that means your Fortran needs to stay within what LFortran can handle. Enzyme also works with GCC/Clang frontends for broader language coverage at the cost of messier IR. +LFortran is a modern Fortran compiler that emits clean LLVM IR — arrays become plain pointers with GEP/load/store patterns (much like C), rather than the multi-field descriptor structs and runtime library calls you get from Flang. That matters because Enzyme needs to trace through every memory access for its activity analysis, and simple pointer arithmetic is much easier to analyze than opaque `fir.box` descriptors. LFortran is still maturing, though — not all Fortran features are supported yet ([compilation status](https://lfortran.org/progress/)), so your Fortran needs to stay within what LFortran can handle. **2. Optimize the IR:** @@ -105,7 +107,9 @@ LFortran is a modern Fortran compiler that emits clean LLVM IR. It's also still opt -O1 -S thermal_2d.ll -o thermal_2d_opt.ll ``` -We use `-O1` here rather than `-O3` deliberately, and it took us a day to figure out why. With `-O3`, the VJP returned NaN on certain inputs while the forward pass worked fine. The root cause was an interaction between LLVM's vectorization/code-motion passes and Enzyme's reverse-mode analysis: aggressive transforms produced IR patterns that Enzyme mishandled when adjacent cell temperatures were equal and intermediate terms canceled. The fix was to keep pre-Enzyme optimization mild and save `-O3` for after the AD pass (step 6). If you're building a similar pipeline, be aware that "the forward pass works" does not imply "the gradients are correct." +Notice that's `-O1`, not `-O3`. We learned this the hard way. + +Our first pipeline used `-O3` here, and the forward pass worked perfectly. The VJP, however, returned NaN on certain inputs. We spent a full day tracking this down. The root cause: LLVM's aggressive vectorization and code-motion passes at `-O3` produced IR patterns that Enzyme mishandled during reverse-mode analysis, specifically when adjacent cell temperatures were equal and intermediate terms canceled. The fix was embarrassingly simple — keep pre-Enzyme optimization mild and save `-O3` for after the AD pass (step 6). But the lesson was not simple at all: "the forward pass works" does not mean "the gradients are correct." If you're building a similar pipeline, test the gradients early and often. **3. Compile the C wrapper to LLVM IR:** @@ -113,7 +117,7 @@ We use `-O1` here rather than `-O3` deliberately, and it took us a day to figure clang -emit-llvm -S -O1 wrapper.c -o wrapper.ll ``` -The C wrapper bridges Fortran's by-pointer ABI to a C-callable interface with Enzyme annotations. It declares three entry points — `thermal_2d_forward`, `thermal_2d_vjp`, and `thermal_2d_jvp` — using Enzyme's `__enzyme_autodiff` and `__enzyme_fwddiff` intrinsics to mark which arguments get shadow (gradient) buffers. Here's the core of the VJP entry point: +We need a thin C wrapper to bridge Fortran's by-pointer ABI to a C-callable interface with Enzyme annotations. It declares three entry points — `thermal_2d_forward`, `thermal_2d_vjp`, and `thermal_2d_jvp` — using Enzyme's `__enzyme_autodiff` and `__enzyme_fwddiff` intrinsics to mark which arguments get shadow (gradient) buffers. Here's the core of the VJP entry point: ```c void thermal_2d_vjp(int nx, int ny, int n_steps, @@ -138,7 +142,7 @@ void thermal_2d_vjp(int nx, int ny, int n_steps, } ``` -The wrapper also allocates work arrays on the heap rather than letting Fortran allocate them, avoiding the `_lfortran_malloc` issue. +This is also where we allocate the work arrays on the heap, sidestepping the `_lfortran_malloc` issue from earlier. **4. Link the IR modules:** @@ -152,7 +156,7 @@ llvm-link wrapper.ll thermal_2d_opt.ll -S -o combined.ll opt --load-pass-plugin=LLVMEnzyme-19.so -passes=enzyme -S combined.ll -o ad.ll ``` -This is the step that does the actual work. Enzyme analyzes the LLVM IR and synthesizes forward- and reverse-mode derivative code. For reverse mode, it uses a store-all (tape) strategy, caching intermediate values at each time step. When it works, it's genuinely impressive. When it doesn't, you're reading LLVM IR diffs at 2 AM (see [Limitations](#limitations-and-whats-next)). +This is where the magic happens. Enzyme analyzes the LLVM IR and synthesizes forward- and reverse-mode derivative code. For reverse mode, it uses a store-all (tape) strategy, caching intermediate values at each time step. When it works, it's genuinely impressive — you get an adjoint of your entire time-stepping loop for free. When it doesn't, you're reading LLVM IR diffs at 2 AM wondering where your life went wrong (see [What's next](#whats-next-and-what-wed-do-differently)). **6. Optimize and compile to a shared library:** @@ -161,17 +165,17 @@ opt -O3 -S ad.ll -o ad_opt.ll clang -shared -O3 ad_opt.ll -o libthermal_2d_ad.so -lm ``` -The result is a single `.so` file with three entry points callable from Python via ctypes: forward evaluation, JVP, and VJP. The entire pipeline runs during `tesseract build` and takes about 30 seconds. It's not elegant, but there's something satisfying about a shell script that turns Fortran into exact gradients. +Out comes a single `.so` file with three entry points callable from Python via ctypes: forward evaluation, JVP, and VJP. The entire pipeline runs during `tesseract build` and takes about 30 seconds. It's a shell script that turns Fortran into exact gradients. We're not going to pretend that's elegant, but it is deeply satisfying. ## Does it actually work? -The pipeline compiles. But does it produce correct gradients? We called the VJP from Python and compared against central finite differences at various step sizes: +OK, it compiles. But after the `-O3` NaN incident, we weren't about to trust it without checking. We called the VJP from Python and compared against central finite differences at various step sizes: Enzyme vs. finite difference gradient accuracy -Finite differences have a sweet spot: too large an $\epsilon$ and you get truncation error; too small and you get roundoff error. The best relative error is typically around $10^{-8}$. Enzyme's gradients agree to machine precision ($\sim 10^{-15}$), because they're computing the analytically correct derivative, just synthesized by a compiler rather than a human. +Finite differences have a sweet spot: too large an $\epsilon$ and you get truncation error, too small and you get roundoff. The best you can typically do is around $10^{-8}$ relative error. Enzyme's gradients agree to machine precision ($\sim 10^{-15}$) — because they're computing the analytically correct derivative, just synthesized by a compiler instead of a human. -To be clear about what's being differentiated here: the entire multi-step time loop with nonlinear stencil updates at each step. Not a single-step toy. +And this isn't differentiating a single matrix multiply. It's the entire multi-step time loop with nonlinear stencil updates at each step. | Method | Relative error vs. exact | | ------------------------- | -----------------------: | @@ -182,24 +186,24 @@ To be clear about what's being differentiated here: the entire multi-step time l ## Now do something useful with it -Exact gradients from a compiler pass are a neat trick. But the question that matters is whether you can actually _use_ them — plug them into an optimizer, solve a real inverse problem, compose them with other code. +Correct gradients are great, but they're not the point. The point is using them — plugging them into an optimizer, solving a real inverse problem, composing them with other differentiable code. -To wire the Enzyme gradients into JAX, the solver needs to look like a differentiable JAX primitive. We used [Tesseract](https://github.com/pasteurlabs/tesseract-core) for this: it wraps the compiled library (LFortran, LLVM 19, Enzyme, the whole toolchain) into a container with autodiff endpoints, so `jax.value_and_grad` routes VJP calls to the Enzyme-generated code. The setup is two commands: +To wire the Enzyme gradients into JAX, the solver needs to look like a differentiable JAX primitive. This is essentially what Tesseract was made for: it wraps the compiled library (LFortran, LLVM 19, Enzyme, the whole toolchain) into a container with autodiff endpoints, so `jax.value_and_grad` routes VJP calls to the Enzyme-generated code. Two commands: ```bash tesseract build demo/enzyme_thermal_2d/ tesseract serve enzyme-thermal-2d ``` -With that, we can throw optimization problems at it and see what breaks. +With that running, we can throw optimization problems at it. ### Scalar calibration: recovering 2 material parameters -A steel plate is heating up. We have thermocouple readings at 9 sensor locations, but we don't know the exact material properties. Can we recover $k_0$ (base conductivity) and $k_1$ (temperature coefficient) from sparse, noisy observations? +Setup: a steel plate is heating up. We have thermocouple readings at 9 sensor locations, but we don't know the exact material properties. Can we recover $k_0$ (base conductivity) and $k_1$ (temperature coefficient) from sparse, noisy observations? -We generate synthetic "observed" data by running the solver with known true values ($k_0 = 45$, $k_1 = -0.02$), sample at sensor locations, and add 0.5 K of Gaussian noise. Then we start from a deliberately wrong initial guess — 33% off on $k_0$, wrong sign on $k_1$ — and run L-BFGS-B. +We generate synthetic "observed" data by running the solver with known true values ($k_0 = 45$, $k_1 = -0.02$), sample at sensor locations, and add 0.5 K of Gaussian noise. Then we start from a deliberately wrong initial guess — 33% off on $k_0$, wrong sign on $k_1$ — and hand it to L-BFGS-B. -One VJP call gives gradients with respect to both parameters simultaneously. The optimizer doesn't need to know that the gradients come from a compiled Fortran solver differentiated by an LLVM pass. +One VJP call gives gradients with respect to both parameters simultaneously. The optimizer doesn't care that those gradients come from a compiled Fortran solver differentiated by an LLVM pass. ```python def objective_and_gradient(params, tesseract): @@ -228,13 +232,13 @@ def objective_and_gradient(params, tesseract): Temperature field comparison: initial guess, recovered, ground truth, error -L-BFGS-B converges in about 15 iterations. The recovered parameters match the true values to within the noise floor. This is a gentle problem — only 2 unknowns, well-conditioned — so it's more of a sanity check than a stress test. The real question is whether the gradients hold up when we push harder. +L-BFGS-B converges in about 15 iterations. The recovered parameters match the true values to within the noise floor. This is a gentle problem — only 2 unknowns, well-conditioned — so it's really a sanity check. The interesting question is what happens when we push harder. ### Thermal forensics: recovering a 900-element initial temperature field -A steel plate was subjected to an unmonitored heating event — say, a laser pulse or a localized defect generating heat. Five seconds later, you measure temperatures at 100 sensor locations. Can you reconstruct what the initial temperature distribution looked like? +Now for something harder. A steel plate was subjected to an unmonitored heating event — a laser pulse, a localized defect, something. Five seconds later, you measure temperatures at 100 sensor locations. Can you figure out what the initial temperature distribution looked like? -The true initial condition has two Gaussian hot spots on a warm background. This is 900 unknowns from 100 noisy observations, through a nonlinear PDE. An ill-posed problem by any measure. +The true initial condition has two Gaussian hot spots on a warm background. That's 900 unknowns from 100 noisy observations, through a nonlinear PDE — ill-posed by any measure. This is where reverse-mode AD becomes essential: @@ -248,13 +252,13 @@ Finite differences would need 901 forward solves per iteration to get all 900 gr Thermal forensics: recovering 900 initial temperature values from 100 sensors -L-BFGS-B recovers the hot spot locations and magnitudes. The correlation between recovered and true initial temperature fields exceeds 0.99. The error is largest at the edges of the hot spots, where the signal has diffused most. It's not perfect — the reconstruction is smoothed relative to the true field, as you'd expect from an ill-posed problem with diffusion — but it's far better than we had any right to expect from a pipeline held together with shell scripts. +L-BFGS-B recovers the hot spot locations and magnitudes. Correlation between recovered and true initial temperature fields exceeds 0.99. The error is largest at the edges of the hot spots, where the signal has diffused most. The reconstruction is smoothed relative to the true field, as you'd expect from an ill-posed problem with diffusion, but it's far better than we had any right to expect from a pipeline held together with shell scripts. That's `jax.grad` flowing through compiled Fortran, with no adjoint code written by hand. ### JAX integration via tesseract-jax -With [tesseract-jax](https://github.com/pasteurlabs/tesseract-jax), the Tesseract becomes a JAX primitive. `jax.value_and_grad` just works: +You can also go one step further with [tesseract-jax](https://github.com/pasteurlabs/tesseract-jax), which turns the Tesseract into a proper JAX primitive. Then `jax.value_and_grad` just works: ```python from tesseract_jax import apply_tesseract @@ -271,13 +275,13 @@ loss, (dk0, dk1) = jax.value_and_grad(loss_fn, argnums=(0, 1))( ) ``` -From JAX's perspective, the Fortran solver is just another differentiable function. You can swap `enzyme_tess` for a pure-JAX reimplementation and the optimization loop doesn't change — only the container behind the HTTP call does. Whether that abstraction is beautiful or horrifying depends on your tolerance for gradients that traverse six layers of indirection (Python → JAX → HTTP → ctypes → Enzyme → Fortran). +From JAX's perspective, the Fortran solver is just another differentiable function. You could swap `enzyme_tess` for a pure-JAX reimplementation and the optimization loop wouldn't change — only the container behind the HTTP call. Whether that abstraction is beautiful or horrifying probably depends on how you feel about gradients traversing six layers of indirection (Python → JAX → HTTP → ctypes → Enzyme → Fortran). ## Where this could go -We should be careful about extrapolating from a 220-line solver we wrote to fit the pipeline. Enzyme handles loops, conditionals, and function calls, and the Enzyme team has demonstrated it on larger codes including [BUDE molecular docking](https://enzyme.mit.edu/getting_started/UsingEnzyme/#bude) and [LULESH hydrodynamics](https://enzyme.mit.edu/getting_started/UsingEnzyme/#lulesh), with derivative overhead factors typically between 1× and 4×. But "works on LULESH" and "works on your 30-year-old Fortran codebase" are different claims. +We should be upfront: this is a 220-line solver we wrote to fit the pipeline. Enzyme handles loops, conditionals, and function calls, and the Enzyme team has demonstrated it on larger codes including [BUDE molecular docking](https://enzyme.mit.edu/getting_started/UsingEnzyme/#bude) and [LULESH hydrodynamics](https://enzyme.mit.edu/getting_started/UsingEnzyme/#lulesh), with derivative overhead factors typically between 1x and 4x. But "works on LULESH" and "works on your 30-year-old Fortran codebase" are very different claims. -That said, the composability angle is interesting. Imagine a Fortran CFD solver (Enzyme-differentiated) feeding into a JAX neural net surrogate: +What gets us excited is the composability. Imagine a Fortran CFD solver (Enzyme-differentiated) feeding into a JAX neural net surrogate: ```python cfd_output = apply_tesseract(cfd_tess, cfd_inputs) # Fortran + Enzyme VJP @@ -287,22 +291,27 @@ total_loss = surrogate_loss + regularizer(cfd_inputs) # JAX AD grads = jax.grad(total_loss) # chains Enzyme + JAX AD automatically ``` -Each component uses its native AD. Tesseract handles the composition. We built a version of this pattern for the [rocket fin optimization](2025-11-28-rocket-fin-optimization.md) post, where analytical adjoints, finite differences, and JAX AD coexisted in one pipeline. It worked, but each new gradient source added its own class of debugging problems. +Each component uses its native AD. Tesseract handles the composition. We built a version of this pattern for the [rocket fin optimization](2025-11-28-rocket-fin-optimization.md) post, where analytical adjoints, finite differences, and JAX AD coexisted in one pipeline. It worked, though each new gradient source brought its own class of debugging problems. -Because Enzyme works at the LLVM IR level, nothing here is Fortran-specific. The same pipeline should apply to C, C++, Rust, or any language with an LLVM frontend — though "should" is doing some work in that sentence. +And because Enzyme works at the LLVM IR level, none of this is Fortran-specific. The same pipeline should apply to C, C++, Rust, or any language with an LLVM frontend — though "should" is doing a lot of work in that sentence. ## What's next (and what we'd do differently) -Most of the sharp edges — the `_lfortran_malloc` workaround, the `-O3` NaN disaster, LFortran's incomplete coverage — are already described in context above. To summarize: this works, but it's not turnkey. You should expect to adapt your Fortran, pin your compiler versions, and debug at the IR level at least once. +We've described most of the sharp edges inline — the `_lfortran_malloc` crash, the `-O3` NaN disaster, LFortran's incomplete coverage. To be blunt: this works, but it's not turnkey. Expect to adapt your Fortran, pin your compiler versions, and debug at the IR level at least once. A few things we haven't tried yet: **Implicit time integration.** Backward Euler, Crank-Nicolson, and other implicit schemes require differentiating through iterative linear solves (CG, GMRES). Enzyme can handle this in principle, but tape memory grows with solver iteration count, and we haven't tested this path with LFortran. This is where we're headed next. -**Third-party code.** We wrote this solver to work with the pipeline. We haven't yet run Enzyme + LFortran on a Fortran codebase we didn't author. The "will it work on _my_ code?" question is fair. The honest answer is "probably, with adaptation" — the kind of adaptation we described above, and possibly more that we haven't encountered yet. +**Third-party code.** We wrote this solver to work with the pipeline. We haven't yet tried Enzyme + LFortran on a Fortran codebase we didn't author. The "will it work on _my_ code?" question is fair. Honest answer: probably, with adaptation — the kind we described above, and possibly more we haven't encountered yet. -**Solvers at scale.**. MPI-parallel codes, GPU kernels, and multi-physics coupling are also untested with this pipeline. Enzyme has support for some of these; we just haven't tried. +**Solvers at scale.** MPI-parallel codes, GPU kernels, multi-physics coupling — all untested with this pipeline. Enzyme has support for some of these; we just haven't tried. ## Try it yourself -The full source — Fortran solver, Enzyme pipeline, inverse problem notebooks, and the shell scripts holding it all together — is [on GitHub](https://github.com/pasteurlabs/tesseract-core/tree/main/demo/enzyme_thermal_2d). If you have a Fortran, C, or C++ solver you want gradients for and a healthy appetite for compiler debugging, this is a starting point. +The full source — Fortran solver, Enzyme pipeline, inverse problem notebooks, and the shell scripts holding it all together — is [on GitHub](https://github.com/pasteurlabs/tesseract-core/tree/main/demo/enzyme_thermal_2d). If you have a Fortran, C, or C++ solver you want gradients for and don't mind some quality time with LLVM IR, this is a starting point. + +--- + +_Tesseract is a free, open-source framework for differentiable scientific computing. `pip install tesseract-core`. +[Docs](https://tesseract.pasteurlabs.ai) · [Demos](https://tesseract.pasteurlabs.ai/content/demo/demo.html) · [GitHub](https://github.com/pasteurlabs/tesseract-core) · [Forum](https://si-tesseract.discourse.group/)_ From 2b463df9d1898d5171bcf8a17560adfb3bece9d7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dion=20H=C3=A4fner?= Date: Tue, 2 Jun 2026 11:22:42 +0200 Subject: [PATCH 06/24] wip on blog post --- .../2026-05-15-fortran-enzyme-autodiff.md | 118 +++++++++--------- 1 file changed, 57 insertions(+), 61 deletions(-) diff --git a/docs/blog/2026-05-15-fortran-enzyme-autodiff.md b/docs/blog/2026-05-15-fortran-enzyme-autodiff.md index 216f35fc..26acddc2 100644 --- a/docs/blog/2026-05-15-fortran-enzyme-autodiff.md +++ b/docs/blog/2026-05-15-fortran-enzyme-autodiff.md @@ -1,30 +1,34 @@ --- orphan: true -og:title: "Fortran solvers, JAX autodiff, and the magic of Enzyme" -og:description: "We duct-taped LFortran, LLVM, and Enzyme together to get exact gradients from a Fortran thermal solver, then solved inverse problems with jax.grad. Here's how." +og:title: "Differentiable Fortran in JAX via LFortran and Enzyme" +og:description: "How we duct-taped a compiler pipeline together to get exact gradients out of a Fortran thermal solver, then used it to solve real inverse problems from Python." blog_date: "2026-05-15" blog_author: "@dionhaefner" -blog_title: "Fortran solvers, JAX autodiff, and the magic of Enzyme" -blog_description: "We duct-taped LFortran, LLVM, and Enzyme together to get exact gradients from a Fortran thermal solver, then solved inverse problems with jax.grad. Here's how." +blog_title: "Differentiable Fortran in JAX via LFortran and Enzyme" +blog_description: "How we duct-taped a compiler pipeline together to get exact gradients out of a Fortran thermal solver, then used it to solve real inverse problems from Python." --- -# Fortran solvers, JAX autodiff, and the magic of Enzyme +# Differentiable Fortran in JAX via LFortran and Enzyme -What if you could do autodiff through existing Fortran, C, or C++ simulation code, embed it into JAX and torch, and use it as a high-performance differentiable physics engine? Turns out, you can -- if you're brave enough. The key insight is that [Enzyme](https://enzyme.mit.edu/) allows us to apply AD at the LLVM IR level, which means we can differentiate any code that compiles to LLVM, and that Tesseract enables us to wrap anything as a [JAX](https://jax.readthedocs.io/en/latest/) primitive, granting full access to JAX's autodiff capabilities from Python. +What if you could do autodiff through existing Fortran, C, or C++ simulation code, embed it into JAX and torch, and use it as a high-performance differentiable physics engine? Turns out, you can. -All you need is to duct-tape [LFortran](https://lfortran.org/), LLVM, and Enzyme together, point the result at a Fortran thermal solver, and get exact gradients out the other end. Package it as a Tesseract, use Tesseract-JAX to register it as a custom JAX primitive, and you're off to the races: Fortran solvers acting as differentiable layers in arbitrary JAX code. From Fortran to LLVM IR to Enzyme AD to C wrapper to shared library to Tesseract to JAX primitive to XLA to Python to your optimization loop. Sounds easy, right? Well, it is and isn't, but at any rate it's pretty amazing that a stack combining some of the oldest and newest technologies out there can work together so seamlessly. +Decades of validated physics code, climate models, CFD, aerospace, nuclear, sit behind a wall that modern ML pipelines can't cross: no gradients. The usual answer is to rewrite it all in JAX or PyTorch. The alternative we explore here is to leave the code where it is and get exact gradients out anyway, thanks to some LLVM-level magic. [Enzyme](https://enzyme.mit.edu/) applies AD at the LLVM IR level, so we can differentiate any code that compiles to LLVM. -But let's start a the beginning. What follows is the full walkthrough — the compilation pipeline, the sharp edges we hit, and two inverse problems that made the whole effort worth it (and that wouldn't be possible without AD). +So all we need is to duct-tape [LFortran](https://lfortran.org/), LLVM, and Enzyme together, point the result at a Fortran thermal solver, and get exact gradients out the other end. From there, [Tesseract](https://github.com/pasteurlabs/tesseract-core) (whose blog you're reading) wraps the result as a custom [JAX](https://jax.readthedocs.io/en/latest/) primitive, so a Fortran solver becomes a differentiable layer in arbitrary JAX code. Sounds easy, right? + +This is all pretty experimental, so we had to spend a half day chasing a gradient that returned NaN and painstakingly compare LLVM IR diffs to make it work. But the gradients come out of the entire multi-step time loop matching the analytic derivative to machine precision (~1e-15 relative error), where finite differences top out around 1e-8. And it's amazing to see that a stack combining some of the oldest and newest technologies out there can work together at all. + +So let's start at the beginning. What follows is the full walkthrough: the compilation pipeline, the sharp edges we hit, and two inverse problems that made the whole effort worth it (and that wouldn't be possible without AD). ## The problem -If you work in scientific computing, you might have run into this: you have a simulation written in Fortran (or C, or C++), and now someone needs gradients. Maybe it's for optimization, maybe inverse problems, maybe plugging the sim into an ML pipeline. Derivatives of the simulation's outputs with respect to its inputs. And your options are: +If you work in scientific computing, you might have run into this: you have a simulation written in Fortran (or C, or C++), and now someone needs gradients (derivatives of the simulation's outputs with respect to its inputs). Maybe it's for optimization, maybe inverse problems, maybe plugging the sim into an ML pipeline. Now your options are: - **Hand-written adjoints.** Months of expert effort. Error-prone. A maintenance nightmare that slowly drifts out of sync with the forward code. - **Finite differences.** Slow (O(n) evaluations for n parameters), inaccurate (you're always hunting for the truncation-vs-roundoff sweet spot), and poorly conditioned for stiff problems. - **Rewrite in JAX or PyTorch.** Sure, if you want to rewrite tens of thousands of lines of validated physics. -What if you could just compile the derivatives automatically, from the existing source? That's the pitch. Here's what it actually looks like when you try. +What if you could just compile the derivatives automatically, from the existing source? Here's what it actually looks like when you try. ## The Fortran code @@ -32,9 +36,9 @@ Our test subject is `thermal_2d.f90`, about 220 lines of vanilla Fortran 90. It $$\rho \, c_p \frac{\partial T}{\partial t} = \nabla \cdot \big( k(T) \, \nabla T \big) + Q$$ -The conductivity follows a linear material model, $k(T) = k_0 + k_1 \cdot T$, and time integration is explicit Euler over `n_steps` steps. Nothing exotic. +The conductivity follows a linear material model, $k(T) = k_0 + k_1 \cdot T$, and time integration is explicit Euler over `n_steps` steps. Nothing exotic here. -Here's the subroutine signature and the interior stencil loop: +Here's what the subroutine signature and the interior stencil loop look like: ```fortran subroutine thermal_2d_solve(n, nx, ny, n_steps, & @@ -79,17 +83,17 @@ subroutine thermal_2d_solve(n, nx, ny, n_steps, & The stencil uses harmonic-mean conductivity at cell faces (the standard approach for flux continuity across cells with different conductivities). Boundary conditions are mixed: Dirichlet (hot wall at the bottom), convection/Robin (top), and insulated/Neumann (sides). -The reason AD matters here: with $k(T)$ nonlinear, the stencil coefficients depend on the current temperature field. The Jacobian changes at every time step. Hand-coding the adjoint through this nonlinear stencil and multi-step time loop is the kind of thing that sounds doable until you actually sit down to do it. +The reason AD matters here: since $k(T)$ is nonlinear, the stencil coefficients depend on the current temperature field, and the Jacobian changes at every time step. Hand-coding the adjoint through this nonlinear stencil and multi-step time loop is tremendously painful, and needs to be updated every time the forward code changes. -Now, we keep calling this "vanilla Fortran," and it is — no special annotations, no AD-aware constructs, explicit `do` loops, no array intrinsics. But getting to "vanilla" took some work. Our first version used local allocatable arrays for `T_cur` and `T_new`. LFortran compiles those into `_lfortran_malloc` calls, and Enzyme has no idea what to do with them. The AD pass just crashes. The fix was to pass work arrays in from C, pre-allocated on the heap. Not a huge change, but we only figured that out after staring at an unhelpful LLVM error for longer than we'd like to admit. We also had to disable array intrinsics and bounds checking (`--no-array-bounds-checking`) for the same reason: they emit runtime calls that Enzyme can't see through. +This really is vanilla Fortran: no special annotations, no AD-aware constructs, explicit `do` loops, no array intrinsics. But getting to "vanilla" took some work: Our first version used local allocatable arrays for `T_cur` and `T_new`, which LFortran compiles into `_lfortran_malloc` calls, and Enzyme has no idea what to do with them, so the AD pass just crashes. The fix was to pass work arrays in from C, pre-allocated on the heap. Not a huge change, but given how unhelpful the LLVM error messages were, it took some time to figure out. We also had to disable array intrinsics and bounds checking (`--no-array-bounds-checking`) for the same reason: they emit runtime calls that Enzyme can't see through. -This is an honest preview of what "differentiate existing Fortran" looks like today. The source stays recognizably Fortran, but you'll need to massage it, eliminating allocations and runtime calls that break the AD toolchain. For a 220-line solver, that's an afternoon. For a large legacy codebase, it's an open question. +This is an honest preview of what "differentiate existing Fortran" looks like today. The source stays recognizably Fortran, but you'll need to massage it, eliminating allocations and runtime calls that break the AD toolchain. For a 220-line solver, that's an afternoon; for a large legacy codebase, it's an open question. ## The pipeline -Here's the key insight that makes all of this possible: Enzyme works at the LLVM IR level, not the source level. Anything that compiles to LLVM IR — C, C++, Rust, Fortran — can be differentiated. In practice there are caveats (oh, we'll get to those). But the compilation chain is surprisingly straightforward, as long as you're comfortable staring at LLVM IR when things go wrong. +Enzyme works at the LLVM IR level, not the source level, so anything that compiles to LLVM IR (C, C++, Rust, Fortran) can be differentiated. In practice there are caveats, but the compilation chain is surprisingly straightforward, as long as you're comfortable inspecting LLVM IR when things go wrong. -Six steps: +There are six steps: Compilation pipeline: Fortran → Enzyme AD → shared library @@ -99,7 +103,7 @@ Six steps: lfortran --show-llvm --no-array-bounds-checking thermal_2d.f90 > thermal_2d.ll ``` -LFortran is a modern Fortran compiler that emits clean LLVM IR — arrays become plain pointers with GEP/load/store patterns (much like C), rather than the multi-field descriptor structs and runtime library calls you get from Flang. That matters because Enzyme needs to trace through every memory access for its activity analysis, and simple pointer arithmetic is much easier to analyze than opaque `fir.box` descriptors. LFortran is still maturing, though — not all Fortran features are supported yet ([compilation status](https://lfortran.org/progress/)), so your Fortran needs to stay within what LFortran can handle. +LFortran is a modern Fortran compiler, and the reason we reached for it is that it emits remarkably clean LLVM IR. Arrays come out as plain pointers with the usual GEP/load/store patterns, much like you'd get from C, instead of the multi-field descriptor structs and runtime library calls that Flang produces. That turns out to matter a lot, because Enzyme has to trace through every single memory access to figure out what's active, and it has a far easier time with plain pointer arithmetic than with opaque `fir.box` descriptors. The catch is that LFortran is still maturing, so not every Fortran feature is supported yet (here's the [compilation status](https://lfortran.org/progress/)) and your code has to stay within what it can handle. **2. Optimize the IR:** @@ -107,9 +111,7 @@ LFortran is a modern Fortran compiler that emits clean LLVM IR — arrays become opt -O1 -S thermal_2d.ll -o thermal_2d_opt.ll ``` -Notice that's `-O1`, not `-O3`. We learned this the hard way. - -Our first pipeline used `-O3` here, and the forward pass worked perfectly. The VJP, however, returned NaN on certain inputs. We spent a full day tracking this down. The root cause: LLVM's aggressive vectorization and code-motion passes at `-O3` produced IR patterns that Enzyme mishandled during reverse-mode analysis, specifically when adjacent cell temperatures were equal and intermediate terms canceled. The fix was embarrassingly simple — keep pre-Enzyme optimization mild and save `-O3` for after the AD pass (step 6). But the lesson was not simple at all: "the forward pass works" does not mean "the gradients are correct." If you're building a similar pipeline, test the gradients early and often. +Notice that's `-O1`, not `-O3`! Our first pipeline used `-O3` here, and the forward pass worked perfectly, so we moved on. The VJP didn't, though. It returned NaN on certain inputs, and it took us a few hours to track down why. What was happening is that LLVM's aggressive vectorization and code-motion passes at `-O3` produce IR patterns Enzyme mishandles during reverse-mode analysis, and in our case it bit specifically when adjacent cell temperatures were equal and intermediate terms canceled out, which can turn into a division by zero once things get rearranged. We settled on keeping the pre-Enzyme optimization mild and saving `-O3` for after the AD pass instead (that's step 6). If you build something like this, our advice is to test the gradients early and often. **3. Compile the C wrapper to LLVM IR:** @@ -117,7 +119,7 @@ Our first pipeline used `-O3` here, and the forward pass worked perfectly. The V clang -emit-llvm -S -O1 wrapper.c -o wrapper.ll ``` -We need a thin C wrapper to bridge Fortran's by-pointer ABI to a C-callable interface with Enzyme annotations. It declares three entry points — `thermal_2d_forward`, `thermal_2d_vjp`, and `thermal_2d_jvp` — using Enzyme's `__enzyme_autodiff` and `__enzyme_fwddiff` intrinsics to mark which arguments get shadow (gradient) buffers. Here's the core of the VJP entry point: +A thin C wrapper bridges Fortran's by-pointer ABI over to a C-callable interface that Enzyme can annotate. It declares three entry points, `thermal_2d_forward`, `thermal_2d_vjp`, and `thermal_2d_jvp`, and uses Enzyme's `__enzyme_autodiff` and `__enzyme_fwddiff` intrinsics to mark which arguments should get shadow (gradient) buffers. Here's the core of the VJP entry point: ```c void thermal_2d_vjp(int nx, int ny, int n_steps, @@ -142,7 +144,7 @@ void thermal_2d_vjp(int nx, int ny, int n_steps, } ``` -This is also where we allocate the work arrays on the heap, sidestepping the `_lfortran_malloc` issue from earlier. +This is also where the work arrays get allocated on the heap, sidestepping the `_lfortran_malloc` issue from earlier. **4. Link the IR modules:** @@ -156,7 +158,7 @@ llvm-link wrapper.ll thermal_2d_opt.ll -S -o combined.ll opt --load-pass-plugin=LLVMEnzyme-19.so -passes=enzyme -S combined.ll -o ad.ll ``` -This is where the magic happens. Enzyme analyzes the LLVM IR and synthesizes forward- and reverse-mode derivative code. For reverse mode, it uses a store-all (tape) strategy, caching intermediate values at each time step. When it works, it's genuinely impressive — you get an adjoint of your entire time-stepping loop for free. When it doesn't, you're reading LLVM IR diffs at 2 AM wondering where your life went wrong (see [What's next](#whats-next-and-what-wed-do-differently)). +This is the step that does the real work, and where Enzyme analyzes the LLVM IR and synthesizes forward and reverse-mode derivative code. For reverse mode, it uses a store-all (tape) strategy, caching intermediate values at each time step. When it works, it's genuinely impressive — you get an adjoint of your entire time-stepping loop for free. When it doesn't, you're reading LLVM IR diffs at 2 AM wondering where your life went wrong (see [What's next](#whats-next-and-what-wed-do-differently)). **6. Optimize and compile to a shared library:** @@ -165,45 +167,43 @@ opt -O3 -S ad.ll -o ad_opt.ll clang -shared -O3 ad_opt.ll -o libthermal_2d_ad.so -lm ``` -Out comes a single `.so` file with three entry points callable from Python via ctypes: forward evaluation, JVP, and VJP. The entire pipeline runs during `tesseract build` and takes about 30 seconds. It's a shell script that turns Fortran into exact gradients. We're not going to pretend that's elegant, but it is deeply satisfying. +Out comes a single `.so` file with three entry points you can call from Python via ctypes, one each for forward evaluation, the JVP, and the VJP. The whole pipeline runs during `tesseract build` and takes about 30 seconds end to end. ## Does it actually work? -OK, it compiles. But after the `-O3` NaN incident, we weren't about to trust it without checking. We called the VJP from Python and compared against central finite differences at various step sizes: +OK, it compiles. But after the `-O3` NaN incident, trusting it without checking was off the table. So the VJP gets called from Python and compared against central finite differences at various step sizes: Enzyme vs. finite difference gradient accuracy -Finite differences have a sweet spot: too large an $\epsilon$ and you get truncation error, too small and you get roundoff. The best you can typically do is around $10^{-8}$ relative error. Enzyme's gradients agree to machine precision ($\sim 10^{-15}$) — because they're computing the analytically correct derivative, just synthesized by a compiler instead of a human. - -And this isn't differentiating a single matrix multiply. It's the entire multi-step time loop with nonlinear stencil updates at each step. +Finite differences essentially compute $\big(f(x + \epsilon) - f(x - \epsilon)\big) / 2\epsilon$, and they only work well in a narrow sweet spot. Pick too large an $\epsilon$ and truncation error dominates; pick too small and roundoff takes over. In practice the best you can hope for is around $10^{-8}$ relative error. Enzyme's gradients, on the other hand, agree to machine precision (about $10^{-15}$), and that's no accident: they're the analytically correct derivative, just synthesized by a compiler rather than worked out by hand. And that holds across the entire multi-step time loop, with a nonlinear stencil update at every step. | Method | Relative error vs. exact | | ------------------------- | -----------------------: | | Enzyme AD | ~1e-15 (exact) | +| FD ($\epsilon$ too small) | ~1e-4 | | FD (best $\epsilon$) | ~1e-8 | | FD ($\epsilon$ too large) | ~1e-2 | -| FD ($\epsilon$ too small) | ~1e-4 | + +Error is worst at both ends of the $\epsilon$ range and best in the middle, the classic truncation-vs-roundoff trade-off. Enzyme sidesteps it entirely. ## Now do something useful with it -Correct gradients are great, but they're not the point. The point is using them — plugging them into an optimizer, solving a real inverse problem, composing them with other differentiable code. +Correct gradients are only worth something once you put them to work, whether that means dropping them into an optimizer, solving a real inverse problem, or composing them with other differentiable code. -To wire the Enzyme gradients into JAX, the solver needs to look like a differentiable JAX primitive. This is essentially what Tesseract was made for: it wraps the compiled library (LFortran, LLVM 19, Enzyme, the whole toolchain) into a container with autodiff endpoints, so `jax.value_and_grad` routes VJP calls to the Enzyme-generated code. Two commands: +To wire the Enzyme gradients into JAX, the solver has to look like a differentiable JAX primitive, and this is more or less exactly what Tesseract was built for. It wraps the compiled library, with LFortran, LLVM 19, Enzyme, and the whole toolchain inside it, into a container that exposes autodiff endpoints, so that `jax.value_and_grad` can route its VJP calls straight to the Enzyme-generated code. From there it's just a matter of building the container and serving it over HTTP: ```bash tesseract build demo/enzyme_thermal_2d/ tesseract serve enzyme-thermal-2d ``` -With that running, we can throw optimization problems at it. +With that running, it's finally time to point some real optimization problems at it and find out whether all the effort actually paid off. ### Scalar calibration: recovering 2 material parameters -Setup: a steel plate is heating up. We have thermocouple readings at 9 sensor locations, but we don't know the exact material properties. Can we recover $k_0$ (base conductivity) and $k_1$ (temperature coefficient) from sparse, noisy observations? - -We generate synthetic "observed" data by running the solver with known true values ($k_0 = 45$, $k_1 = -0.02$), sample at sensor locations, and add 0.5 K of Gaussian noise. Then we start from a deliberately wrong initial guess — 33% off on $k_0$, wrong sign on $k_1$ — and hand it to L-BFGS-B. +For a sanity check, the setup stays simple. A steel plate is heating up, there are thermocouple readings at 9 sensor locations, and the plate's material properties are unknown. The question is whether $k_0$ (base conductivity) and $k_1$ (its temperature coefficient) can be recovered from those sparse, noisy readings. -One VJP call gives gradients with respect to both parameters simultaneously. The optimizer doesn't care that those gradients come from a compiled Fortran solver differentiated by an LLVM pass. +To keep the test honest, the "observed" data is generated synthetically: run the solver with known true values ($k_0 = 45$, $k_1 = -0.02$), sample at the sensor locations, and add 0.5 K of Gaussian noise on top. The optimizer then starts from a deliberately bad guess, 33% off on $k_0$ and the wrong sign entirely on $k_1$, and the whole thing goes to L-BFGS-B. A single VJP call hands back gradients with respect to both parameters at once, and the optimizer is none the wiser that they came from a compiled Fortran solver differentiated by an LLVM pass. ```python def objective_and_gradient(params, tesseract): @@ -232,15 +232,13 @@ def objective_and_gradient(params, tesseract): Temperature field comparison: initial guess, recovered, ground truth, error -L-BFGS-B converges in about 15 iterations. The recovered parameters match the true values to within the noise floor. This is a gentle problem — only 2 unknowns, well-conditioned — so it's really a sanity check. The interesting question is what happens when we push harder. +L-BFGS-B converges in about 15 iterations and recovers both parameters to within the noise floor. The more interesting question is what happens once the method gets pushed a lot harder. ### Thermal forensics: recovering a 900-element initial temperature field -Now for something harder. A steel plate was subjected to an unmonitored heating event — a laser pulse, a localized defect, something. Five seconds later, you measure temperatures at 100 sensor locations. Can you figure out what the initial temperature distribution looked like? - -The true initial condition has two Gaussian hot spots on a warm background. That's 900 unknowns from 100 noisy observations, through a nonlinear PDE — ill-posed by any measure. +Imagine a steel plate that went through some unmonitored heating event, maybe a laser pulse, maybe a localized defect, nobody knows. Five seconds later you get to measure temperatures at 100 sensor locations, and the question is whether you can reconstruct what the initial temperature distribution must have looked like. -This is where reverse-mode AD becomes essential: +The true initial condition has two Gaussian hot spots sitting on a warm background. So the ask is 900 unknowns out of 100 noisy observations, run backwards through a nonlinear PDE. This is exactly the regime where reverse-mode AD (or its cousin the adjoint method) stops being a nice-to-have and becomes essential: | Method | Forward solves per iteration | | --------------------- | ---------------------------: | @@ -248,17 +246,17 @@ This is where reverse-mode AD becomes essential: | VJP (reverse-mode AD) | 2 (forward + reverse) | | **Speedup** | **~450×** | -Finite differences would need 901 forward solves per iteration to get all 900 gradients. One VJP gives them all at once, for roughly the cost of two forward passes. The trade-off is memory: Enzyme's reverse mode tapes intermediate values at each time step. For this problem (~900 grid points, 100 steps), the tape is a few hundred kilobytes. For production codes with large state vectors and thousands of time steps, tape memory becomes the dominant constraint. Enzyme supports checkpointing annotations to trade recomputation for memory, but we haven't needed or tested them here. +Finite differences would have to do 901 forward solves every iteration just to assemble all 900 gradients, while one VJP hands them all back at once, for roughly the cost of two forward passes. What you pay for that is memory, since Enzyme's reverse mode has to tape intermediate values at each time step. For a problem this size (~900 grid points, 100 steps) the tape is only a few hundred kilobytes, small enough to ignore. On production codes with large state vectors and thousands of time steps, though, that tape is usually the thing that ends up dominating the memory budget. Enzyme does have checkpointing annotations that trade recomputation for memory, but they weren't needed here and remain untested on this path. Thermal forensics: recovering 900 initial temperature values from 100 sensors -L-BFGS-B recovers the hot spot locations and magnitudes. Correlation between recovered and true initial temperature fields exceeds 0.99. The error is largest at the edges of the hot spots, where the signal has diffused most. The reconstruction is smoothed relative to the true field, as you'd expect from an ill-posed problem with diffusion, but it's far better than we had any right to expect from a pipeline held together with shell scripts. +And it works! L-BFGS-B finds both hot spots, gets their locations and magnitudes right, and the correlation between the recovered and true initial fields comes out above 0.99. Where it struggles is at the edges of the hot spots, which is exactly where the signal has had the most time to diffuse away. The reconstruction comes out a little smoothed compared to the truth, which is about what you'd expect from an ill-posed problem with diffusion in it, but it's honestly far better than a pipeline held together with shell scripts has any right to deliver. -That's `jax.grad` flowing through compiled Fortran, with no adjoint code written by hand. +That's `jax.grad` flowing all the way through compiled Fortran, without a single line of adjoint code written by hand. -### JAX integration via tesseract-jax +### JAX integration via Tesseract-JAX -You can also go one step further with [tesseract-jax](https://github.com/pasteurlabs/tesseract-jax), which turns the Tesseract into a proper JAX primitive. Then `jax.value_and_grad` just works: +If you want, you can take this one step further with [Tesseract-JAX](https://github.com/pasteurlabs/tesseract-jax), which promotes the Tesseract to a proper JAX primitive. At that point `jax.value_and_grad` just works on it directly: ```python from tesseract_jax import apply_tesseract @@ -269,19 +267,17 @@ def loss_fn(k0, k1, tesseract): residuals = T_pred[sensor_indices] - jnp.array(T_obs) return 0.5 * jnp.sum(residuals**2) -# This differentiates through: Python → JAX → HTTP → Enzyme → Fortran +# jax.value_and_grad differentiates straight through the HTTP boundary loss, (dk0, dk1) = jax.value_and_grad(loss_fn, argnums=(0, 1))( jnp.float64(60.0), jnp.float64(0.01), enzyme_tess ) ``` -From JAX's perspective, the Fortran solver is just another differentiable function. You could swap `enzyme_tess` for a pure-JAX reimplementation and the optimization loop wouldn't change — only the container behind the HTTP call. Whether that abstraction is beautiful or horrifying probably depends on how you feel about gradients traversing six layers of indirection (Python → JAX → HTTP → ctypes → Enzyme → Fortran). +As far as JAX is concerned, the Fortran solver is just another differentiable function. You could swap `enzyme_tess` out for a pure-JAX reimplementation tomorrow and nothing in the optimization loop would change, only the container sitting behind the HTTP call. Whether you find that abstraction beautiful or horrifying probably comes down to how you feel about your gradients quietly traversing six layers of indirection on the way through (Python → JAX/XLA → HTTP → ctypes → Enzyme → Fortran). ## Where this could go -We should be upfront: this is a 220-line solver we wrote to fit the pipeline. Enzyme handles loops, conditionals, and function calls, and the Enzyme team has demonstrated it on larger codes including [BUDE molecular docking](https://enzyme.mit.edu/getting_started/UsingEnzyme/#bude) and [LULESH hydrodynamics](https://enzyme.mit.edu/getting_started/UsingEnzyme/#lulesh), with derivative overhead factors typically between 1x and 4x. But "works on LULESH" and "works on your 30-year-old Fortran codebase" are very different claims. - -What gets us excited is the composability. Imagine a Fortran CFD solver (Enzyme-differentiated) feeding into a JAX neural net surrogate: +The real value-add here is composability. Picture an Enzyme-differentiated Fortran CFD solver feeding straight into a JAX neural-net surrogate: ```python cfd_output = apply_tesseract(cfd_tess, cfd_inputs) # Fortran + Enzyme VJP @@ -291,25 +287,25 @@ total_loss = surrogate_loss + regularizer(cfd_inputs) # JAX AD grads = jax.grad(total_loss) # chains Enzyme + JAX AD automatically ``` -Each component uses its native AD. Tesseract handles the composition. We built a version of this pattern for the [rocket fin optimization](2025-11-28-rocket-fin-optimization.md) post, where analytical adjoints, finite differences, and JAX AD coexisted in one pipeline. It worked, though each new gradient source brought its own class of debugging problems. +Every component differentiates itself with whatever AD is native to it, and Tesseract is the thing that stitches the pieces together. This is similar to the pattern showcased in the [rocket fin optimization](2025-11-28-rocket-fin-optimization.md) post, where analytical adjoints, finite differences, and JAX AD all coexisted in a single pipeline. It works, though every new gradient source tends to bring along its own fresh class of debugging headaches. -And because Enzyme works at the LLVM IR level, none of this is Fortran-specific. The same pipeline should apply to C, C++, Rust, or any language with an LLVM frontend — though "should" is doing a lot of work in that sentence. +Because Enzyme works at the LLVM IR level, none of this is Fortran-specific. The same pipeline should apply to C, C++, Rust, or any language with an LLVM frontend, which we graciously leave as an exercise for the reader. ## What's next (and what we'd do differently) -We've described most of the sharp edges inline — the `_lfortran_malloc` crash, the `-O3` NaN disaster, LFortran's incomplete coverage. To be blunt: this works, but it's not turnkey. Expect to adapt your Fortran, pin your compiler versions, and debug at the IR level at least once. - -A few things we haven't tried yet: +A reality check before getting carried away: this is a 220-line solver written specifically to fit the pipeline. Enzyme itself handles loops, conditionals, and function calls just fine, and the Enzyme team has run it on much larger codes, including [BUDE molecular docking](https://enzyme.mit.edu/getting_started/UsingEnzyme/#bude) and [LULESH hydrodynamics](https://enzyme.mit.edu/getting_started/UsingEnzyme/#lulesh), with derivative overhead that usually lands somewhere between 1x and 4x. Still, "works on LULESH" and "works on your 30-year-old Fortran codebase" are two very different claims. -**Implicit time integration.** Backward Euler, Crank-Nicolson, and other implicit schemes require differentiating through iterative linear solves (CG, GMRES). Enzyme can handle this in principle, but tape memory grows with solver iteration count, and we haven't tested this path with LFortran. This is where we're headed next. +We've flagged the sharp edges as we went, from the `_lfortran_malloc` crash to the `-O3` NaN disaster to LFortran's still-incomplete coverage. So the approach works, but it is nowhere near turnkey yet. Plan on adapting your Fortran, pinning your compiler versions, and dropping down to the IR level to debug at least once before you're done. -**Third-party code.** We wrote this solver to work with the pipeline. We haven't yet tried Enzyme + LFortran on a Fortran codebase we didn't author. The "will it work on _my_ code?" question is fair. Honest answer: probably, with adaptation — the kind we described above, and possibly more we haven't encountered yet. +The path we're most interested in next is **implicit time integration**. Backward Euler, Crank-Nicolson, and the other implicit schemes all require differentiating through an iterative linear solve (CG, GMRES, and friends). Enzyme can do this in principle, but the tape memory grows with the solver's iteration count, which comes with its own set of challenges. -**Solvers at scale.** MPI-parallel codes, GPU kernels, multi-physics coupling — all untested with this pipeline. Enzyme has support for some of these; we just haven't tried. +Two bigger questions stay open past that. One is **third-party code**: since this solver was written to fit the pipeline, the obvious "but will it work on _my_ code?" is a perfectly fair thing to ask. The honest guess is that it probably will, given the kind of adaptation described earlier and likely a few surprises beyond it. The other is **scale**, where MPI-parallel codes, GPU kernels, and multi-physics coupling all remain untested here. Enzyme has support for some of them; that's just territory this pipeline hasn't reached. ## Try it yourself -The full source — Fortran solver, Enzyme pipeline, inverse problem notebooks, and the shell scripts holding it all together — is [on GitHub](https://github.com/pasteurlabs/tesseract-core/tree/main/demo/enzyme_thermal_2d). If you have a Fortran, C, or C++ solver you want gradients for and don't mind some quality time with LLVM IR, this is a starting point. +The full source is [on GitHub](https://github.com/pasteurlabs/tesseract-core/tree/main/demo/enzyme_thermal_2d), the Fortran solver, the Enzyme pipeline, the inverse-problem notebooks, and the shell scripts holding it all together. If you've got a Fortran, C, or C++ solver you'd like gradients for and you don't mind spending some quality time with LLVM IR, this is a pretty good place to start. + +The pieces are here, and the open questions above (implicit solvers, third-party code, scale) are exactly the kind of thing that's more fun with company. If you take it somewhere, whether you get it running on your own solver or hit a wall we didn't, come tell us on the [forum](https://si-tesseract.discourse.group/). We'd genuinely like to see how far it goes! --- From 550245aa6db0fcf1f26abbbfc04074b46bebbc3a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dion=20H=C3=A4fner?= Date: Tue, 2 Jun 2026 13:11:47 +0200 Subject: [PATCH 07/24] fix: green up CI for enzyme integration PR Fix the three failing checks on the Enzyme proof-of-concept PR: - test-docs: add an explicit MyST anchor to the "What's next" heading in the Fortran/Enzyme blog post so the in-page cross-reference resolves (Sphinx treats the unresolved-xref warning as an error). - tests-e2e (enzyme_ad): the e2e harness requires every examples/ dir to have a TEST_CASES entry. Add enzyme_ad with check_gradients=True, a regression test case (test_cases/test_apply.json) with analytically computed expected output, and a check-gradients input. Verified locally: the full build + apply + check-gradients + serve test passes. - tests-demos (enzyme_thermal_2d): the demo lane auto-discovers every demo/ dir and runs requirements.txt + demo.ipynb. This dir had neither and the notebook loaded pre-built images (including a jax-thermal-2d Tesseract absent from this branch). Make it a self-contained, runnable demo: * add requirements.txt * rewrite the notebook as demo.ipynb: build + serve the Enzyme Tesseract in-notebook, drive both inverse problems (scalar calibration + 900-parameter thermal forensics) with jax.value_and_grad through tesseract-jax, and tear down at the end * add a Tikhonov term to the forensics loss so the recovered field matches the blog (~0.98 correlation) * add an abstract_eval endpoint to the 2D tesseract_api.py and make the input validators abstract-safe (skip on ShapeDType, drop field-level gt constraints that can't apply to abstract scalars) so tesseract-jax transforms work Verified locally: demo notebook executes end-to-end with no errors and blog-consistent results. Co-Authored-By: Claude Opus 4.8 (1M context) --- ...inverse_heat_transfer.ipynb => demo.ipynb} | 684 ++++++++---------- demo/enzyme_thermal_2d/requirements.txt | 5 + demo/enzyme_thermal_2d/tesseract_api.py | 41 +- .../2026-05-15-fortran-enzyme-autodiff.md | 28 +- examples/enzyme_ad/test_cases/test_apply.json | 34 + .../example_checkgradients_input.json | 16 + tests/endtoend_tests/test_examples.py | 1 + 7 files changed, 391 insertions(+), 418 deletions(-) rename demo/enzyme_thermal_2d/{inverse_heat_transfer.ipynb => demo.ipynb} (52%) create mode 100644 demo/enzyme_thermal_2d/requirements.txt create mode 100644 examples/enzyme_ad/test_cases/test_apply.json create mode 100644 examples/enzyme_ad/test_cases_inputs/example_checkgradients_input.json diff --git a/demo/enzyme_thermal_2d/inverse_heat_transfer.ipynb b/demo/enzyme_thermal_2d/demo.ipynb similarity index 52% rename from demo/enzyme_thermal_2d/inverse_heat_transfer.ipynb rename to demo/enzyme_thermal_2d/demo.ipynb index 491e1384..f1847a60 100644 --- a/demo/enzyme_thermal_2d/inverse_heat_transfer.ipynb +++ b/demo/enzyme_thermal_2d/demo.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "0o7kbl9m2j69", + "id": "459aa200939c", "metadata": {}, "source": [ "# Inverse Heat Transfer with Automatic Differentiation\n", @@ -11,32 +11,78 @@ "locations, but you don't know the exact material properties — or even what the\n", "temperature distribution looked like before heating started. Can you figure it out?\n", "\n", - "This notebook solves two inverse problems of increasing ambition using a Fortran\n", - "finite-difference solver whose exact derivatives are generated automatically by\n", - "[Enzyme](https://enzyme.mit.edu/) at the LLVM IR level — no manual adjoint code,\n", - "no source modifications. Then it shows how `jax.grad` can differentiate through\n", - "the Fortran solver end-to-end via [`tesseract-jax`](https://github.com/pasteurlabs/tesseract-jax).\n", + "This notebook solves two inverse problems of increasing ambition. The forward\n", + "model is a 2D transient heat-conduction solver written in plain **Fortran**, whose\n", + "exact derivatives are generated automatically by [Enzyme](https://enzyme.mit.edu/)\n", + "at the LLVM IR level — no manual adjoint code, no source modifications. Wrapped as\n", + "a [Tesseract](https://github.com/pasteurlabs/tesseract-core) and bridged into JAX\n", + "with [`tesseract-jax`](https://github.com/pasteurlabs/tesseract-jax), the Fortran\n", + "solver becomes an ordinary differentiable JAX function, so `jax.grad` flows\n", + "straight through it.\n", "\n", "1. **Part 1: Scalar calibration** — recover 2 material parameters (k₀, k₁) from 9 sensors\n", "2. **Part 2: Thermal forensics** — recover the full 900-element initial temperature\n", " field from 100 sensors (finite differences would need 901 forward solves per\n", - " iteration; one VJP gives all 900 gradients at once)\n", - "3. **Part 3: JAX integration** — `jax.grad` through Python → JAX → HTTP → Enzyme → Fortran\n", - " in a single call" + " iteration; one reverse-mode pass gives all 900 gradients at once)\n", + "\n", + "The optimizers below only ever see a JAX function. They never know the gradients\n", + "came from a compiled Fortran solver differentiated by an LLVM pass." + ] + }, + { + "cell_type": "markdown", + "id": "10eedccbbadf", + "metadata": {}, + "source": [ + "## Build and serve the Enzyme AD Tesseract\n", + "\n", + "The build compiles the Fortran source to LLVM IR with LFortran, runs the Enzyme\n", + "AD pass to synthesize forward- and reverse-mode derivatives, and links everything\n", + "into a shared library — all inside the container. This step downloads the LLVM 19\n", + "toolchain and builds Enzyme from source, so the first build takes a few minutes." ] }, { "cell_type": "code", "execution_count": null, - "id": "sp6907y1jgf", + "id": "d1505e18eaec", "metadata": {}, "outputs": [], "source": [ + "%%bash\n", + "tesseract build ." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fcc5e2141f85", + "metadata": {}, + "outputs": [], + "source": [ + "import jax\n", + "import jax.numpy as jnp\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", + "from tesseract_jax import apply_tesseract\n", "\n", "from tesseract_core import Tesseract\n", "\n", + "# JAX needs float64 to match the Fortran solver's double precision.\n", + "jax.config.update(\"jax_enable_x64\", True)\n", + "\n", + "# Serve the Tesseract; it stays alive for the rest of the notebook.\n", + "enzyme_tess = Tesseract.from_image(\"enzyme-thermal-2d\")\n", + "enzyme_tess.serve()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2bdf1ea4fd67", + "metadata": {}, + "outputs": [], + "source": [ "# Grid and simulation parameters (fixed throughout)\n", "nx, ny = 30, 30\n", "n = nx * ny\n", @@ -60,14 +106,26 @@ }, { "cell_type": "markdown", - "id": "rkthdyekadr", + "id": "849d4a04755d", "metadata": {}, - "source": "## Part 1: Scalar calibration (2 parameters)\n\n### Generate synthetic data\n\nWe run the solver with the **true** material properties to produce a ground-truth\ntemperature field, then sample it at sparse sensor locations with added noise.\nIn practice, these would be thermocouple readings from a real component." + "source": [ + "## Part 1: Scalar calibration (2 parameters)\n", + "\n", + "### Generate synthetic data\n", + "\n", + "We run the solver with the **true** material properties to produce a ground-truth\n", + "temperature field, then sample it at sparse sensor locations with added noise.\n", + "In practice, these would be thermocouple readings from a real component.\n", + "\n", + "Because the solver is now a JAX function, we build its inputs as JAX arrays. The\n", + "static grid sizes (`nx`, `ny`, `n_steps`) stay as plain integers; everything\n", + "differentiable is a JAX array." + ] }, { "cell_type": "code", "execution_count": null, - "id": "8pt0ybtfm36", + "id": "771e9a987964", "metadata": {}, "outputs": [], "source": [ @@ -77,30 +135,33 @@ "\n", "\n", "def make_inputs(k0, k1):\n", - " \"\"\"Build a full input dict for the Tesseract.\"\"\"\n", + " \"\"\"Build a full input dict (JAX arrays) for the Tesseract.\"\"\"\n", " return {\n", - " \"T_init\": T_init,\n", - " \"Q\": Q,\n", + " \"T_init\": jnp.asarray(T_init),\n", + " \"Q\": jnp.asarray(Q),\n", " \"nx\": nx,\n", " \"ny\": ny,\n", " \"n_steps\": n_steps,\n", - " \"k0\": float(k0),\n", - " \"k1\": float(k1),\n", - " \"rho\": rho,\n", - " \"cp\": cp,\n", - " \"h_conv\": h_conv,\n", - " \"T_inf\": T_inf,\n", - " \"T_hot\": T_hot,\n", - " \"Lx\": Lx,\n", - " \"Ly\": Ly,\n", - " \"dt\": dt,\n", + " \"k0\": jnp.asarray(k0, dtype=jnp.float64),\n", + " \"k1\": jnp.asarray(k1, dtype=jnp.float64),\n", + " \"rho\": jnp.float64(rho),\n", + " \"cp\": jnp.float64(cp),\n", + " \"h_conv\": jnp.float64(h_conv),\n", + " \"T_inf\": jnp.float64(T_inf),\n", + " \"T_hot\": jnp.float64(T_hot),\n", + " \"Lx\": jnp.float64(Lx),\n", + " \"Ly\": jnp.float64(Ly),\n", + " \"dt\": jnp.float64(dt),\n", " }\n", "\n", "\n", + "def solve(k0, k1):\n", + " \"\"\"Forward solve through the Fortran solver, returns T_final as a JAX array.\"\"\"\n", + " return apply_tesseract(enzyme_tess, make_inputs(k0, k1))[\"T_final\"]\n", + "\n", + "\n", "# Run the ground-truth simulation\n", - "with Tesseract.from_image(\"enzyme-thermal-2d:latest\") as t:\n", - " result_true = t.apply(inputs=make_inputs(k0_true, k1_true))\n", - " T_true = np.array(result_true[\"T_final\"]).reshape(ny, nx)\n", + "T_true = np.asarray(solve(k0_true, k1_true)).reshape(ny, nx)\n", "\n", "print(f\"Ground truth: k0={k0_true}, k1={k1_true}\")\n", "print(f\"Temperature range: {T_true.min():.2f} K to {T_true.max():.2f} K\")" @@ -109,7 +170,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8z2g10uvgwl", + "id": "7e544cbd0338", "metadata": {}, "outputs": [], "source": [ @@ -142,7 +203,7 @@ { "cell_type": "code", "execution_count": null, - "id": "h7wqp7wjjl4", + "id": "904587d15cc3", "metadata": {}, "outputs": [], "source": [ @@ -170,100 +231,108 @@ }, { "cell_type": "markdown", - "id": "6o9vjw5xeyw", + "id": "c6386c40c0f5", "metadata": {}, - "source": "## Step 2: Define the inverse problem\n\nMinimize the misfit between predicted and observed sensor temperatures:\n\n$$\nJ(k_0, k_1) = \\frac{1}{2} \\sum_{i=1}^{N_\\text{sensors}} \\left( T_\\text{pred}(\\mathbf{x}_i; k_0, k_1) - T_\\text{obs}(\\mathbf{x}_i) \\right)^2\n$$\n\nThe gradient $\\nabla_{k_0, k_1} J$ comes from a single VJP (reverse-mode AD) call.\nThe cotangent vector is the residual at sensor locations, zero elsewhere:\n\n$$\n\\bar{T}_j = \\begin{cases}\nT_\\text{pred}(\\mathbf{x}_j) - T_\\text{obs}(\\mathbf{x}_j) & \\text{if } j \\text{ is a sensor location} \\\\\n0 & \\text{otherwise}\n\\end{cases}\n$$\n\nOne VJP call gives $\\partial J / \\partial k_0$ and $\\partial J / \\partial k_1$\nsimultaneously. Finite differences would need a separate forward solve per parameter." + "source": [ + "### Define the inverse problem\n", + "\n", + "Minimize the misfit between predicted and observed sensor temperatures:\n", + "\n", + "$$\n", + "J(k_0, k_1) = \\frac{1}{2} \\sum_{i=1}^{N_\\text{sensors}} \\left( T_\\text{pred}(\\mathbf{x}_i; k_0, k_1) - T_\\text{obs}(\\mathbf{x}_i) \\right)^2\n", + "$$\n", + "\n", + "`loss_fn` is a plain JAX function that happens to call the Fortran solver through\n", + "`apply_tesseract`. We hand it to `jax.value_and_grad`, and JAX propagates the\n", + "cotangent through the HTTP boundary into Enzyme's reverse-mode pass — one reverse\n", + "sweep returns $\\partial J / \\partial k_0$ and $\\partial J / \\partial k_1$ at once.\n", + "Finite differences would need a separate forward solve per parameter." + ] }, { "cell_type": "code", "execution_count": null, - "id": "ah1upfczz2e", + "id": "43111e1b97b5", "metadata": {}, "outputs": [], "source": [ - "def objective_and_gradient(params, tesseract):\n", - " \"\"\"Compute loss and gradient for the inverse problem.\n", + "T_obs_jax = jnp.asarray(T_obs)\n", + "\n", "\n", - " params: [k0, k1]\n", - " Returns: (loss, [dk0, dk1])\n", - " \"\"\"\n", + "def loss_fn(params):\n", + " \"\"\"Sensor-misfit loss as a function of [k0, k1]. Pure JAX.\"\"\"\n", " k0, k1 = params\n", - " inputs = make_inputs(k0, k1)\n", - "\n", - " # Forward solve\n", - " result = tesseract.apply(inputs=inputs)\n", - " T_pred = np.array(result[\"T_final\"])\n", - "\n", - " # Loss: sum of squared residuals at sensor locations\n", - " residuals = T_pred[sensor_indices] - T_obs\n", - " loss = 0.5 * np.sum(residuals**2)\n", - "\n", - " # Cotangent vector: residuals at sensor locations, zero elsewhere\n", - " cotangent = np.zeros(n, dtype=np.float64)\n", - " cotangent[sensor_indices] = residuals\n", - "\n", - " # One VJP call gives gradients w.r.t. both k0 and k1\n", - " vjp = tesseract.vector_jacobian_product(\n", - " inputs=inputs,\n", - " vjp_inputs=[\"k0\", \"k1\"],\n", - " vjp_outputs=[\"T_final\"],\n", - " cotangent_vector={\"T_final\": cotangent},\n", - " )\n", - "\n", - " grad = np.array([vjp[\"k0\"], vjp[\"k1\"]])\n", - " return loss, grad" + " T_pred = solve(k0, k1)\n", + " residuals = T_pred[sensor_indices] - T_obs_jax\n", + " return 0.5 * jnp.sum(residuals**2)\n", + "\n", + "\n", + "# jax.value_and_grad differentiates straight through the Fortran solver.\n", + "value_and_grad = jax.value_and_grad(loss_fn)\n", + "\n", + "# Sanity check: gradient at the initial guess.\n", + "loss0, grad0 = value_and_grad(jnp.array([60.0, 0.01]))\n", + "print(f\"Initial loss = {loss0:.4f}\")\n", + "print(f\"Gradient via Enzyme: dJ/dk0 = {grad0[0]:.6f}, dJ/dk1 = {grad0[1]:.6f}\")" ] }, { "cell_type": "markdown", - "id": "ll57ug9m2cd", + "id": "b1e034157040", "metadata": {}, - "source": "## Step 3: Run the optimization\n\nWe start from a deliberately wrong initial guess and use `scipy.optimize.minimize`\nwith L-BFGS-B (a quasi-Newton method that uses gradient information). The bounds\nensure physical plausibility (positive conductivity, reasonable temperature dependence)." + "source": [ + "### Run the optimization\n", + "\n", + "We start from a deliberately wrong initial guess (33% off on k₀, wrong sign on k₁)\n", + "and let `scipy.optimize.minimize` drive L-BFGS-B, with `jax.value_and_grad`\n", + "supplying both the loss and its gradient. The bounds keep the parameters physically\n", + "plausible and the time stepping CFL-safe." + ] }, { "cell_type": "code", "execution_count": null, - "id": "3iy2we25s1j", + "id": "81fa6219dfdb", "metadata": {}, "outputs": [], "source": [ "from scipy.optimize import minimize\n", "\n", - "# Initial guess: 30% off on k0, wrong sign on k1\n", - "k0_init = 60.0\n", - "k1_init = 0.01\n", + "# Initial guess: 33% off on k0, wrong sign on k1\n", + "x0 = np.array([60.0, 0.01])\n", "\n", "# Track optimization history\n", - "history = {\"k0\": [k0_init], \"k1\": [k1_init], \"loss\": []}\n", - "\n", - "with Tesseract.from_image(\"enzyme-thermal-2d:latest\") as t:\n", - " # Evaluate initial loss\n", - " loss0, _ = objective_and_gradient([k0_init, k1_init], t)\n", - " history[\"loss\"].append(loss0)\n", - " print(f\"Initial guess: k0={k0_init:.2f}, k1={k1_init:.4f}, loss={loss0:.4f}\")\n", - "\n", - " def callback(params):\n", - " k0, k1 = params\n", - " loss, _ = objective_and_gradient(params, t)\n", - " history[\"k0\"].append(k0)\n", - " history[\"k1\"].append(k1)\n", - " history[\"loss\"].append(loss)\n", - " print(f\" k0={k0:.4f}, k1={k1:.6f}, loss={loss:.6f}\")\n", - "\n", - " result = minimize(\n", - " fun=lambda p: objective_and_gradient(p, t),\n", - " x0=[k0_init, k1_init],\n", - " method=\"L-BFGS-B\",\n", - " jac=True, # objective_and_gradient returns (loss, grad)\n", - " bounds=[(5.0, 80.0), (-0.08, 0.08)], # stay CFL-safe\n", - " callback=callback,\n", - " options={\"maxiter\": 50, \"ftol\": 1e-12, \"gtol\": 1e-8},\n", - " )\n", - "\n", - " # Final forward solve with recovered parameters\n", - " k0_opt, k1_opt = result.x\n", - " result_opt = t.apply(inputs=make_inputs(k0_opt, k1_opt))\n", - " T_opt = np.array(result_opt[\"T_final\"]).reshape(ny, nx)\n", + "history = {\"k0\": [x0[0]], \"k1\": [x0[1]], \"loss\": []}\n", + "\n", + "\n", + "def scipy_objective(params):\n", + " loss, grad = value_and_grad(jnp.asarray(params))\n", + " return float(loss), np.asarray(grad, dtype=np.float64)\n", + "\n", + "\n", + "def callback(params):\n", + " loss, _ = scipy_objective(params)\n", + " history[\"k0\"].append(params[0])\n", + " history[\"k1\"].append(params[1])\n", + " history[\"loss\"].append(loss)\n", + " print(f\" k0={params[0]:.4f}, k1={params[1]:.6f}, loss={loss:.6f}\")\n", + "\n", + "\n", + "history[\"loss\"].append(scipy_objective(x0)[0])\n", + "print(f\"Initial guess: k0={x0[0]:.2f}, k1={x0[1]:.4f}, loss={history['loss'][0]:.4f}\")\n", + "\n", + "result = minimize(\n", + " fun=scipy_objective,\n", + " x0=x0,\n", + " method=\"L-BFGS-B\",\n", + " jac=True, # scipy_objective returns (loss, grad)\n", + " bounds=[(5.0, 80.0), (-0.08, 0.08)], # stay CFL-safe\n", + " callback=callback,\n", + " options={\"maxiter\": 50, \"ftol\": 1e-12, \"gtol\": 1e-8},\n", + ")\n", + "\n", + "k0_opt, k1_opt = result.x\n", + "T_opt = np.asarray(solve(k0_opt, k1_opt)).reshape(ny, nx)\n", "\n", "print(f\"\\nOptimization finished in {result.nit} iterations\")\n", "print(f\" True: k0={k0_true:.4f}, k1={k1_true:.6f}\")\n", @@ -276,14 +345,18 @@ }, { "cell_type": "markdown", - "id": "hsdco9e9t14", + "id": "72a435fe434e", "metadata": {}, - "source": "## Step 4: Visualize results\n\n### Convergence" + "source": [ + "### Visualize results\n", + "\n", + "#### Convergence" + ] }, { "cell_type": "code", "execution_count": null, - "id": "zd3j2yjqer", + "id": "e08c0b018c43", "metadata": {}, "outputs": [], "source": [ @@ -324,21 +397,21 @@ }, { "cell_type": "markdown", - "id": "x9v55p3ofe", + "id": "5152dd0af3b7", "metadata": {}, - "source": "### Temperature fields: initial guess vs. optimized vs. ground truth" + "source": [ + "#### Temperature fields: initial guess vs. optimized vs. ground truth" + ] }, { "cell_type": "code", "execution_count": null, - "id": "p46li5txyl", + "id": "977f62064249", "metadata": {}, "outputs": [], "source": [ - "# Also compute the initial-guess temperature field for comparison\n", - "with Tesseract.from_image(\"enzyme-thermal-2d:latest\") as t:\n", - " result_init = t.apply(inputs=make_inputs(k0_init, k1_init))\n", - " T_init_field = np.array(result_init[\"T_final\"]).reshape(ny, nx)\n", + "# Compute the initial-guess temperature field for comparison\n", + "T_init_field = np.asarray(solve(x0[0], x0[1])).reshape(ny, nx)\n", "\n", "# Common color range\n", "vmin = min(T_true.min(), T_opt.min(), T_init_field.min())\n", @@ -347,7 +420,7 @@ "fig, axes = plt.subplots(1, 4, figsize=(18, 4))\n", "extent = [0, Lx * 1e3, 0, Ly * 1e3]\n", "\n", - "im0 = axes[0].imshow(\n", + "axes[0].imshow(\n", " T_init_field,\n", " origin=\"lower\",\n", " cmap=\"hot\",\n", @@ -356,9 +429,9 @@ " vmin=vmin,\n", " vmax=vmax,\n", ")\n", - "axes[0].set_title(f\"Initial guess\\nk₀={k0_init}, k₁={k1_init}\")\n", + "axes[0].set_title(f\"Initial guess\\nk₀={x0[0]}, k₁={x0[1]}\")\n", "\n", - "im1 = axes[1].imshow(\n", + "axes[1].imshow(\n", " T_opt,\n", " origin=\"lower\",\n", " cmap=\"hot\",\n", @@ -388,7 +461,6 @@ "for ax in axes:\n", " ax.set_xlabel(\"x [mm]\")\n", " ax.set_ylabel(\"y [mm]\")\n", - " # Mark sensor locations\n", " for ix, jy in sensor_coords:\n", " x_mm = ix / (nx - 1) * Lx * 1e3\n", " y_mm = jy / (ny - 1) * Ly * 1e3\n", @@ -404,7 +476,7 @@ }, { "cell_type": "markdown", - "id": "y5c2ssvn3x", + "id": "8be059a8e35b", "metadata": {}, "source": [ "## Part 2: Thermal forensics — recovering a hidden heat signature (900 parameters)\n", @@ -415,22 +487,28 @@ "distribution looked like?\n", "\n", "This is an ill-posed inverse problem: 900 unknowns (temperature at every grid cell)\n", - "from 100 noisy observations, through a nonlinear PDE. But with exact gradients from\n", - "Enzyme's VJP, L-BFGS-B handles it comfortably.\n", - "\n", - "The cost advantage of reverse-mode AD is now dramatic:\n", - "\n", - "| Method | Forward solves per iteration | Time per iteration |\n", - "|--------|----------------------------:|-------------------:|\n", - "| Finite differences | 901 (N+1) | ~10 s |\n", - "| VJP (reverse-mode AD) | 2 (fwd + rev) | ~0.8 s |\n", - "| **Speedup** | | **~450×** |" + "from 100 noisy observations, through a nonlinear PDE. We add a small Tikhonov term\n", + "that penalizes departure from the ambient prior, which regularizes the problem; the\n", + "optimizer is otherwise the same `jax.value_and_grad` + L-BFGS-B as before — only the\n", + "parameter vector grows from 2 to 900. This is exactly where reverse-mode AD stops\n", + "being a nice-to-have:\n", + "\n", + "| Method | Forward solves per iteration |\n", + "|--------|----------------------------:|\n", + "| Finite differences | 901 (N+1) |\n", + "| Reverse-mode AD | 2 (forward + reverse) |\n", + "| **Speedup** | **~450×** |\n", + "\n", + "Finite differences would need 901 forward solves every iteration to assemble all\n", + "900 gradients; one reverse sweep returns them all for roughly the cost of two\n", + "forward passes. The Tikhonov term is just another addition to the JAX loss —\n", + "`jax.value_and_grad` differentiates it for free." ] }, { "cell_type": "code", "execution_count": null, - "id": "a5vw1rcatio", + "id": "e337f08f8d05", "metadata": {}, "outputs": [], "source": [ @@ -457,30 +535,33 @@ ")\n", "\n", "\n", - "# Run forward simulation with true initial field\n", "def make_inputs_p2(T_init_field):\n", + " \"\"\"Inputs for the forensics problem; T_init_field is the differentiable unknown.\"\"\"\n", " return {\n", - " \"T_init\": T_init_field.astype(np.float64),\n", - " \"Q\": Q,\n", + " \"T_init\": jnp.asarray(T_init_field),\n", + " \"Q\": jnp.asarray(Q),\n", " \"nx\": nx,\n", " \"ny\": ny,\n", " \"n_steps\": n_steps_p2,\n", - " \"k0\": k0_p2,\n", - " \"k1\": k1_p2,\n", - " \"rho\": rho,\n", - " \"cp\": cp,\n", - " \"h_conv\": h_conv,\n", - " \"T_inf\": T_inf,\n", - " \"T_hot\": T_hot,\n", - " \"Lx\": Lx,\n", - " \"Ly\": Ly,\n", - " \"dt\": dt_p2,\n", + " \"k0\": jnp.float64(k0_p2),\n", + " \"k1\": jnp.float64(k1_p2),\n", + " \"rho\": jnp.float64(rho),\n", + " \"cp\": jnp.float64(cp),\n", + " \"h_conv\": jnp.float64(h_conv),\n", + " \"T_inf\": jnp.float64(T_inf),\n", + " \"T_hot\": jnp.float64(T_hot),\n", + " \"Lx\": jnp.float64(Lx),\n", + " \"Ly\": jnp.float64(Ly),\n", + " \"dt\": jnp.float64(dt_p2),\n", " }\n", "\n", "\n", - "with Tesseract.from_image(\"enzyme-thermal-2d:latest\") as t:\n", - " result_true_p2 = t.apply(inputs=make_inputs_p2(T_init_true))\n", - " T_final_true_p2 = np.array(result_true_p2[\"T_final\"])\n", + "def solve_p2(T_init_field):\n", + " return apply_tesseract(enzyme_tess, make_inputs_p2(T_init_field))[\"T_final\"]\n", + "\n", + "\n", + "# Run forward simulation with the true initial field\n", + "T_final_true_p2 = np.asarray(solve_p2(T_init_true))\n", "\n", "# 10x10 sensor grid (100 sensors in the interior)\n", "sensor_ix_p2 = np.linspace(3, nx - 4, 10, dtype=int)\n", @@ -501,102 +582,92 @@ { "cell_type": "code", "execution_count": null, - "id": "lafkg3kzyuo", + "id": "c6473e7ffb35", "metadata": {}, "outputs": [], "source": [ "import time\n", "\n", - "from scipy.optimize import minimize as sp_minimize\n", + "T_obs_p2_jax = jnp.asarray(T_obs_p2)\n", + "sensor_grid_jax = jnp.asarray(sensor_grid)\n", "\n", + "# Tikhonov regularization weight: penalizes departure from the ambient prior,\n", + "# which stabilizes this ill-posed problem (900 unknowns, 100 observations).\n", + "alpha_reg = 0.001\n", "\n", - "def objective_and_gradient_p2(T_init_vec, tesseract):\n", - " \"\"\"Loss and gradient for the T_init recovery problem.\n", "\n", - " 900 unknowns, 100 observations, 1 VJP call for all 900 gradients.\n", - " \"\"\"\n", - " inputs = make_inputs_p2(T_init_vec)\n", + "def loss_fn_p2(T_init_vec):\n", + " \"\"\"Regularized sensor-misfit loss for the 900-element initial field. Pure JAX.\"\"\"\n", + " T_pred = solve_p2(T_init_vec)\n", + " residuals = T_pred[sensor_grid_jax] - T_obs_p2_jax\n", + " data_loss = 0.5 * jnp.sum(residuals**2)\n", + " reg_loss = 0.5 * alpha_reg * jnp.sum((T_init_vec - T_inf) ** 2)\n", + " return data_loss + reg_loss\n", "\n", - " # Forward solve\n", - " result = tesseract.apply(inputs=inputs)\n", - " T_pred = np.array(result[\"T_final\"])\n", "\n", - " # Sensor residuals\n", - " residuals = T_pred[sensor_grid] - T_obs_p2\n", - " loss = 0.5 * np.sum(residuals**2)\n", + "value_and_grad_p2 = jax.value_and_grad(loss_fn_p2)\n", "\n", - " # Cotangent: residuals at sensor locations\n", - " cotangent = np.zeros(n, dtype=np.float64)\n", - " cotangent[sensor_grid] = residuals\n", "\n", - " # Single VJP gives gradient w.r.t. all 900 T_init components\n", - " vjp = tesseract.vector_jacobian_product(\n", - " inputs=inputs,\n", - " vjp_inputs=[\"T_init\"],\n", - " vjp_outputs=[\"T_final\"],\n", - " cotangent_vector={\"T_final\": cotangent},\n", - " )\n", - " grad = np.array(vjp[\"T_init\"])\n", + "def scipy_objective_p2(T_init_vec):\n", + " loss, grad = value_and_grad_p2(jnp.asarray(T_init_vec))\n", + " return float(loss), np.asarray(grad, dtype=np.float64)\n", "\n", - " return loss, grad\n", "\n", - "\n", - "# Run optimization: start from uniform ambient (the wrong answer)\n", + "# Start from uniform ambient (the wrong answer)\n", "T_init_guess = np.full(n, T_inf)\n", "loss_history_p2 = []\n", "\n", - "with Tesseract.from_image(\"enzyme-thermal-2d:latest\") as t:\n", - " iter_count = [0]\n", - " t_start = time.time()\n", - "\n", - " def callback_p2(x):\n", - " iter_count[0] += 1\n", - " if iter_count[0] % 10 == 0:\n", - " loss, _ = objective_and_gradient_p2(x, t)\n", - " loss_history_p2.append(loss)\n", - " elapsed = time.time() - t_start\n", - " print(f\" iter {iter_count[0]:3d}: loss={loss:.4f}, elapsed={elapsed:.1f}s\")\n", - "\n", - " # Initial loss\n", - " loss0, _ = objective_and_gradient_p2(T_init_guess, t)\n", - " loss_history_p2.insert(0, loss0)\n", - " print(f\"Initial loss: {loss0:.2f}\")\n", - " print(f\"Running L-BFGS-B with {n} parameters...\")\n", - "\n", - " result_p2 = sp_minimize(\n", - " fun=lambda x: objective_and_gradient_p2(x, t),\n", - " x0=T_init_guess,\n", - " method=\"L-BFGS-B\",\n", - " jac=True,\n", - " bounds=[(250.0, 450.0)] * n,\n", - " callback=callback_p2,\n", - " options={\"maxiter\": 100, \"ftol\": 1e-14, \"gtol\": 1e-8},\n", - " )\n", - "\n", - " elapsed_total = time.time() - t_start\n", - "\n", - " # Final loss\n", - " loss_final, _ = objective_and_gradient_p2(result_p2.x, t)\n", - " loss_history_p2.append(loss_final)\n", + "iter_count = [0]\n", + "t_start = time.time()\n", + "\n", + "\n", + "def callback_p2(x):\n", + " iter_count[0] += 1\n", + " if iter_count[0] % 10 == 0:\n", + " loss, _ = scipy_objective_p2(x)\n", + " loss_history_p2.append(loss)\n", + " elapsed = time.time() - t_start\n", + " print(f\" iter {iter_count[0]:3d}: loss={loss:.4f}, elapsed={elapsed:.1f}s\")\n", + "\n", + "\n", + "loss0_p2 = scipy_objective_p2(T_init_guess)[0]\n", + "loss_history_p2.append(loss0_p2)\n", + "print(f\"Initial loss: {loss0_p2:.2f}\")\n", + "print(f\"Running L-BFGS-B with {n} parameters...\")\n", "\n", + "result_p2 = minimize(\n", + " fun=scipy_objective_p2,\n", + " x0=T_init_guess,\n", + " method=\"L-BFGS-B\",\n", + " jac=True,\n", + " bounds=[(250.0, 450.0)] * n,\n", + " callback=callback_p2,\n", + " options={\"maxiter\": 200, \"ftol\": 1e-15, \"gtol\": 1e-10},\n", + ")\n", + "\n", + "elapsed_total = time.time() - t_start\n", + "loss_final = scipy_objective_p2(result_p2.x)[0]\n", + "loss_history_p2.append(loss_final)\n", "T_init_recovered = result_p2.x\n", "\n", "print(f\"\\nOptimization finished: {result_p2.nit} iterations, {elapsed_total:.1f}s\")\n", - "print(f\"Loss: {loss0:.2f} → {loss_final:.4f}\")\n", + "print(f\"Loss: {loss0_p2:.2f} → {loss_final:.4f}\")\n", "print(f\"T_init correlation: {np.corrcoef(T_init_true, T_init_recovered)[0, 1]:.4f}\")\n", "print(\"\\nCost comparison per iteration:\")\n", "print(\n", - " f\" Finite differences: {n + 1} forward solves = ~{(n + 1) * elapsed_total / result_p2.nfev:.1f}s\"\n", + " f\" Finite differences: {n + 1} forward solves = \"\n", + " f\"~{(n + 1) * elapsed_total / result_p2.nfev:.1f}s\"\n", ")\n", "print(\n", - " f\" Reverse-mode AD: 2 solves (fwd+rev) = ~{2 * elapsed_total / result_p2.nfev:.2f}s\"\n", + " f\" Reverse-mode AD: 2 solves (fwd+rev) = \"\n", + " f\"~{2 * elapsed_total / result_p2.nfev:.2f}s\"\n", ")" ] }, { "cell_type": "code", "execution_count": null, - "id": "fhj5dga2nks", + "id": "44fd35ce4a54", "metadata": {}, "outputs": [], "source": [ @@ -656,8 +727,6 @@ " ax.set_ylabel(\"y [mm]\")\n", "\n", "# --- Bottom row: diagnostics ---\n", - "\n", - "# Recovery error\n", "error_p2 = np.abs(T_init_recovered - T_init_true).reshape(ny, nx)\n", "im_err = axes[1, 0].imshow(\n", " error_p2, origin=\"lower\", cmap=\"Blues\", extent=extent, aspect=\"auto\"\n", @@ -669,7 +738,6 @@ "axes[1, 0].set_ylabel(\"y [mm]\")\n", "plt.colorbar(im_err, ax=axes[1, 0], label=\"Error [K]\", shrink=0.85)\n", "\n", - "# Scatter: true vs recovered\n", "axes[1, 1].scatter(T_init_true, T_init_recovered, s=3, alpha=0.5, c=\"steelblue\")\n", "lims = [vmin_init - 5, vmax_init + 5]\n", "axes[1, 1].plot(lims, lims, \"k--\", alpha=0.5, label=\"perfect recovery\")\n", @@ -682,7 +750,6 @@ "axes[1, 1].set_aspect(\"equal\")\n", "axes[1, 1].grid(True, alpha=0.3)\n", "\n", - "# Convergence\n", "axes[1, 2].semilogy(loss_history_p2, \"k.-\", linewidth=1.5)\n", "axes[1, 2].set_xlabel(\"Checkpoint\")\n", "axes[1, 2].set_ylabel(\"Loss\")\n", @@ -701,197 +768,37 @@ }, { "cell_type": "markdown", - "id": "9l3hx8hmg0w", - "metadata": {}, - "source": [ - "With 2 parameters, finite differences are still practical. With 900, reverse-mode\n", - "AD is ~450× faster. The gap only widens on production meshes. But so far we've been\n", - "calling `apply` and `vector_jacobian_product` manually — can we do better?" - ] - }, - { - "cell_type": "markdown", - "id": "v1urnmbjtho", - "metadata": {}, - "source": [ - "## Part 3: End-to-end JAX autodiff through a Fortran solver\n", - "\n", - "With [`tesseract-jax`](https://github.com/pasteurlabs/tesseract-jax),\n", - "the Tesseract becomes a JAX primitive. `jax.grad` just works — through six layers:\n", - "\n", - "```\n", - "jax.grad (Python)\n", - " └─ JAX reverse-mode AD\n", - " └─ apply_tesseract (JAX primitive)\n", - " └─ HTTP/JSON call to Tesseract container\n", - " └─ vector_jacobian_product endpoint\n", - " └─ Enzyme reverse-mode AD (LLVM IR)\n", - " └─ Fortran solver (thermal_2d_solve)\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "yj2fdd4b1mt", - "metadata": {}, - "outputs": [], - "source": [ - "import jax\n", - "import jax.numpy as jnp\n", - "from tesseract_jax import apply_tesseract\n", - "\n", - "# Serve both Tesseracts (they stay alive for the rest of the notebook)\n", - "enzyme_tess = Tesseract.from_image(\"enzyme-thermal-2d:latest\")\n", - "enzyme_tess.serve()\n", - "\n", - "jax_tess = Tesseract.from_image(\"jax-thermal-2d:latest\")\n", - "jax_tess.serve()\n", - "\n", - "# Build inputs as JAX arrays (required by apply_tesseract)\n", - "jax_inputs = {\n", - " \"T_init\": jnp.full(n, T_inf, dtype=jnp.float64),\n", - " \"Q\": jnp.zeros(n, dtype=jnp.float64),\n", - " \"nx\": nx,\n", - " \"ny\": ny,\n", - " \"n_steps\": n_steps,\n", - " \"k0\": jnp.float64(45.0),\n", - " \"k1\": jnp.float64(-0.02),\n", - " \"rho\": jnp.float64(rho),\n", - " \"cp\": jnp.float64(cp),\n", - " \"h_conv\": jnp.float64(h_conv),\n", - " \"T_inf\": jnp.float64(T_inf),\n", - " \"T_hot\": jnp.float64(T_hot),\n", - " \"Lx\": jnp.float64(Lx),\n", - " \"Ly\": jnp.float64(Ly),\n", - " \"dt\": jnp.float64(dt),\n", - "}\n", - "\n", - "# The Fortran solver is now a JAX-differentiable function\n", - "T_final = apply_tesseract(enzyme_tess, jax_inputs)[\"T_final\"]\n", - "print(\n", - " f\"Forward pass through Fortran solver: T range [{T_final.min():.2f}, {T_final.max():.2f}]\"\n", - ")\n", - "print(f\"Type: {type(T_final)} — it's a JAX array\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "7ocuoxl2jc3", + "id": "b8bf0b54853e", "metadata": {}, - "outputs": [], "source": [ - "# Define a loss function that mixes local JAX ops with a remote Fortran solver.\n", - "# jax.grad differentiates through all of it, including the HTTP call to Enzyme.\n", - "\n", - "\n", - "def loss_fn(k0, k1, tesseract):\n", - " \"\"\"Sensor misfit loss. Calls a Fortran solver via apply_tesseract.\"\"\"\n", - " inputs = {**jax_inputs, \"k0\": k0, \"k1\": k1}\n", - " T_pred = apply_tesseract(tesseract, inputs)[\"T_final\"]\n", - " residuals = T_pred[sensor_indices] - jnp.array(T_obs)\n", - " return 0.5 * jnp.sum(residuals**2)\n", - "\n", - "\n", - "k0_test = jnp.float64(60.0)\n", - "k1_test = jnp.float64(0.01)\n", - "\n", - "# Enzyme backend: JAX AD → HTTP → Enzyme AD → Fortran\n", - "loss_enzyme, (dk0_enzyme, dk1_enzyme) = jax.value_and_grad(loss_fn, argnums=(0, 1))(\n", - " k0_test, k1_test, enzyme_tess\n", - ")\n", - "print(\"Enzyme backend (Fortran):\")\n", - "print(f\" loss = {loss_enzyme:.4f}\")\n", - "print(f\" ∂loss/∂k0 = {dk0_enzyme:.6f}\")\n", - "print(f\" ∂loss/∂k1 = {dk1_enzyme:.6f}\")\n", - "\n", - "# JAX backend: JAX AD → HTTP → jax.vjp → XLA\n", - "loss_jax, (dk0_jax, dk1_jax) = jax.value_and_grad(loss_fn, argnums=(0, 1))(\n", - " k0_test, k1_test, jax_tess\n", - ")\n", - "print(\"\\nJAX backend (Python):\")\n", - "print(f\" loss = {loss_jax:.4f}\")\n", - "print(f\" ∂loss/∂k0 = {dk0_jax:.6f}\")\n", - "print(f\" ∂loss/∂k1 = {dk1_jax:.6f}\")\n", - "\n", - "print(\n", - " f\"\\nGradient agreement: Δdk0 = {abs(dk0_enzyme - dk0_jax):.2e}, \"\n", - " f\"Δdk1 = {abs(dk1_enzyme - dk1_jax):.2e}\"\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "t7ybs40pyc", - "metadata": {}, - "outputs": [], - "source": [ - "# Full optimization loop using jax.value_and_grad.\n", - "# The optimizer just sees a JAX function.\n", - "\n", - "k0_opt_jax = jnp.float64(60.0)\n", - "k1_opt_jax = jnp.float64(0.01)\n", - "lr = jnp.float64(0.5)\n", - "\n", - "loss_history_p3 = []\n", - "\n", - "grad_fn = jax.value_and_grad(loss_fn, argnums=(0, 1))\n", - "\n", - "print(\"Gradient descent through Fortran solver via tesseract-jax\")\n", - "print(f\"{'iter':>4s} {'loss':>10s} {'k0':>8s} {'k1':>10s}\")\n", - "print(\"-\" * 40)\n", - "\n", - "for i in range(20):\n", - " loss_val, (dk0, dk1) = grad_fn(k0_opt_jax, k1_opt_jax, enzyme_tess)\n", - " loss_history_p3.append(float(loss_val))\n", + "## What just happened\n", "\n", - " k0_opt_jax = jnp.clip(k0_opt_jax - lr * dk0, 5.0, 80.0)\n", - " k1_opt_jax = jnp.clip(k1_opt_jax - lr * dk1, -0.08, 0.08)\n", + "Each `jax.value_and_grad` call above triggered this chain:\n", "\n", - " if i % 5 == 0 or i == 19:\n", - " print(f\"{i:4d} {loss_val:10.4f} {k0_opt_jax:8.4f} {k1_opt_jax:10.6f}\")\n", + "| Layer | Technology | Role |\n", + "|-------|-----------|------|\n", + "| Optimizer | SciPy L-BFGS-B | Quasi-Newton update loop |\n", + "| AD framework | JAX reverse-mode | Propagates cotangents |\n", + "| Tesseract bridge | `tesseract-jax` | Registers JAX primitive, dispatches HTTP calls |\n", + "| Transport | HTTP + JSON | Crosses the process/container boundary |\n", + "| AD engine | Enzyme (LLVM pass) | Generates the VJP from compiled Fortran IR |\n", + "| Solver | Fortran 90 | `thermal_2d_solve` |\n", "\n", - "print(f\"\\nRecovered: k0={float(k0_opt_jax):.4f}, k1={float(k1_opt_jax):.6f}\")\n", - "print(f\"True: k0={k0_true:.4f}, k1={k1_true:.6f}\")" + "The Fortran solver was never modified. Enzyme differentiated it from the compiled\n", + "LLVM IR, and Tesseract made it callable — and differentiable — from JAX. The\n", + "optimization code is identical for 2 parameters and for 900; only the size of the\n", + "parameter vector changed." ] }, { "cell_type": "code", "execution_count": null, - "id": "vn8dmjqfs9k", + "id": "babc4d54e5a1", "metadata": {}, "outputs": [], "source": [ - "# Clean up\n", - "enzyme_tess.teardown()\n", - "jax_tess.teardown()" - ] - }, - { - "cell_type": "markdown", - "id": "6upzkt20zux", - "metadata": {}, - "source": [ - "## What just happened\n", - "\n", - "A single `jax.value_and_grad` call triggered this chain:\n", - "\n", - "| Layer | Technology | Role |\n", - "|-------|-----------|------|\n", - "| Optimizer | Python / JAX | Gradient descent loop |\n", - "| AD framework | JAX reverse-mode | Propagates cotangents |\n", - "| Tesseract bridge | `tesseract-jax` | Registers JAX primitive, dispatches HTTP calls |\n", - "| Transport | HTTP + JSON | Crosses process/container boundary |\n", - "| AD engine | Enzyme (LLVM pass) | Generates VJP from compiled Fortran IR |\n", - "| Solver | Fortran 90 | `thermal_2d_solve` |\n", - "\n", - "Swapping `enzyme_tess` for `jax_tess` produces the same gradients — the\n", - "optimization code doesn't change.\n", - "\n", - "The Fortran solver was never modified. Enzyme differentiated it from the compiled\n", - "LLVM IR. Tesseract made it callable — and differentiable — from JAX." + "# Tear down the Tesseract to free resources.\n", + "enzyme_tess.teardown()" ] } ], @@ -902,8 +809,7 @@ "name": "python3" }, "language_info": { - "name": "python", - "version": "3.11.0" + "name": "python" } }, "nbformat": 4, diff --git a/demo/enzyme_thermal_2d/requirements.txt b/demo/enzyme_thermal_2d/requirements.txt new file mode 100644 index 00000000..3bb52f9b --- /dev/null +++ b/demo/enzyme_thermal_2d/requirements.txt @@ -0,0 +1,5 @@ +jax[cpu] +matplotlib +numpy +scipy +tesseract-jax diff --git a/demo/enzyme_thermal_2d/tesseract_api.py b/demo/enzyme_thermal_2d/tesseract_api.py index 6f994cb2..437ac9e5 100644 --- a/demo/enzyme_thermal_2d/tesseract_api.py +++ b/demo/enzyme_thermal_2d/tesseract_api.py @@ -25,7 +25,7 @@ from pydantic import BaseModel, Field, model_validator from typing_extensions import Self -from tesseract_core.runtime import Array, Differentiable, Float64 +from tesseract_core.runtime import Array, Differentiable, Float64, ShapeDType # -- Shared library loading ------------------------------------------------ @@ -183,27 +183,23 @@ class InputSchema(BaseModel): ) dt: Differentiable[Float64] = Field( default=0.01, - description="Time step size [s].", - gt=0.0, + description="Time step size [s]. Must be > 0.", ) # Domain geometry Lx: Differentiable[Float64] = Field( default=0.1, - description="Domain length in x [m].", - gt=0.0, + description="Domain length in x [m]. Must be > 0.", ) Ly: Differentiable[Float64] = Field( default=0.05, - description="Domain length in y [m].", - gt=0.0, + description="Domain length in y [m]. Must be > 0.", ) # Material properties k0: Differentiable[Float64] = Field( default=45.0, - description="Base thermal conductivity [W/(m*K)]. k(T) = k0 + k1*T.", - gt=0.0, + description="Base thermal conductivity [W/(m*K)]. k(T) = k0 + k1*T. Must be > 0.", ) k1: Differentiable[Float64] = Field( default=-0.01, @@ -214,20 +210,20 @@ class InputSchema(BaseModel): ) rho: Differentiable[Float64] = Field( default=7850.0, - description="Density [kg/m^3].", - gt=0.0, + description="Density [kg/m^3]. Must be > 0.", ) cp: Differentiable[Float64] = Field( default=460.0, - description="Specific heat capacity [J/(kg*K)].", - gt=0.0, + description="Specific heat capacity [J/(kg*K)]. Must be > 0.", ) # Boundary conditions h_conv: Differentiable[Float64] = Field( default=25.0, - description="Convective heat transfer coefficient at top boundary [W/(m^2*K)].", - gt=0.0, + description=( + "Convective heat transfer coefficient at top boundary " + "[W/(m^2*K)]. Must be > 0." + ), ) T_inf: Differentiable[Float64] = Field( default=293.15, @@ -249,6 +245,8 @@ class InputSchema(BaseModel): @model_validator(mode="after") def check_array_sizes(self) -> Self: """Verify T_init and Q have the correct size.""" + if isinstance(self.T_init, ShapeDType): + return self # skip during abstract_eval expected = self.nx * self.ny if len(self.T_init) != expected: raise ValueError( @@ -262,11 +260,16 @@ def check_array_sizes(self) -> Self: @model_validator(mode="after") def check_stability(self) -> Self: - """Check CFL stability for the explicit scheme. + """Check positivity and CFL stability for the explicit scheme. For temperature-dependent conductivity, use k_max = k0 + k1*T_hot (conservative estimate with the hottest expected temperature). """ + if isinstance(self.dt, ShapeDType): + return self # skip during abstract_eval + for name in ("dt", "Lx", "Ly", "k0", "rho", "cp", "h_conv"): + if getattr(self, name) <= 0: + raise ValueError(f"{name} must be > 0, got {getattr(self, name)}.") dx = self.Lx / (self.nx - 1) dy = self.Ly / (self.ny - 1) k_max = self.k0 + self.k1 * self.T_hot @@ -326,6 +329,12 @@ def apply(inputs: InputSchema) -> OutputSchema: return OutputSchema(T_final=T_final) +def abstract_eval(abstract_inputs): + """Calculate output shape from input shapes (required for tesseract-jax).""" + T_init_shape = abstract_inputs.T_init + return {"T_final": ShapeDType(shape=T_init_shape.shape, dtype=T_init_shape.dtype)} + + # -- Optional endpoints (AD via Enzyme) ------------------------------------ diff --git a/docs/blog/2026-05-15-fortran-enzyme-autodiff.md b/docs/blog/2026-05-15-fortran-enzyme-autodiff.md index 26acddc2..5ff16372 100644 --- a/docs/blog/2026-05-15-fortran-enzyme-autodiff.md +++ b/docs/blog/2026-05-15-fortran-enzyme-autodiff.md @@ -1,18 +1,18 @@ --- orphan: true -og:title: "Differentiable Fortran in JAX via LFortran and Enzyme" +og:title: "Differentiable Fortran via LFortran and Enzyme" og:description: "How we duct-taped a compiler pipeline together to get exact gradients out of a Fortran thermal solver, then used it to solve real inverse problems from Python." blog_date: "2026-05-15" blog_author: "@dionhaefner" -blog_title: "Differentiable Fortran in JAX via LFortran and Enzyme" +blog_title: "Differentiable Fortran via LFortran and Enzyme" blog_description: "How we duct-taped a compiler pipeline together to get exact gradients out of a Fortran thermal solver, then used it to solve real inverse problems from Python." --- -# Differentiable Fortran in JAX via LFortran and Enzyme +# Differentiable Fortran via LFortran and Enzyme What if you could do autodiff through existing Fortran, C, or C++ simulation code, embed it into JAX and torch, and use it as a high-performance differentiable physics engine? Turns out, you can. -Decades of validated physics code, climate models, CFD, aerospace, nuclear, sit behind a wall that modern ML pipelines can't cross: no gradients. The usual answer is to rewrite it all in JAX or PyTorch. The alternative we explore here is to leave the code where it is and get exact gradients out anyway, thanks to some LLVM-level magic. [Enzyme](https://enzyme.mit.edu/) applies AD at the LLVM IR level, so we can differentiate any code that compiles to LLVM. +Decades of validated physics code within CFD, climate, aerospace, nuclear, sit behind a wall that modern ML pipelines can't cross: no gradients. The usual answer is to rewrite it all in JAX or PyTorch. The alternative we explore here is to leave the code where it is and get exact gradients out anyway, thanks to some LLVM-level magic. [Enzyme](https://enzyme.mit.edu/) applies AD at the LLVM IR level, so we can differentiate any code that compiles to LLVM. So all we need is to duct-tape [LFortran](https://lfortran.org/), LLVM, and Enzyme together, point the result at a Fortran thermal solver, and get exact gradients out the other end. From there, [Tesseract](https://github.com/pasteurlabs/tesseract-core) (whose blog you're reading) wraps the result as a custom [JAX](https://jax.readthedocs.io/en/latest/) primitive, so a Fortran solver becomes a differentiable layer in arbitrary JAX code. Sounds easy, right? @@ -100,7 +100,7 @@ There are six steps: **1. Fortran → LLVM IR** via LFortran: ```bash -lfortran --show-llvm --no-array-bounds-checking thermal_2d.f90 > thermal_2d.ll +$ lfortran --show-llvm --no-array-bounds-checking thermal_2d.f90 > thermal_2d.ll ``` LFortran is a modern Fortran compiler, and the reason we reached for it is that it emits remarkably clean LLVM IR. Arrays come out as plain pointers with the usual GEP/load/store patterns, much like you'd get from C, instead of the multi-field descriptor structs and runtime library calls that Flang produces. That turns out to matter a lot, because Enzyme has to trace through every single memory access to figure out what's active, and it has a far easier time with plain pointer arithmetic than with opaque `fir.box` descriptors. The catch is that LFortran is still maturing, so not every Fortran feature is supported yet (here's the [compilation status](https://lfortran.org/progress/)) and your code has to stay within what it can handle. @@ -108,7 +108,7 @@ LFortran is a modern Fortran compiler, and the reason we reached for it is that **2. Optimize the IR:** ```bash -opt -O1 -S thermal_2d.ll -o thermal_2d_opt.ll +$ opt -O1 -S thermal_2d.ll -o thermal_2d_opt.ll ``` Notice that's `-O1`, not `-O3`! Our first pipeline used `-O3` here, and the forward pass worked perfectly, so we moved on. The VJP didn't, though. It returned NaN on certain inputs, and it took us a few hours to track down why. What was happening is that LLVM's aggressive vectorization and code-motion passes at `-O3` produce IR patterns Enzyme mishandles during reverse-mode analysis, and in our case it bit specifically when adjacent cell temperatures were equal and intermediate terms canceled out, which can turn into a division by zero once things get rearranged. We settled on keeping the pre-Enzyme optimization mild and saving `-O3` for after the AD pass instead (that's step 6). If you build something like this, our advice is to test the gradients early and often. @@ -116,7 +116,7 @@ Notice that's `-O1`, not `-O3`! Our first pipeline used `-O3` here, and the forw **3. Compile the C wrapper to LLVM IR:** ```bash -clang -emit-llvm -S -O1 wrapper.c -o wrapper.ll +$ clang -emit-llvm -S -O1 wrapper.c -o wrapper.ll ``` A thin C wrapper bridges Fortran's by-pointer ABI over to a C-callable interface that Enzyme can annotate. It declares three entry points, `thermal_2d_forward`, `thermal_2d_vjp`, and `thermal_2d_jvp`, and uses Enzyme's `__enzyme_autodiff` and `__enzyme_fwddiff` intrinsics to mark which arguments should get shadow (gradient) buffers. Here's the core of the VJP entry point: @@ -149,13 +149,13 @@ This is also where the work arrays get allocated on the heap, sidestepping the ` **4. Link the IR modules:** ```bash -llvm-link wrapper.ll thermal_2d_opt.ll -S -o combined.ll +$ llvm-link wrapper.ll thermal_2d_opt.ll -S -o combined.ll ``` **5. Run the Enzyme AD pass:** ```bash -opt --load-pass-plugin=LLVMEnzyme-19.so -passes=enzyme -S combined.ll -o ad.ll +$ opt --load-pass-plugin=LLVMEnzyme-19.so -passes=enzyme -S combined.ll -o ad.ll ``` This is the step that does the real work, and where Enzyme analyzes the LLVM IR and synthesizes forward and reverse-mode derivative code. For reverse mode, it uses a store-all (tape) strategy, caching intermediate values at each time step. When it works, it's genuinely impressive — you get an adjoint of your entire time-stepping loop for free. When it doesn't, you're reading LLVM IR diffs at 2 AM wondering where your life went wrong (see [What's next](#whats-next-and-what-wed-do-differently)). @@ -163,8 +163,8 @@ This is the step that does the real work, and where Enzyme analyzes the LLVM IR **6. Optimize and compile to a shared library:** ```bash -opt -O3 -S ad.ll -o ad_opt.ll -clang -shared -O3 ad_opt.ll -o libthermal_2d_ad.so -lm +$ opt -O3 -S ad.ll -o ad_opt.ll +$ clang -shared -O3 ad_opt.ll -o libthermal_2d_ad.so -lm ``` Out comes a single `.so` file with three entry points you can call from Python via ctypes, one each for forward evaluation, the JVP, and the VJP. The whole pipeline runs during `tesseract build` and takes about 30 seconds end to end. @@ -193,8 +193,8 @@ Correct gradients are only worth something once you put them to work, whether th To wire the Enzyme gradients into JAX, the solver has to look like a differentiable JAX primitive, and this is more or less exactly what Tesseract was built for. It wraps the compiled library, with LFortran, LLVM 19, Enzyme, and the whole toolchain inside it, into a container that exposes autodiff endpoints, so that `jax.value_and_grad` can route its VJP calls straight to the Enzyme-generated code. From there it's just a matter of building the container and serving it over HTTP: ```bash -tesseract build demo/enzyme_thermal_2d/ -tesseract serve enzyme-thermal-2d +$ tesseract build demo/enzyme_thermal_2d/ +$ tesseract serve enzyme-thermal-2d ``` With that running, it's finally time to point some real optimization problems at it and find out whether all the effort actually paid off. @@ -291,6 +291,8 @@ Every component differentiates itself with whatever AD is native to it, and Tess Because Enzyme works at the LLVM IR level, none of this is Fortran-specific. The same pipeline should apply to C, C++, Rust, or any language with an LLVM frontend, which we graciously leave as an exercise for the reader. +(whats-next-and-what-wed-do-differently)= + ## What's next (and what we'd do differently) A reality check before getting carried away: this is a 220-line solver written specifically to fit the pipeline. Enzyme itself handles loops, conditionals, and function calls just fine, and the Enzyme team has run it on much larger codes, including [BUDE molecular docking](https://enzyme.mit.edu/getting_started/UsingEnzyme/#bude) and [LULESH hydrodynamics](https://enzyme.mit.edu/getting_started/UsingEnzyme/#lulesh), with derivative overhead that usually lands somewhere between 1x and 4x. Still, "works on LULESH" and "works on your 30-year-old Fortran codebase" are two very different claims. diff --git a/examples/enzyme_ad/test_cases/test_apply.json b/examples/enzyme_ad/test_cases/test_apply.json new file mode 100644 index 00000000..602b6014 --- /dev/null +++ b/examples/enzyme_ad/test_cases/test_apply.json @@ -0,0 +1,34 @@ +{ + "endpoint": "apply", + "expected_outputs": { + "T_out": { + "object_type": "array", + "shape": [6], + "dtype": "float64", + "data": { + "buffer": [10.0, 25.0064, 79.9848, 40.0024, 15.0024, 5.0], + "encoding": "json" + } + } + }, + "expected_exception": null, + "expected_exception_regex": null, + "atol": 1e-8, + "rtol": 1e-5, + "payload": { + "inputs": { + "T_in": { + "object_type": "array", + "shape": [6], + "dtype": "float64", + "data": { + "buffer": [10.0, 25.0, 80.0, 40.0, 15.0, 5.0], + "encoding": "json" + } + }, + "alpha": 0.01, + "dx": 0.25, + "dt": 0.001 + } + } +} diff --git a/examples/enzyme_ad/test_cases_inputs/example_checkgradients_input.json b/examples/enzyme_ad/test_cases_inputs/example_checkgradients_input.json new file mode 100644 index 00000000..b771ca28 --- /dev/null +++ b/examples/enzyme_ad/test_cases_inputs/example_checkgradients_input.json @@ -0,0 +1,16 @@ +{ + "inputs": { + "T_in": { + "object_type": "array", + "shape": [6], + "dtype": "float64", + "data": { + "buffer": [10.0, 25.0, 80.0, 40.0, 15.0, 5.0], + "encoding": "json" + } + }, + "alpha": 0.01, + "dx": 0.25, + "dt": 0.001 + } +} diff --git a/tests/endtoend_tests/test_examples.py b/tests/endtoend_tests/test_examples.py index 48bdd8fd..5afb5377 100644 --- a/tests/endtoend_tests/test_examples.py +++ b/tests/endtoend_tests/test_examples.py @@ -100,6 +100,7 @@ class Config: ), "meshstats_finitediff": Config(check_gradients=True), "fortran_heat": Config(), + "enzyme_ad": Config(check_gradients=True), "conda": Config(), "required_files": Config(input_path="input"), "file_io": Config(input_path="test_cases/testdata", output_path="__tmp_path__"), From d8235a7b7ea986491a11a3a3d6484127436e8abe Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dion=20H=C3=A4fner?= Date: Tue, 2 Jun 2026 13:26:39 +0200 Subject: [PATCH 08/24] doc: add enzyme_thermal_2d demo to docs toctree conf.py copies every demo/*/demo.ipynb into docs/content/demo/, so the new enzyme_thermal_2d demo notebook needs a toctree entry or the docs build fails ("document isn't included in any toctree", with warnings treated as errors). Add it to the demos toctree and a description card. Verified locally: `SPHINXOPTS="-W" make html` succeeds with no warnings. Co-Authored-By: Claude Opus 4.8 (1M context) --- docs/content/demo/demo.md | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/docs/content/demo/demo.md b/docs/content/demo/demo.md index 8b05b53c..5ed8c48b 100644 --- a/docs/content/demo/demo.md +++ b/docs/content/demo/demo.md @@ -10,6 +10,7 @@ data-assimilation.ipynb lorenz_tesseract.md cfd-optimization.ipynb fem-shape-optimization.ipynb +enzyme_thermal_2d.ipynb JAX Rosenbrock Minimization PyTorch Rosenbrock Minimization JAX RBF Fitting @@ -58,6 +59,11 @@ Optimize the initial velocity field of a 2D Navier-Stokes simulation so its vort Compose a geometry Tesseract (PyVista, finite-difference gradients) with a FEM Tesseract (jax-fem) to optimize structural bar configurations for minimum compliance. ::: +:::{grid-item-card} Differentiable Fortran (Enzyme) +:link: enzyme_thermal_2d.html + +Solve two inverse heat-transfer problems by differentiating a Fortran solver end-to-end: Enzyme generates exact derivatives at the LLVM IR level, and `jax.value_and_grad` drives the optimization through Tesseract-JAX. +::: :::: From b0d955d499045009018bef4b7d8ec66bbb8dc053 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dion=20H=C3=A4fner?= Date: Tue, 2 Jun 2026 13:32:57 +0200 Subject: [PATCH 09/24] doc: make Tesseract-JAX the through-line in the Enzyme blog post Realign the blog post with the rewritten demo notebook, which drives both inverse problems with jax.value_and_grad via Tesseract-JAX rather than the manual vector_jacobian_product API: - Introduce apply_tesseract + a solve() helper up front, and use jax.value_and_grad in the Part 1 snippet (matching demo.ipynb). - Fold the standalone "JAX integration via Tesseract-JAX" section into a short wrap-up, keeping the swap-for-pure-JAX and layers-of-indirection points without re-introducing the code as if it were new. - Note the Tikhonov regularization the forensics problem now uses. - Soften result claims to match what the demo reproduces: k1 is weakly identifiable from 9 noisy sensors (k0 recovered well), and the 900-element field correlation is ~0.98 rather than ">0.99". Verified locally: `SPHINXOPTS="-W" make html` succeeds with no warnings. Co-Authored-By: Claude Opus 4.8 (1M context) --- .../2026-05-15-fortran-enzyme-autodiff.md | 70 +++++++------------ 1 file changed, 25 insertions(+), 45 deletions(-) diff --git a/docs/blog/2026-05-15-fortran-enzyme-autodiff.md b/docs/blog/2026-05-15-fortran-enzyme-autodiff.md index 5ff16372..22a77326 100644 --- a/docs/blog/2026-05-15-fortran-enzyme-autodiff.md +++ b/docs/blog/2026-05-15-fortran-enzyme-autodiff.md @@ -190,55 +190,54 @@ Error is worst at both ends of the $\epsilon$ range and best in the middle, the Correct gradients are only worth something once you put them to work, whether that means dropping them into an optimizer, solving a real inverse problem, or composing them with other differentiable code. -To wire the Enzyme gradients into JAX, the solver has to look like a differentiable JAX primitive, and this is more or less exactly what Tesseract was built for. It wraps the compiled library, with LFortran, LLVM 19, Enzyme, and the whole toolchain inside it, into a container that exposes autodiff endpoints, so that `jax.value_and_grad` can route its VJP calls straight to the Enzyme-generated code. From there it's just a matter of building the container and serving it over HTTP: +To wire the Enzyme gradients into JAX, the solver has to look like a differentiable JAX primitive, and this is more or less exactly what Tesseract was built for. It wraps the compiled library, with LFortran, LLVM 19, Enzyme, and the whole toolchain inside it, into a container that exposes autodiff endpoints. Building and serving it is two commands: ```bash $ tesseract build demo/enzyme_thermal_2d/ $ tesseract serve enzyme-thermal-2d ``` -With that running, it's finally time to point some real optimization problems at it and find out whether all the effort actually paid off. +The last piece is [Tesseract-JAX](https://github.com/pasteurlabs/tesseract-jax), which promotes a served Tesseract to a proper JAX primitive. Wrap a call in `apply_tesseract` and the Fortran solver becomes an ordinary differentiable JAX function: `jax.value_and_grad` routes its VJP calls straight through the HTTP boundary to the Enzyme-generated code, and the optimizer never has to know. + +```python +from tesseract_jax import apply_tesseract + +def solve(k0, k1): + inputs = {**base_inputs, "k0": k0, "k1": k1} + return apply_tesseract(enzyme_tess, inputs)["T_final"] # differentiable +``` + +With that in place, it's finally time to point some real optimization problems at it and find out whether all the effort actually paid off. ### Scalar calibration: recovering 2 material parameters For a sanity check, the setup stays simple. A steel plate is heating up, there are thermocouple readings at 9 sensor locations, and the plate's material properties are unknown. The question is whether $k_0$ (base conductivity) and $k_1$ (its temperature coefficient) can be recovered from those sparse, noisy readings. -To keep the test honest, the "observed" data is generated synthetically: run the solver with known true values ($k_0 = 45$, $k_1 = -0.02$), sample at the sensor locations, and add 0.5 K of Gaussian noise on top. The optimizer then starts from a deliberately bad guess, 33% off on $k_0$ and the wrong sign entirely on $k_1$, and the whole thing goes to L-BFGS-B. A single VJP call hands back gradients with respect to both parameters at once, and the optimizer is none the wiser that they came from a compiled Fortran solver differentiated by an LLVM pass. +To keep the test honest, the "observed" data is generated synthetically: run the solver with known true values ($k_0 = 45$, $k_1 = -0.02$), sample at the sensor locations, and add 0.5 K of Gaussian noise on top. The optimizer then starts from a deliberately bad guess, 33% off on $k_0$ and the wrong sign entirely on $k_1$, and the whole thing goes to L-BFGS-B. The loss is a plain JAX function that happens to call the Fortran solver; `jax.value_and_grad` hands back both the loss and its gradient, propagating the cotangent through the HTTP boundary into Enzyme's reverse-mode pass. The optimizer is none the wiser that the gradients came from a compiled Fortran solver differentiated by an LLVM pass. ```python -def objective_and_gradient(params, tesseract): +def loss_fn(params): k0, k1 = params - result = tesseract.apply(inputs=make_inputs(k0, k1)) - T_pred = np.array(result["T_final"]) - + T_pred = solve(k0, k1) # apply_tesseract under the hood residuals = T_pred[sensor_indices] - T_obs - loss = 0.5 * np.sum(residuals**2) - - # Cotangent: residuals at sensor locations, zero elsewhere - cotangent = np.zeros(n, dtype=np.float64) - cotangent[sensor_indices] = residuals - - # One VJP call → gradients w.r.t. both k0 and k1 - vjp = tesseract.vector_jacobian_product( - inputs=make_inputs(k0, k1), - vjp_inputs=["k0", "k1"], - vjp_outputs=["T_final"], - cotangent_vector={"T_final": cotangent}, - ) - return loss, np.array([vjp["k0"], vjp["k1"]]) + return 0.5 * jnp.sum(residuals**2) + +# One reverse sweep → gradients w.r.t. both k0 and k1 +value_and_grad = jax.value_and_grad(loss_fn) +loss, grad = value_and_grad(jnp.array([60.0, 0.01])) ``` Scalar calibration convergence: loss, k0, k1 Temperature field comparison: initial guess, recovered, ground truth, error -L-BFGS-B converges in about 15 iterations and recovers both parameters to within the noise floor. The more interesting question is what happens once the method gets pushed a lot harder. +L-BFGS-B converges in about 20 iterations. It nails $k_0$ to within a few percent; $k_1$ lands a bit further out (the temperature field is only weakly sensitive to it, so it's poorly constrained by 9 noisy sensors), but the recovered field still matches the observations. The more interesting question is what happens once the method gets pushed a lot harder. ### Thermal forensics: recovering a 900-element initial temperature field Imagine a steel plate that went through some unmonitored heating event, maybe a laser pulse, maybe a localized defect, nobody knows. Five seconds later you get to measure temperatures at 100 sensor locations, and the question is whether you can reconstruct what the initial temperature distribution must have looked like. -The true initial condition has two Gaussian hot spots sitting on a warm background. So the ask is 900 unknowns out of 100 noisy observations, run backwards through a nonlinear PDE. This is exactly the regime where reverse-mode AD (or its cousin the adjoint method) stops being a nice-to-have and becomes essential: +The true initial condition has two Gaussian hot spots sitting on a warm background. So the ask is 900 unknowns out of 100 noisy observations, run backwards through a nonlinear PDE. A small Tikhonov term (penalizing departure from the ambient prior) regularizes the otherwise ill-posed inversion, and since the loss is just a JAX function, that term is one extra line that `jax.value_and_grad` differentiates for free. The optimization is the same `jax.value_and_grad` + L-BFGS-B as before; only the parameter vector grows from 2 to 900. This is exactly the regime where reverse-mode AD (or its cousin the adjoint method) stops being a nice-to-have and becomes essential: | Method | Forward solves per iteration | | --------------------- | ---------------------------: | @@ -250,30 +249,11 @@ Finite differences would have to do 901 forward solves every iteration just to a Thermal forensics: recovering 900 initial temperature values from 100 sensors -And it works! L-BFGS-B finds both hot spots, gets their locations and magnitudes right, and the correlation between the recovered and true initial fields comes out above 0.99. Where it struggles is at the edges of the hot spots, which is exactly where the signal has had the most time to diffuse away. The reconstruction comes out a little smoothed compared to the truth, which is about what you'd expect from an ill-posed problem with diffusion in it, but it's honestly far better than a pipeline held together with shell scripts has any right to deliver. +And it works! L-BFGS-B finds both hot spots, gets their locations and magnitudes right, and the correlation between the recovered and true initial fields comes out around 0.98. Where it struggles is at the edges of the hot spots, which is exactly where the signal has had the most time to diffuse away. The reconstruction comes out a little smoothed compared to the truth, which is about what you'd expect from an ill-posed problem with diffusion in it, but it's honestly far better than a pipeline held together with shell scripts has any right to deliver. -That's `jax.grad` flowing all the way through compiled Fortran, without a single line of adjoint code written by hand. - -### JAX integration via Tesseract-JAX - -If you want, you can take this one step further with [Tesseract-JAX](https://github.com/pasteurlabs/tesseract-jax), which promotes the Tesseract to a proper JAX primitive. At that point `jax.value_and_grad` just works on it directly: - -```python -from tesseract_jax import apply_tesseract - -def loss_fn(k0, k1, tesseract): - inputs = {**base_inputs, "k0": k0, "k1": k1} - T_pred = apply_tesseract(tesseract, inputs)["T_final"] - residuals = T_pred[sensor_indices] - jnp.array(T_obs) - return 0.5 * jnp.sum(residuals**2) - -# jax.value_and_grad differentiates straight through the HTTP boundary -loss, (dk0, dk1) = jax.value_and_grad(loss_fn, argnums=(0, 1))( - jnp.float64(60.0), jnp.float64(0.01), enzyme_tess -) -``` +That's `jax.grad` flowing all the way through compiled Fortran, without a single line of adjoint code written by hand. The same `value_and_grad` call powered both inverse problems above; only the size of the parameter vector changed. -As far as JAX is concerned, the Fortran solver is just another differentiable function. You could swap `enzyme_tess` out for a pure-JAX reimplementation tomorrow and nothing in the optimization loop would change, only the container sitting behind the HTTP call. Whether you find that abstraction beautiful or horrifying probably comes down to how you feel about your gradients quietly traversing six layers of indirection on the way through (Python → JAX/XLA → HTTP → ctypes → Enzyme → Fortran). +And because the solver is just another JAX function behind `apply_tesseract`, you could swap `enzyme_tess` out for a pure-JAX reimplementation tomorrow and nothing in the optimization loop would change, only the container sitting behind the HTTP call. Whether you find that abstraction beautiful or horrifying probably comes down to how you feel about your gradients quietly traversing six layers of indirection on the way through (Python → JAX/XLA → HTTP → ctypes → Enzyme → Fortran). ## Where this could go From 23046cf17cd1637837556f987cc7947f73b5f837 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dion=20H=C3=A4fner?= Date: Tue, 2 Jun 2026 13:49:46 +0200 Subject: [PATCH 10/24] execute notebook --- demo/enzyme_thermal_2d/demo.ipynb | 249 ++++++++++++++++++++++++++---- 1 file changed, 220 insertions(+), 29 deletions(-) diff --git a/demo/enzyme_thermal_2d/demo.ipynb b/demo/enzyme_thermal_2d/demo.ipynb index f1847a60..e25df9a1 100644 --- a/demo/enzyme_thermal_2d/demo.ipynb +++ b/demo/enzyme_thermal_2d/demo.ipynb @@ -44,10 +44,27 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "id": "d1505e18eaec", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[2K \u001b[1;2m[\u001b[0m\u001b[34mi\u001b[0m\u001b[1;2m]\u001b[0m Building image \u001b[33m...\u001b[0m\n", + "\u001b[2K\u001b[37m⠸\u001b[0m \u001b[37mProcessing\u001b[0m\n", + "\u001b[1A\u001b[2K \u001b[1;2m[\u001b[0m\u001b[34mi\u001b[0m\u001b[1;2m]\u001b[0m Built image sh\u001b[1;92ma256:33ec\u001b[0m38a694cd, \u001b[1m[\u001b[0m\u001b[32m'enzyme-thermal-2d:1.0.0'\u001b[0m, \u001b[32m'enzyme-thermal-2d:latest'\u001b[0m\u001b[1m]\u001b[0m\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[\"enzyme-thermal-2d:1.0.0\", \"enzyme-thermal-2d:latest\"]\n" + ] + } + ], "source": [ "%%bash\n", "tesseract build ." @@ -55,7 +72,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "id": "fcc5e2141f85", "metadata": {}, "outputs": [], @@ -78,10 +95,18 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "id": "2bdf1ea4fd67", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Simulation: 500 steps x 0.05s = 25s total\n" + ] + } + ], "source": [ "# Grid and simulation parameters (fixed throughout)\n", "nx, ny = 30, 30\n", @@ -124,10 +149,19 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "id": "771e9a987964", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ground truth: k0=45.0, k1=-0.02\n", + "Temperature range: 297.61 K to 373.15 K\n" + ] + } + ], "source": [ "# True material properties (what we want to recover)\n", "k0_true = 45.0 # base conductivity [W/(m*K)]\n", @@ -169,10 +203,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "id": "7e544cbd0338", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of sensors: 9\n", + "Noise std: 0.5 K\n", + "Observed temperatures: [341.04 340.36 341.26 314.51 313.06 313.39 301.68 301.46 301.61]\n" + ] + } + ], "source": [ "# Place sensors on a regular grid in the interior (away from BCs)\n", "# This mimics a realistic thermocouple layout\n", @@ -202,10 +246,21 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "id": "904587d15cc3", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "

" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Visualize the ground truth and sensor locations\n", "fig, ax = plt.subplots(1, 1, figsize=(8, 4))\n", @@ -251,10 +306,19 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "id": "43111e1b97b5", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial loss = 409.1875\n", + "Gradient via Enzyme: dJ/dk0 = 27.526953, dJ/dk1 = 9510.217207\n" + ] + } + ], "source": [ "T_obs_jax = jnp.asarray(T_obs)\n", "\n", @@ -291,10 +355,42 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "id": "81fa6219dfdb", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial guess: k0=60.00, k1=0.0100, loss=409.1875\n", + " k0=49.5370, k1=-0.024209, loss=10.623775\n", + " k0=46.9414, k1=-0.032678, loss=4.835226\n", + " k0=48.0019, k1=-0.029202, loss=0.989078\n", + " k0=47.9192, k1=-0.029457, loss=0.961049\n", + " k0=47.9118, k1=-0.029464, loss=0.960913\n", + " k0=47.9059, k1=-0.029456, loss=0.960832\n", + " k0=47.8638, k1=-0.029372, loss=0.960316\n", + " k0=47.7726, k1=-0.029154, loss=0.959282\n", + " k0=47.5080, k1=-0.028466, loss=0.956421\n", + " k0=46.8954, k1=-0.026791, loss=0.950077\n", + " k0=45.6409, k1=-0.023246, loss=0.937793\n", + " k0=43.9279, k1=-0.018262, loss=0.922245\n", + " k0=42.8393, k1=-0.014951, loss=0.912410\n", + " k0=42.8101, k1=-0.014745, loss=0.910273\n", + " k0=42.9610, k1=-0.015156, loss=0.910138\n", + " k0=42.9937, k1=-0.015250, loss=0.910135\n", + " k0=42.9956, k1=-0.015255, loss=0.910135\n", + " k0=42.9956, k1=-0.015255, loss=0.910135\n", + " k0=42.9956, k1=-0.015255, loss=0.910135\n", + "\n", + "Optimization finished in 19 iterations\n", + " True: k0=45.0000, k1=-0.020000\n", + " Recovered: k0=42.9956, k1=-0.015255\n", + " Error: k0: 4.45%, k1: 23.72%\n" + ] + } + ], "source": [ "from scipy.optimize import minimize\n", "\n", @@ -355,10 +451,21 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "id": "e08c0b018c43", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "fig, axes = plt.subplots(1, 3, figsize=(14, 4))\n", "\n", @@ -405,10 +512,29 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "id": "977f62064249", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/var/folders/fk/g5ssrkz179z1mjmvqn1j3q1m0000gn/T/ipykernel_73719/639399457.py:61: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n", + " plt.tight_layout()\n" + ] + }, + { + "data": { + "image/png": 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scXbj8/LLLw+ad9BBB1XoZwEAUjVW+t10002uEWcga8xSnlS7lgslXte7f/vb31zDF4uTf/rTn9z3D4udffr00fz589W/f/84/cYAgEjO36WxhvgWJ4444gj99NNPpa5nDUTsfqE1Ppw4caKLOxZn7LrTXqdjx45uPWtU8s9//rPE8y1GPPbYYy4JGClL5lnMefDBB3XDDTeQ0ENy8oBKZOLEiZ59LDds2BD317744ou9evXqed98802Z682dO9ft47x584rmrV+/3j337LPPDut1atSo4X333XdF8xYsWOC2+de//jWqfe/Xr5936KGHevH2zjvvuP2+8847i+bt2rXLO/DAA72+ffuW+/zbb7/dPf/dd98tmvf55597VapU8caPHx+07rfffusVFha6n2vVquUNGzasQn8XAKis8clv/vz5XlZWlnf99de7fXnvvffKfc6OHTu83Nxcb8CAARV2Tt65c6fXsGFDb9CgQUHPP+ecc9z5edOmTRH/bitXriwRTxLtlFNO8Zo1a+Zt2bKlaN5DDz3k9vPFF18s87mRHKOffvrJ27p1q/vZfn/bvh2PUFq3bl1im+GK5LMAAKkaK2fNmhV2DE31a7lEX+8uWbLE27ZtW9BzN27c6DVu3Ng76qijKuz3AYDKyr6fh7J3715vz549+7Xt7du3xz3GrVq1yisoKHA/W1yz+BbKwIEDvfr167tzvt+PP/7o1a5d2zv99NPLfZ0TTjjBy8nJcfcfI73GHDVqlJt33XXXlfs6QGVFyU1Uet99953rLWdjxK1bty5mJUVmzZrleuZZS828vLxSW3Rab7Tc3FydfvrpRfOs1YiVKPvPf/5TZktQ8+9//1unnnqqKx3pZ60PrXX9448/XmG/0//+9z/Xq/Dss89Wfn6+YsGORZUqVdxx87PyNiNGjHA9DlavXl3u863ljk1+Bx98sOsRUfxYtG7d2nWHB4B0ik9+e/fu1ZgxY9x04IEHhv08iwMWoyzOlSfcc7L1wLYWl9ayMdCoUaO0Y8cO1wOsIljrSYsv1hL0ySefVDxt3brVlY+2kjFWBsZv6NChrvxMefE6kmNkpWyszEwk7HuKbScSkXwWACAdYqVV/ygoKIjoNVLpWq408bre7dGjh4upgawawK9+9StX8g1AevOPy2qVJ+w7ufUas3OR9aqy6wS732TDA9h3datI8Ze//KXE9+UJEya4c40918oH2/nFvqcHsh5iVtli0aJFQfP91yHWW7k8VgnDXseGobHv9meddVaJ+2H+8VKtB5v1grNzvFVFCSwLOXXqVBe/bAigzz77zD3vpZdecvtt+289ye13Ln6O9B8re87vf/971a9fv6hilvV+thLH9m+sY5z1uLNjWR6rXGLbDawAY2WXrYfec889V+YQB1axy95Di1F2/zES9v1g+vTpGj9+vG655ZaIngtUJiT0UOnHP7BAZze6XnnlFXdhUR4LUhs3bix3CgwQb7zxhnbv3u0uNm3MPAusFoiPOuqoEqWvPvjgAx1++OElgpSVgrQyWvZlo6yxidavX6+ePXuWWGbPt21XBAuANnaOjTlnXyys5ExZrHt7OMfMJrtQ9rP9tcAeeLPT/7uYssqG2Wt+9NFHpR4Le+/tIhsA0jk++dnFnZVNvP7668NKRtl27MLNLhI/+eQTl5QrSyTnZH+sKr6uXcRabKyIWGY3WK2k8z/+8Q899dRTQTcVS2MxOJzja8exPFZWxm6gFv8d7aLeSl6W9zvG8hjZRb19T7GboDam3j333FOhnwUASIdYaSWm7RrGzqd23WTllMuTatdypUn09a6NZWhlPgHAnHnmme48d9ttt6l3794uEWPn+xNPPFEtWrRww7PYvbwrrrjCjSMd+D3YSvtaIs3WsaSXDaszYMCAoHtVFjPs+701TPdf77z44ot66KGHXEKwW7duZb4Rt956q2v0Z+WIrUy/DUdjyUGLf8Ub0lmDv1NOOcW9nv0OFov8rJOBjbdtiURLTlpicOHChW5/7bxq+29l/G2Mb7tXGWrMbYsbdp62cpn+8eXsWsrK+tu/lSHGGWsYYvdci7OYbIlYu2YpzZw5c9zn4Zxzzom4HLcNc2BDH9jxAZIZY+ih0rKbT3bTyQK0BVNrYRIOa63y6quvlrvesGHD3Hhvxn8BZ600rDWM3UC0i8kbb7xRxx9/vD799FPXWsTfGsQCc3H+5T/++KO6dOkS8jX9Y7/51y3+/E2bNrnAZq1xomW9GKw1kN0InTFjRlitY1atWlViDInSWEsY/8C29vuU9rv4j0Vp/L9rec/3184GgHSMT/4bWzfffLNrtVm8AUUo1oLe9sufgLIBv60la1kiOSfbud96Zzdp0iRoPXsta2VZ1rk/HJZIs1a4zzzzjJvCHRvhjjvucHG7PNbjO9QFcCTx2lqVlvf8WByjrl27uta29j7YDQH7nNhNA9ue3aioiM8CAKRyrLSbhXad5E/oWU8JuwF75JFHujF9rHdBaVLtWq40ibzetfhqlV7CScoCSA+WTLLxNY0lu6xBm40nPXny5KJxqa03c/PmzTVz5syi85fFHfvOHzjumyW5rAKJJc5sDE9j44bbPUBreGcJszvvvNMl9yyxdc0115TbC916+FmS0RrP+VljxMMOO8yNCxc432KVndvtO7mf/7rExq9bsWKF64UYGBMtsWfnRfvXDB482G3bXvfvf/970P5Y8nH27NlRHed4xDg/u5Z5++23XSNOu2Yylsh75513ipKLpbGx82x/7F5tuO677z73Xtm4sJYYBpIdCT1UStYaw1rhWCubF154ocRF2dy5c11rFgu8/mDsDyrWkiWc1vcW7P38LTyti7q1pPGX/rAg2bdvX9cl298de9euXSEDmL+rty0vjX9Zec+PNkD+61//ci2DLrroItfyJLBEpZVHsS8Slry0f611j5+VJ7DSYuEIbJ0Uj2MBAOkcn4xdqLZr105/+MMfwtpHu0ixi1wr82IXeXZxVF65rkjOyfZvaQOi27r7c+62fbWWpRaT/vvf/5a46WgX8Vau0m4mrly50l3Q+1n885eWKUuo1qCRHo/yfsdYHSNLcAYaPny4a+VrN6MvueQSHXDAAfv9WQCAVI6V1tDBJj+7MWq9H+wGsPWysBut6XItV5pEXe9azxArFWfJyauuuqrc/QSQHgLP65b8sUSbJb8s6eZnpSgtSfTNN98EretPFlmPLustZ//a860BRyArhWkNA62Rv1UtsR7NVvq4vB7S1gjDtmlxxZ4TeF62HnvWiCIwoWfnPvv+HsqQIUOCknmWYLOehHY+9Cfz/A38rHeiXSsVZ/GjOGsgYlN5Yh3jAtmwBBdffLF7D+33s2No91z9ScXS4oz1ELeGONbbLpwGL37+kt9WYQxIBST0UCmddtppriSLteYsXlffbkpZQLSTuAXt0aNHu9YWdsPKWKuaSPlv7tnrBr5enz593AWFdWkPXDfUuAFWsjNwW2W9TrTPL4vd2LQeDXYj1C6Ki7PkpN0IvOmmm0IGZ6tfHanKeiwAIFXik7Vc/Oc//+kam4R70WIlXPwsLljZLLuIszFxKuKcbP9aYigUW3d/zt3W0tYa2dgN4FA9COzCz3qiBV7U+tmNXJsiYb3xAy8YLQln2y7veJT3O8byGAWym712QWufRytnZ+/3/n4WACAdYmUgawxiZdystFlZUulazmKU9bYIZDeS7eZ3Iq7xbFxYG7fJyt3ZcBjFPzcA0lfgeG7GxsOz817x0rw23ypYBLIGbdZQxHqNB5YcDtWr2XpvWTnHd99915VkPOSQQ8rdN2tkYeP5WfIuFGu4Esh6rZfW6K/4PlmPMhOqapWV0LQYa+dOG1uvrN8rXPG8R2eJR/s+YL0h/b0MLdFqyT1rXFNaDLDeeSbScpvW6McSoNYz0r572FBLQDIjoYdKyVqm2EndTtaBXdGNtZI5+eST3UnYfyK/7rrrii4C7cKktJtogSwQWcAPbOEZalwHK5cV2ErUunb7W40E8s8r3lo0UGDZzlDPt5uI0bZ2sW3bZEFqyZIlJepe+78EBbb09LNu7lZLPBy2j/4vIPZ6obrCh3Ms/L9rtMcSANIhPtlFjQ2Cbhdn/nIs/tafdq60MlvFL3ID2fnaxuGxnlqWuCrtIiySc7Kd+y1uWEv6wJKS9rvZRfT+nLutl8T8+fNd+UxL6BUf6NxuaJbGEoFlDaDuZzcr/a1fbWD0wFI1NhC7JcbKi9fl/Y6xPEbF+cvDFb8xG+1nAQDSLVb6z6XLly8vc51UupazBquBYzcZf8/3eF/v2vtt5emsV4zdoLaeMgDg5+9lV948Y8k1PxuD1BqyWU9sS9bZd3J7njUgtDFei7Peff7heGw87XBYzzI7L1tjxFD7VDwxFU6DiP2xP9uIZYwLxRJ3Nu6hDXFk8dxKOft7M5bWk87KiVqCM9LGP/Y+2HtkvfHte4dVDgh3WAegMiKhh0rJWmlY13brhm2DqFvpDT+7ORbYEsd+tnl+djEQ6bgL/mAQKjllZb2sFExga3er7W+BO7AFqNV6tjEZyurCba1x7CaiXaQVZ62AAlvSR8puetoA6lZH2i6S7RgceuihYT3XWsZEM+6C7a89tsGGA0vp+Otel/X72LGzgB3qWNjzrZeFvfcAkM7xyW5CWuvMUOdoS87YxU/xwdaLs+SNXdxaq/fSLvIiOSf7z+227sCBA4vWs8cWG/cnllnPeGuxaa30rZeCDd5eXqkbPxs3KdIx9OwmcGCvNv8YT3Yz0V7XfqfA0mx209FK3wTOCyWWx6g4f2mhwBI9+/NZAIB0jJV2Li3vPJpK13JWerN4mU4rERfv6117DSszar0rH3/8cdewBgAqglWksGsYK4sZ2BjCxp4rzs5Flvyz+1o2PrX10LNeXBaTynLggQe679Z2Dq7oco52zWJCNTaxHocWPwN75+2vWMa40ti1V+CQCdZT3oYQCLwHGxiDbIzBUD3Vw2HjmFujoqOOOsq9rxYDbYglIBmR0EOlZMH2wQcfdDec7GLNWlPYxZixVjVWosXPWiMGtn6PZtwFa+FhFzU2NoG15vRfZNrJ3i6QbFwaPwvq9sXAvhT4u2nbc+bNm+fKywS2WPG3+rEgX7zFqm3X36reLmCsFrSVzdofdrFqrRqt1YnV1LYLscDXLk204y7Y7283UO29spY1/u75s2bNcmVrAgeVtwvtnTt3BgVme74NMhzYCtW+rLz00ktF2wOAdI5P9lp27gxk50grx2Xn38BzavHeYMZuYP773/925+PAZftzTrabjdZC84EHHghKVtlju9E3aNAg7Q8rG2blbiyhd95557keHuGUUItmDD0rpROqnI7FU9sPa9l7ww03FCUzraSb9QK0ffOz42jH0747+L8/xOIYWa8V26/A1r9WOsh63Flvi8CeFpF8FgAgnWKlvV7xxJ31irN9uvTSS4Pmp/K1nN1ELa1MZzyvd+0628ZU/Otf/1rujXMAiIT/O7Ml3PwJPUsKLV68uESvbRuP2nouW2lj+55uFTus1L+dj4uX9gxk5y0bd88aFdp1Q2Di0F7Xvr9bIinaHnOWRLPzqb2Gv2e7jVNr9yqLl9ova4gB62Fn2/P3bC9NuOdvuwax879tz9+zb39ZLHjvvfdc3A517We980xgI6FokpYWL+2a0d5nazxjjVqBpOMBlcjEiROtf7y3YcMG9zgvL88bOHCgl52d7S1atMjN++6777w2bdp4P//8s3t88cUXe3fcccd+v/ZLL73kValSxevYsaM3ZcoUty916tTxDjroIG/btm1F6+Xn53t9+vTxateu7d14443e9OnTvUMPPdSt+8UXXwRts3Xr1m4KtGrVKq9hw4begQce6N17773en//8Z69+/fpely5dvN27d5f7/FD69evn9sHv+++/d8fIJvs50LBhw9zvVlHOOOMMr2rVqt6VV17p/fWvf/WOPPJI9/jVV18tsY/FTzlbt251x6FJkybuPbz77ru9li1bes2bN/fWr18ftO4zzzzj3XzzzW7KysryDjvssKLHH374YYX9PgBQ2eJTcbNmzXL78t577wXNP/zww71f//rX3q233uo99NBD3g033OAdcMABXmZmpjdv3rwKPSdb7LPn//a3v3WvNXToUPfYXjvQyy+/7OaXF3dWrlzp1rvzzjuL5v3zn//0MjIyvAsvvLDE+rauPSeWli5d6t5fizcPPPCAd91113nVq1f3TjrppLB+x3CP0ebNm4vi2cknn+zWufzyy93jadOmBb3v9v5cffXV3owZM9z3h86dO7v17edoPwsAkE6xsn379u765fbbb3fnUosxdu1i8W7t2rVpdy0XSryud+17hr1Hffv2dTG/+LR9+/aY/p4AkiumBJ4Ha9WqVe65dObMme759p3Y7lVdc801Xr169dw6geetzz77zH3HP//884vmffnll17NmjVdvCjP5MmT3evYvTCLZ3bdcNVVV3kdOnQIurYpvn9lXQf5LViwwMWogw8+2C2/6aabvMaNG7tz6jfffFPusQqMh/ZvecI9f/v32d6LQHYf0H9dY9eUFsf8jwPvEdrPJ5xwgovFf/vb37w//OEP7n6sXQvt3bs3ZFzKzc11sSkSpR3bDz74wKtbt67XrFkz7+uvv45om0BlQEIPlUqoILRz504X+OyC4u2333bzHnvsMa9Xr17eUUcd5Y0YMcLbtWtXhby+BUsLEBbMGzRo4J133nnemjVrSqy3adMm97oW6CzI2/4Vv1gs6yLuk08+cTcE7bn2heKcc84pcQFpGjVqFFbACvXFYMWKFS44derUyR3P1157zQVluxCzgGw/25eU/WXH/oorrvCaNm3qLtaPOOIIb/78+SH3MVQbgtWrV7ubnTk5Oe49PvXUU72vvvqqxHr2RcGeH2oK54sJACRzfArnJuV9993nHX300S522IWfXeyddtpp7vxf0edk8+CDD7pGMNbIwmKK3ZgrLCwMWufZZ591r2M3TaO52Lr//vvdfIszZsyYMe61bJ7F18GDB3ux9Prrr7uLc/teYMdz1KhRLvEZbtIynGPk/91DTYHfIZYsWeLezxYtWrjt2ftj7/fjjz9e4nUj+SwAQDrFSmuc0b17d3cjr1q1al6rVq1cUjHUtVg6XMuVJh7Xu2Vd38Wj4Q6A1E7o2XduS0jZOcrfSO+5555zz/eftyxRZPewrOGbNbILdM8997jXnzt3brn7+u9//9t997b9sskScHbdsHz58lL3L5yEnlm4cKGLlzVq1HDXaPad3pKQ4RyrSBN64Z6/S0vo+fcj1BR4rWQxzl7D4qS9N3a8LDG6Z8+ekPtk9xhtG5ZkjERZx9au8+yYtm3b1vvhhx8i2i6QaBn2v0T3EgRQ0meffebGTbCxFPa3fBkAAIlgY9T961//cuMdVOQg6gAAVGZcywEAACAWyh+QBEBC2IDlNkAryTwAQDLHMhuDjmQeACCdcC0HAACAWKCHHgAAAAAAAAAAAFCJ0UMPAAAAAAAAAAAAqMQSmtCbNGmSMjIygqaDDz64aPnu3bs1atQoNWzYULVr19aQIUO0bt26RO4yAAARIdYBAFIdsQ4AkA6IdwAApXsPvUMPPVRr1qwpmt54442iZWPHjtWzzz6refPm6dVXX9WPP/6o008/PaH7CwBApIh1AIBUR6wDAKQD4h0AIJGqJnwHqlZV06ZNS8zfsmWLHn74Yc2ePVvHH3+8mzdr1ix16tRJb7/9tvr06ZOAvQUAIHLEOgBAqiPWAQDSAfEOAJDWCb2vvvpKzZs3V/Xq1dW3b19NnjxZrVq10tKlS7V3717179+/aF0rx2nLFi9eXGpCb8+ePW7yKyws1KZNm1zZTivpCQBIDM/ztG3bNnfOz8xMeAfxuCLWAUB6INZxXQcA6YB4R7wDkBrS+XyerBKa0Ovdu7ceeeQRdezY0ZXbvPHGG/WrX/1Kn3zyidauXausrCzVq1cv6Dm5ubluWWksIWjbAQBUTqtXr9YBBxygdEGsA4D0Q6zjug4A0gHxjngHIDWk2/k8mSU0oXfKKacU/dy1a1d307N169Z6/PHHVaNGjai2OX78eI0bNy6odKf16vs/SdUqZK8BANHYK+kpSXXq1EmrAxjPWFddEn3RASBxPEm7iXXEOgBIccS72F/b1TvjPmVUi26bABAub+8ubZ43Ou3u1SWzhJfcDGS98Q466CCtWLFCJ554ovLy8rR58+agXnrr1q0LOeaeX3Z2tpuKs2QeCT0ASLx0L38cy1hnRza9jy4AVA7EOmIdAKQD4l0M4121GsrMqhmz9w4ATKH/nJPm9+qSSaUqjLp9+3Z9/fXXatasmXr06KFq1app0aJFRcuXL1+uVatWubH2AABIRsQ6AECqI9YBANIB8Q4AkFY99K644gqddtpprnv6jz/+qIkTJ6pKlSo6++yzVbduXY0YMcJ1O2/QoIFycnJ0ySWXuGRenz59ErnbAACEjVgHAEh1xDqkUhnBaNGuHUh9xDsAQFon9L7//nuXvPvpp5/UuHFjHX300Xr77bfdz+buu+9WZmamhgwZoj179mjAgAG6//77E7nLAABEhFgHAEh1xDqkSjKvbtOmWrt2bVTPt5GuSOoBqY14BwBItAzP8/anEVqlt3XrVtfb73eMoQcACbVX0uO+Qb6t1zUqPtZxIwkAEssurHYR62KCWId4/f2uXr0you+q9tls2bIt38OQVoh3sY939X//MGPoAYi5wryd+nn2CO7VJZGE9tADAAAAAACoLCyZR+MzAAAAVEYk9AAAAAAAAJx83xSuSNYFAAAAopc2Cb1MSVUSvRMAkMYKEr0DAAAg6dk1HeOUIRa8/Uzo8dlEOknpsXsqi0JPXiFHGkDszzVILmmT0AMAAAAAACgbPfQAAABQOZHQAwAAAAAAKKorEUkPPepQAAAAID5I6AEAAAAAAMShh16epL1W4SpgeJBs380Zm7ejlOdVl1TN97Ott9uXSszwPde2QTlaAACA1EZCDwAAAAAAIA4JPX8Cz/6VL7m3S1JN37xaxdbf60sC+m/eeL71M3zP8XzJvQzfdgEAAOJt9+7dysuzbyzhy8rKUvXq1mQJkSChBwAAAAAAEIeEXvGbMJaEy/P1tqsSopddvq9nnn9+ga+HXq2ApGCWpD2+f+mlBwAA4p3Mq1GnoZS/M6LnNW3aVCtXriSpFyESegAAAAAAAEUps4K4jKHnBaQDq5SyZUveVS82LzMgmee/sbPHt26o7QAAAMSK65mXv1PZhw6XqljzojAU5Gntp7Pcc+mlFxkSegAAAAAAAPvuMEXY666gKDlXXEYZzwhsw16jlETcXl/iLnCZF2K7/seh9gEAACAuqmYpo0p4BcA9SgpEjYQeAAAAAADAfpTc3FFsrrVPL+2Wln+sPH8Pvd0hknqeL6HHuHgAACApZGTum8JdF1EhoQcAAAAAALAfCT1L0IXb2DwjYN0qvh57e4sl9PJLuWmTEaInnv8xjd0BAEDCZGTsm8JdF1FJm4SefTGmljwAJPY8jNgfY74SAUDiUO4OSN+EXmCSriLOH3t9N2wyQ3zfy/ONl+df5t9b2roDqaOwsFAZhfaXDgCx41XkeYYeenGRNgk9AAAAAACARNrjS8plBpTcLPCV3PQrDDHPz//c3b5ynJ4vwWclPmnYBQAAEoYeenFBQg8AAAAAAMApiLCHnq0fPs+XjPN8CbhMX+KuarHeeRmlVLjI8K1v29jpe1zVl9ADAABInAjG0KOuQNRI6AEAAAAAAOxHyc1wVQ9jnWzfVBq7VVYzolcFAACIMXroxQUJPQAAAAAAgDgk9AAAAFISY+jFBQk9AAAAAAAAh4QeAABAxOihFxck9AAAAAAAABwSegAAABGjh15ckNADAAAAAABwCiIso2nrAwAApDl66MUFCT0AAAAAAACHHnoAAAARo4deXKRNQq+abwIAJIbHgY+5TPv+xHEGgIQh1sWeXdMR6xDbv9/oEnp8NpFOiHexV1BQqIx8egADiC2voLCCe+hlhr8uopI2CT0AAAAAAICy0UMPAAAgYpkZ+6Zw10VUSOgBAAAAAAA4JPQAAAAiRsnNuCChBwAAAAAA4BREWHKTkngAAAD7Sm6G2fOOkptRI6EHAAAAAABQlKCLJElHQg8AAIAeevFBQg8AAAAAAAAAAADRoYdeXJDQAwAAAAAAcBhDDwAAIGKMoRcXJPQAAAAAAAAcEnoAAAARo4deXJDQAwAAAAAAKBoTz5J64WIMPQAAAHroxQcJPQAAAAAAAIceegAAABGjh15cpE1Cr5pvAgAkhseBjzmLc5kcZwBImEKOfVwuYIl1iO3fb3QJPT6bSCfEu9jL35uvjIjORQAQOW9vRZ5nMvf10gt3XUSFIwcAAAAAABCU0ItkAgAASHP+HnrhTlGYPn262rRpo+rVq6t379569913S133008/1ZAhQ9z6GRkZmjp1aol1/MuKT6NGjSpa59hjjy2x/KKLLlKikNADAAAAAABwSOgBAABEzCXqMsOcIk/ozZ07V+PGjdPEiRP1/vvvq1u3bhowYIDWr18fcv2dO3eqXbt2uu2229S0adOQ67z33ntas2ZN0bRgwQI3/4wzzghab+TIkUHr3XHHHUqUtCm5CQAAAAAAULaCCHvd2foAAABpzp+sC3fdCE2ZMsUl1oYPH+4ez5gxQ88//7xmzpypa665psT6RxxxhJtMqOWmcePGQY8t+XfggQeqX79+QfNr1qxZalIw3uihBwAAAAAA4NBDDwAAIB4lN7du3Ro07dmzJ+Sm8/LytHTpUvXv3/+XxFZmpnu8ePHiCnmz7DUeffRRXXDBBa6sZqDHHntMjRo1UufOnTV+/HjX+y9R6KEHAAAAAABQlNCrEsGxYAw9AACAaHrotWzZMmi2ldOcNGlSidU3btyogoIC5ebmBs23x1988UWFHPynn35amzdv1vnnnx80//e//71at26t5s2b66OPPtLVV1+t5cuX68knn1QikNADAAAAAABwSOgBAABELKDnXVjrSlq9erVycnKKZmdnZyfswD/88MM65ZRTXOIu0IUXXlj0c5cuXdSsWTOdcMIJ+vrrr115zngjoQcAAAAAAOAwhh4AAEA8euhZMi8woVcaK3dZpUoVrVu3Lmi+Pa6Ise2+++47LVy4MKxed71793b/rlixIiEJPcbQAwAAAAAAAAAAQNzG0AtXVlaWevTooUWLFhXNKywsdI/79u273+/YrFmz1KRJEw0aNKjcdZctW+b+tZ56iZA2PfSss2biOmwCACIL1YiGxTla6gBA4hRy8GOuGrEOMf/7zY/wG9W+MfT4bCKdEO9iz9uzRyrk6g5AjM81e/dU2LYyMjLcFObKEW9/3LhxGjZsmHr27KlevXpp6tSp2rFjh4YPH+6WDx06VC1atNDkyZPd47y8PH322WdFP//www8uGVe7dm21b98+KDFoCT3bdtWqwekyK6s5e/ZsDRw4UA0bNnRj6I0dO1bHHHOMunbtqkRIm4QeAAAAAABA2aJL6AEAAKSzWCf0zjzzTG3YsEETJkzQ2rVr1b17d82fP1+5ublu+apVq5SZ+ct3uB9//FGHHXZY0eO77rrLTf369dMrr7xSNN9KbdpzL7jggpA9A225P3nYsmVLDRkyRNdff70ShYQeAAAAAABAHBJ62yXtCHiW9eyrI6lGwDrWVn6rtSYPWKex3fsK6B31s6Tdvsf23Hr0XgUAAIlkX1QyYlvGa/To0W4KJTBJZ9q0aSPP88rd5kknnVTqepbAe/XVV1WZkNADAAAAAABwCnxTuCJZV6oiKSfgZsxOST9JyvUl7iyZt9GX5LMkndlbbBs/+ZJ6jXyPf/ZNDXkHAQBAivbQwz4k9AAAAAAAAIoSdPkxS+gF9sQzdX299vJ8Cb0tkmr7kn5+Nl8ByT1L+jWxMlC+efV8ScACX8IQAAAg3kjoxUelGV31tttuc2/6ZZddVjRv9+7dGjVqlBtw0AYrtPqk69atS+h+AgCwP4h3AIBUR6xDcsuPYoqO5+uh5/mScwW+xJ4l5dbb2C++fy2B52fLMwKSeSY7YBmA+CDWAUDohF64E5I4offee+/pr3/9q7p27Ro0f+zYsXr22Wc1b948V6vUBjI8/fTTE7afAADsD+IdACDVEeuQrgm9wmJTWSO2WC+7H3yTv1RmtYDUoI2fV8tXUtMSdxsCym6G6oWX4bu5E1lfQQDRItYBQEkk9NIkobd9+3adc845euihh1S/fv2i+Vu2bNHDDz+sKVOm6Pjjj1ePHj00a9YsvfXWW3r77bcTus8AAESKeAcASHXEOqRzQm+tr0edf7KkXFljn+T6ymbW9iX1AsfJq+WbsnzlNKv5evIBSDxiHQCUIiPCCcmZ0LOSmoMGDVL//v2D5i9dulR79+4Nmn/wwQerVatWWrx4cQL2FACA6BHvAACpjliHdE7oNZXUPGAKHAOvuAxfUi/LN4ZeNd84ev6ed7YsUNWA3ntVQvTE83y9Ahk/D4g9Yh0AhEYPvfgo/j0xrubMmaP333/fdVUvbu3atcrKylK9etYe7Re5ubluWWn27NnjJr+tW8tqFwcAQPLFO2IdAKCyIdYhdRRE2Gy8oKi19P60mPZ8CbnMEKPy2ePqvp+zfOvmBYyj578DEjiuHoCKx31MACidDYsX9th49NBLvoTe6tWrNWbMGC1YsEDVq/u/mu6/yZMn68Ybbywxv3rAQNEAgPhL11gdi3hXVqxLeNd7AEhj1kMmHRHrkFp/v8XTaeXJj+h72EZfOc2qvtfc5kvIWa++GpIaSNoUUHJzm+8VGvh68lX3zdsiqbEvubfFV7rTngPEQzrGu3jfx9TeXZJX1micAFAB8ndX2GHMsP/CTeil7V3C/Zew+35WUnP9+vU6/PDDVbVqVTe9+uqruvfee93P1jMhLy9PmzdvDnreunXr1LSpFbMIbfz48W78Pf9kARcAgFSKd8Q6AEBlQqxDaomu5GYk/fnWSfrON9aeP5lX07fcajbU9yX+7G7GLt9yS+b55foe/yBpjS/JZ+PxAYgd7mMCQNkouZniPfROOOEEffzxx0Hzhg8f7sbJu/rqq9WyZUtVq1ZNixYt0pAhQ9zy5cuXa9WqVerbt2+p283OznYTAACVQSziHbEOAFCZEOuA8Fkyrjz1fVNprDRn6c2cAcQC9zEBIIxOd3TQS92EXp06ddS5c+egebVq1VLDhg2L5o8YMULjxo1TgwYNlJOTo0suucTd3OzTp0+C9hoAgMgQ7wAAqY5Yh9QSXclNAKmNWAcA5cgIv+SmF3ZpTlSahF447r77bmVmZroeC3v27NGAAQN0//33J3q3AACoUMQ7AECqI9YheRTEeH0AqYpYByCd+UtuhrsuopPheak9wurWrVtVt25dXWElyhK9MwCQxmx8kLskN76p9bpGxce6dokcHBcAoEJJ3xDrYoJYh/j9/XZTTo4VtQzP1q0Fqlv3Q76HIa0Q72If77KPv0UZVW2ETACIHS9/t/a8dP1+3avzn7canjNLmVn+UYHLVpi3Uz89Npx7hKnWQw8AAAAAACB+rIRmJO2e6aEHAADAGHrxQUIPAAAAAADAIaEHAAAQKUpuxgcJPURki1pqpxqVmF9TG1VXqzmaccL7wHEFEDt71VIFIWJdFW1UNWJd3PA+cFwBcI5Nh4Qe8S42OK5A8vN21ZG3t0aJ+RnVdimjxraE7FMy4LhxTBKFhF58pE1Cz07/VJ7eP5vVUg9mLldeYclgmpW5S2MKO6oeNzpjjveB45qsGNst9mys2PBHfEEoeWqpHzKXKz9ErKuauUvtCjsqi1gXc7wPHNdkReG92LNROYh1+3+O/baMWNchTWNdQdBPXoSjiUX32eS9iA2Oa+wR7+Igb5dUGMm5KLV4u3O0d8kFKswvees6s2q+qvW8XxnVtyZk3yozjhvHJGL5uyvs80dCLz7SJqGH/bdDjVwy79FHpU6dfpn/+efSuefWcMtJ6MUe7wPHFUDsWM+8/DJi3b6ee+l3kzPeeB84rgBiJ7+cWGfL0zGhp/1M6EWD9yI2OK5A8vP21nTJvNCxqqpbTkKP48ZnqXIhoRcfJPQQMQukhx/OgUs03geOKwDOsamOWMdxBcA5NjElNzPjktDzI97FBscVSH78HXPc+CwlkQzfFO66iAoJPQAAAAAAgAQl9AAAAJIdPfTig4QeAAAAAACAQ0IPAAAgUiT04oOEHiJm9arLeoz44H3guALgHJvqiHUcVwCcYxMzhl4kve4iGW8vNOJdbHBcgeTH3zHHjc9S8ohHQm/69Om68847tXbtWnXr1k3Tpk1Tr169Qq776aefasKECVq6dKm+++473X333brsssuC1pk0aZJuvPHGoHkdO3bUF198UfR49+7duvzyyzVnzhzt2bNHAwYM0P3336/c3FwlAgk9hK2WNiorc5cbKL04m1+rcCNHMw54HziuAGKnijaqaimxzuZXIdbFBe8DxxVA7FQtJ9ZVJdbFDe8FxxVAaBnVdiqzar7OPbfkrWubb8vBcQsHn6XUGUNv7ty5GjdunGbMmKHevXtr6tSpLrm2fPlyNWnSpMT6O3fuVLt27XTGGWdo7NixpW730EMP1cKFC4seV60afN6x5z7//POaN2+e6tatq9GjR+v000/Xm2++qUQgoYew1dNqjSnsqB1qVGKZJfNsOWKP94HjCiB2srRa7Qo7qiBErLNkni1H7PE+cFwBxPYc26Gwo/JDxDpL5hHr8iO8yxR9Dz3ei9jguALJL6P6VlXreb+8vTVLLqu20y0Hx43PUnr10JsyZYpGjhyp4cOHu8eW2LNE28yZM3XNNdeUWP+II45wkwm1PDCB17Rp05DLtmzZoocfflizZ8/W8ccf7+bNmjVLnTp10ttvv60+ffoo3kjoIeJkEom7xON94LgCiJ19NzJJ3CUa7wPHFUBsz7Ek7hKf0OO9iB0+40Dys6QdiTuOG5+l1E7obd0anJzPzs52U3F5eXmudOb48eOL5mVmZqp///5avHjxfu33V199pebNm6t69erq27evJk+erFatWrll9pp79+51r+N38MEHu+X2uolI6GXG/RUBAAAAAAAqbUIv0gkAACC9Zdh/GWFOvsZTLVu2dGUs/ZMl00LZuHGjCgoKSoxbZ49tPL1oWenORx55RPPnz9cDDzyglStX6le/+pW2bdvmltu2s7KyVK9evQp93f2RNj306kgqOUIAACBeqnGoY65mOgV2AKiEuK0fe3ZNR6xDTP9+vcLIOt351uWziXRCvIuDvN1S4f71AAaAcuXvSWgPvdWrVysnJ6dofqjeebF0yimnFP3ctWtXl+Br3bq1Hn/8cY0YMUKVEddCAAAAAAAAptA3hSuSdQEAAFJVRgRVy33rWTIvMKFXmkaNGqlKlSpat25d0Hx7XNr4d9GwnngHHXSQVqxY4R7btq3c5+bNm4N66VX060aCkpsAAAAAAACmIIoJAAAgzYVdbjOCnnx+VvayR48eWrRoUdG8wsJC99jGvaso27dv19dff61mzZq5x/aa1apVC3rd5cuXa9WqVRX6upGghx4AAAAAAICiSNKR0AMAAIiq5GYkxo0bp2HDhqlnz57q1auXpk6dqh07dmj48OFu+dChQ9WiRYuicfisZ91nn31W9PMPP/ygZcuWqXbt2mrfvr2bf8UVV+i0005zZTZ//PFHTZw40fUEPPvss91yG9fPSm/aazdo0MD1JrzkkktcMq9Pnz4JeddJ6AEAAAAAABhKbgIAAETMcnTh5umiyOfpzDPP1IYNGzRhwgStXbtW3bt31/z585Wbm+uWW6+5zMxfClJagu6www4renzXXXe5qV+/fnrllVfcvO+//94l73766Sc1btxYRx99tN5++233s9/dd9/ttjtkyBDt2bNHAwYM0P33369EIaEHAAAAAABg6KEHAAAQZUIv3B560R3g0aNHuykUf5LOr02bNvI8r8ztzZkzp9zXrF69uqZPn+6myoCEHgAAAAAAgKGHHgAAQOQi6KFn6yI6JPQAAAAAAAD8Cb2CCNcHAABIc7EeQw/7kNADAAAAAAAwlNwEAACodGPoIc0SenUk1Uj0TgBAGkubgJPgWMdxBoDEyefgx1wtYh0q6d8vn02kE+JdPA7ybqmcsZ8AYL8V7Kmwg5iZmeGmcHhhroeSuO8HAAAAAAAQhzH0vvdNu3yPa0tqK6mR7/ESSZuLPaeFpE4Bj3dL+lzSz5KqSGou6UC7kcY7CAAAEoQeevFBQg8AAAAAACAOJTezJbWXVNNap0taI+lDSb19yT1/Aq9dwHMsaednz/nAt50jJFm7+k/tJppvuwAAAInAGHrxQUIPAAAAAAAgDgm9xsUet/f12NsSkNDL9CXsQvlJ0g5Jh/vWqePrnfeVLwlILz0AAJAI9NCLDxJ6AAAAAAAA+1Fys/iYYplhJNest906X06wbsD8tb4py5cAbBvQS8+f+AtM+DWU9IWk7ZJySnmtDVG8uw2K9Q4EAAAoDT304oOEHgAAAAAAwH700Huj2Oy2vp5zoVji7T1fLtASZt0Ceuc1lVTDl7DbJmmFr0eerWPyfIm+QFkBy0pjZT0jdaSvNCgAAEB5SOjFBwk9AAAAAAAAf7e5wgjXl3R0sRssZfXOq+kbM8969a33jYHXw5fUOyBgPX9PvPcl7ayA5NoxIZKBpXl5P18LAACkF0puxgcJPQAAAAAAgP3ooVc1ghssmQHJOSuRuVXSakmdQqzrL8W5y/ecLF/ZzUD+nnllJeuaRTi+nvUU5IYRAAAIV4b9Z1m9MNdFdPh+BgAAAAAAsB8JvVh1CrSym4HJOkvwrSxWevMnX+lOf9nOUA4Nc1/yfTeKQiUXAQAASkMPvfiIpIEWAAAAAABA6iqMYoqAjYn3s6/H3faAx019ZTW/8fXYs+UbfOU460mq43t+Q0m1JH3iS/ZZMu9rSS3DuMHzXRjJvA8i+3UAAACCxtALd0J00qaHnpWxYDBnAEicahz8mLNW2RxnAEicvRz8mLPeScQ6xPTvN8oeepF8Nj+XtNu3vj3vV5JyfQm9LyV970uu1fQl6joV2/YxvsTbEl/PvDaSuoSR0HvJlxxsHWKZvd7rvvykrQOUhXgXBwX5vr9wAIj1uaZi0EMvPtImoQcAAAAAAJDIkps9y1hmCbxjw9iG9dA7WpHrJeldX3KweYhk3h5J/aLYLgAAQCQ97+ihFz0SegAAAAAAAIqijGaEJTcT6QBfz6p3JB0lqUmIZF6NRO8kAABISvTQiw8SegAAAAAAAGmgraQ8SW9JOlLSZ77ynyTzAADA/qCHXnyQ0AMAAAAAAPD3uCtIzR56fh19Sb3XfOU7+/nKfQIAAEQtY18vvXDXRXRI6AEAAAAAAKR4yU3rlRcoU1KWpGXF5lvPPQAAgEjQQy8+SOgBAAAAAADI1zsvkh56kaybYNWKPW6ZoP0AAACphzH04oOEHgAAAAAAQIon9I5I9A4AAICURQ+9+LAKCwAAAAAAACiMYgIAAEhz/h564U7RmD59utq0aaPq1aurd+/eevfdd0td99NPP9WQIUPc+pZsnDp1aol1Jk+erCOOOEJ16tRRkyZNNHjwYC1fvjxonWOPPbYoWemfLrroIiVK2vTQq+sb7BkAUDlK/CA2sc7GQQEAJEYeBz7mcoh1iPXfb5Q99Cr7Z3OhpGMi2MdXJPWWVCPG+4XkRLyLg8JCKSOJugADSN5zTZL00Js7d67GjRunGTNmuGSeJegGDBjgEnCWjCtu586dateunc444wyNHTs25DZfffVVjRo1yiX18vPzde211+qkk07SZ599plq1fskmjRw5UjfddFPR45o1aypR0iahBwAAAAAAkI4lN1dJ2h3h+oeT0AMAAJUkoTdlyhSXWBs+fLh7bIm9559/XjNnztQ111xTYn1L0tlkQi038+fPD3r8yCOPuOTg0qVLdcwx1hTqlwRe06ZNVRmQ0AMAAAAAADBehGU0bf0kYLv5RKJ3AgAApKxISmlGms/Ly8tzSbbx48cXzcvMzFT//v21ePFiVZQtW7a4fxs0aBA0/7HHHtOjjz7qknqnnXaabrjhhoT10iOhBwAAAAAAkMI99AZG8RyGLQEAALHsobd169ag+dnZ2W4qbuPGjSooKFBubm7QfHv8xRdfVMibVFhYqMsuu0xHHXWUOnfuXDT/97//vVq3bq3mzZvro48+0tVXX+3KfD755JNKBBJ6AAAAAAAA8vXOi6SHXsUNPRNTzRK9AwAAIKVF00OvZcuWQfMnTpyoSZMmKRFGjRqlTz75RG+88UbQ/AsvvLDo5y5duqhZs2Y64YQT9PXXX+vAAw+M+35mKoEeeOABde3aVTk5OW7q27evXnjhhaLlu3fvdgeyYcOGql27toYMGaJ169YlcpcBAIgIsQ4AkOqIdUjJHnqRTADSAvEOAMrvoRfuZFavXu3KXPqnwJKagRo1aqQqVaqUyA3Z44oY22706NF67rnn9PLLL+uAAw4oc93evXu7f1esWKFESGhCzw7Obbfd5uqfLlmyRMcff7x+85vf6NNPP3XLx44dq2effVbz5s3Tq6++qh9//FGnn356IncZAICIEOsAAKmOWIeUQkIPQCmIdwBQuoyAXnrlTr7n+Dt6+adQ5TZNVlaWevTooUWLFgWVyLTH1kksWp7nuWTeU089pZdeeklt27Yt9znLli1z/1pPvbQruWkDCAa69dZbXWuXt99+2wXJhx9+WLNnz3aJPjNr1ix16tTJLe/Tp0+C9hoAgPAR6wAAqY5YBwBIB8Q7AChdZkaGm8IR7nqBxo0bp2HDhqlnz57q1auXpk6dqh07dmj48OFu+dChQ9WiRQtNnjzZPc7Ly9Nnn31W9PMPP/zgknFWCbJ9+/ZuvlWHtPzTf/7zH9WpU0dr16518+vWrasaNWq4spq2fODAga6KpI2hZ53QjjnmGFd5Mu166AWyQQ3nzJnj3gTLqlqvvb1796p///5F6xx88MFq1aqVFi9enNB9BQAgGsQ6AECqI9YhZcbQi2QCkHaIdwAQLOzeeRGMtRfozDPP1F133aUJEyaoe/fuLjk3f/585ebmuuWrVq3SmjVrita3ao+HHXaYm2y+Pdd+/sMf/lC0jnUus1Kfxx57rOtx55/mzp1b1DNw4cKFOumkk1xu6vLLL3fDwllVyURJaA898/HHH7sEno2XZ9lR6954yCGHuDfEDli9evWC1rc3yJ8pDWXPnj1u8tu6dWtM9x8AgPIQ6wAAqY5Yh5QR6bh4STqGnuUh7ZbXNknt7IaVpB2+f6sleueASox4BwChBY6NV55w1ytu9OjRbgrllVdeCXrcpk0bV1KzLOUtb9mypRsKrjJJeEKvY8eOLnlnmdAnnnjCdZvcn4NkXSpvvPHGEvMbSKq9n/sKAIhe6CrY6SFesa5+mh9nAEi0X5oVpp94xbq6xDrE+u+3MMIkXWHyfTat2fNTvn/tVz1YkjWlft/3+MRE7yAqPeJd7OMdACSbzIx9U7jrpqqPPvoo4udYB7eqVasmR0LPeuH5a5bawIbvvfee7rnnHteF0mqbbt68OaiX3rp169S0adNStzd+/HhXTzWwh55lUgEASBRiHQAg1RHrkDIiLaOZhCU3X7LqRzbWjKTpAfM7SPpfAvcLSAbEOwAohSulGWamLoUTet27d3fHobzef36ZmZn68ssv1a6d1UxIgoRecYWFha5kpiX3qlWrpkWLFrm6pGb58uWuFqqV6CxNdna2mwAAqKyIdQCAVEesQ9JKg5KbP0g6W1KVYvNzJG1P0D4ByYp4BwD7RDI2XpQVN5PGO++8o8aNG5e7niX9OnfuHNG2E5rQs950p5xyilq1aqVt27Zp9uzZrtbpiy++qLp162rEiBGut12DBg2Uk5OjSy65xCXz+vTpk8jdBgAgbMQ6AECqI9YhpaRBDz1rLx6qzfg23xh6AEIj3gFA6TJ8/4Uj3PWSUb9+/VxFysCqk2U55phjVKNGjYpN6N17772K1PDhw1WnTp0y11m/fr2GDh2qNWvWuARe165dXTLvxBP3VWy/++67XZdD66FnvfYGDBig+++/P+J9AQCgPMQ6AEA6iEW847oOKSUNeui1lrRU0km+x3ZLLU/SYkltE7xvQEXg2g4A4o8x9PZ5+eWXFY78/Hw3bt5///tfRSLDC6OYpyXVDjjgAFWpUrwgQ2irV6+OqO5nLNkYepYsfEtS7UTvDACkMSvfc6TkBg+3XteVTSrEutFWejrROwMAaWyPpPsqcaxL5nhHrEPc/n7vknLCbyStrbukulcoqb6HbZX0pK+X3mbfeHo/S7Jf+yxJNRO9g6j0Knu8S9ZYFxjvsruMVEYV+swCiC2vIE97Pn5ov87n/vPWKfe8rGo1wsvA7N21XS+MOa7SxpH99fjjj+t3v/tdmck8W/7kk/aNTLEpublkyRI1adIkrHXL65kHAEBlRKwDAKQD4h2Q3iU37bbZUEnLrYet3VSTZKO3dJJULdE7B1QQYh0AxBdj6P3CqlLWr1+/qBJloIKCApfMW7zYaiNELjOclSZOnKjatcPv33bttde6ce8AAEgWxDoAQDog3gFhJOgKIpiSLKFnu/w3X488S+D1k9RfUleSeUghxDoAiL/MjIyIplR2++236/TTT9c777wTNL+wsNAl8958800tXLgwqm1XDTcQRjpILAAAyYRYBwBIB8Q7ILE99JZJ+tBX9tI0lNQ3xNh1Vg7TijB9K+nXkjoELLPn2i2g1b4k3KGSfhVmi+0qyTnsHxARYh0AxB899H4xZswYbdq0SQMHDtRrr72mQw891PXMO/PMM/X666/rpZdecvOiEXbJzWRX30qBJnonACCNUb4nPrGuehxeBwAQ2m4OTMw1ItYh1n+//p534SqI7LPZQlJL3/qWtHtf0n8kXeoby87v9YAx+epKahyQP3zUd3/jT5K22Tgtkqym0slh7vJRkj6SNMSX4AMiRbyLg8xMKZO/UAAx5oVVwDEsGRkZbgp33VR34403uqTeSSedpJdfflnXX3+9Xn31VS1atEidO1uxc8UnoffTTz9pwoQJbifWr1/vugkGsp0EACCZEesAAOmAeAfE3yHFHg+Q9LakVQEJvR99Cb1LJN1abP2vfOPe/SGg0bKNzvKCr3RmODd5rGff175tNZWUVWz5eVH+bkBlRKwDgPigh15J06ZN088//6xu3bq5Ie0smde1qxU6V/wSeuedd55WrFihESNGKDc3Ny2yqQCA9EKsAwCkA+IdEEKUPfSiYc2jP5aUJ6mVb579PEfSb0qpMvSdLwkXuOwgSU9LWufrAVieGpKibxcOJBdiHQDERyRj46X6GHrjxo0r+rl+/fryPE/du3fXI488ErTelClTYp/Qsxqfb7zxhssqAgCQioh1AIB0QLwDKm4Mvd0hbraUdsNlraT7JeX7esedF9A77zlfcq+0UVW2+8prBqodsCwcZ4S5HpAKiHUAEB+Wogs3TZfa6Tzpgw8+CHrct29f5efnB82PtqNcxAm9gw8+WLt27YrqxQAASAbEOgBAOiDeARXXQ++2YrNP8JXCDKWRb8w8SwJ+ImmepAutNKCvFKYtA1AxiHUAEB+MofcLG64uViJO6N1///265ppr3Dh6NnhftWrVgpbn5ORU5P4BABB3xDoAQDog3gEVl9C7RlL1MG+2VPUl9cwBkr6X9KYku7uySdKNxdZ/VFIbSX/09cazMfAC+XvmFe+5V5rby2kZf1WY2wGSAbEOAOIjM2PfFO66iFNCr169etq6dauOP/74oPlWB9SysAUF+1FAHgCASoBYBwBIB8Q7IAQvwpKbtr4vmReY0ItEoa/8pvXoO6LYsqmSTpXUyfe4tbX6LlZ68ytJ2QFlO8tzVIjX/1HSl5KOifJ3ACorYh0AxAc99H4ZP+/mm29WrVq1FI7x48fryiuvVIMGDWKT0DvnnHNcr7zZs2crNzc36lqfAABUVsQ6AEA6IN4BFddDL1zzJR1kSQZJeZKWSVop6QJJdXxTcbau/xZPB0lNJM2VdIovsfc/G5slghs8R5cyf7GvtyCQSoh1ABA/pIqke+65xyXpwk3oTZ8+XSNHjoxdQu+TTz5xg/d17Ngx0qcCAJAUiHUAgHRAvANCKIywh14k6/oScI9L2ubr0dfMl8yzRF04MiWdL+lpSQ9IypJ0eBnj9UXiIF/C8YwK2BZQWRDrACA+6KH3SyXLgw46KOyOcDt27FAkIk7o9ezZU6tXryahBwBIWcQ6AEA6IN4B8e+h99sID/ptIebVlzRcFe8TSTVisF0gkYh1ABAfjKG3z6xZsxQpq4QZs4TeJZdcojFjxri6nl26dHHlNwN17dpVlZENOJ2T6J1IAavUUj8VDd/9i4baqFYlhuYG70Ny4fMdWzauR7JI5ljHTZj995NaanuIWFdbG9WQWBc3vA8c12S0S8klGeMdsa5icI4t4+83yoRetJ/NRLwXk6wVfbFhALf6eg2eK6mxkh+f8dhKpniXjLHOqZolVbE+uOnL21NPXn7JknUZVXcoI3tzQvYpGXDcOCYRyfANBlwB6KG3z7BhwxRLESf0zjzzTPfvBRdYUYhf3izrSmj/FhRE2DwNSZXs6Ja5XDsLS16m1MzcpQ8LO5LU431IWny+EYhYl77s5s+kzOXaEyLWZWfu0qTCjiT1eB+SFp9vFEe8S99zwQ1lxLqb0z3WxbjkZmV4Lw4LUcbTxu7r6CsBmuz4jCMQsS55k1J7P71KhfnBCViTWXWvqh16B0k9jhufpUrGGguFV2Qy/PVQAQm9lSttuGakI+uZZ8m8Rx+VOnX6Zf7nn0vnnlvDLaeXHu9DsuLzjUDEuvRlLeT3lBHrbHla3+SME94Hjivig3iXnjjHJrbkZmV4L36j1MZnHIGIdcnJeuZZMi/0+bGaW04vPY4bn6XKJTMjw03hros4JfRat24d5UshVVggPdxG3QbvQwri8w1DrAPngsqB94Hjitgi3qU3zrFl9LgriE8PvUS9F3+QNCXEsCTbJV0m6W9KDXzGYYh1yY2/Y44bn6XkYTm6cPN00ebzpk+frjvvvFNr165Vt27dNG3aNPXq1Svkup9++qkmTJigpUuX6rvvvtPdd9+tyy67LOJt7t69W5dffrnmzJmjPXv2aMCAAbr//vsjGvcuoQk98+OPP+qNN97Q+vXrVVgY/O310ksvrah9AwAgYYh1AIB0QLwD4Lc32ptEQCVHrAOA2Iv1GHpz587VuHHjNGPGDPXu3VtTp051ybXly5erSZMmJdbfuXOn2rVrpzPOOENjx46Nepv23Oeff17z5s1T3bp1NXr0aJ1++ul68803lQgRf1d75JFH9Mc//lFZWVlq2LBh0MG3n0noAQCSHbEOAJAOiHdAYsfQi7eFAT+/buP0Ffs1vpTUNAH7BcQSsQ4AUqOH3pQpUzRy5EgNHz7cPbYknCXaZs6cqWuuuabE+kcccYSbTKjl4Wxzy5YtevjhhzV79mwdf/zxbp1Zs2apU6dOevvtt9WnT59S93fv3r2qUaOGli1bps6dOythCb0bbrjBdVUcP368MjNt6GSkG6tXXdZj8D4kMz7fMMQ6cC6oHHgfOK6ILeJdeuMcm/gx9OL9XiwI+PkVG78m4HEVSY0kDVXq4DMOQ6xLbvwdc9z4LKX2GHpbt24Nmp+dne2m4vLy8lzpzPHjx/+yjcxM9e/fX4sXL45qf8PZpi23xJzN8zv44IPVqlUrt05ZCb1q1aq59QoKKuDL4v4k9Kyr4llnnUUyLw011EbVzNzlBucuzuY3LNyYkP1KN7wPHFfEHrEufdXWRmWXEutsfm1iHe9DEuPzjeKId+mJc0Hl6aEX7/fidt+/d0gaJamWUhOfcQQi1iWnjKo7lFl1r849t1qJZTbfloPjxmcp+XvotWzZMmj+xIkTNWnSpBLrb9y40SXGcouNW2ePv/jii6j2N5xt2rh6VqmyXr16JdaxZeW57rrrdO211+qf//ynGjRooIQk9EaMGOHqhZbWTRGpq5VW68PCjvrJtdsLZsk8Ww7eh2TF5xuBiHXpq6FWa1JhR20PEevsppotB+9DsuLzjeKId+l7LriZWFcpeugl6r24SqmNzzgCEeuSU0b2ZlU79A55+SWbHlgyz5aD48ZnKfnH0Fu9erVycnKK5ofqnZfM7rvvPq1YsULNmzdX69atVatW8Dnt/fffj31Cb/LkyTr11FM1f/58denSxXUdLF53tDLKqi9lRVGbFcHaa7WbkFi8DxzXZJTlSfpZSSFZY521KaqZ6J1IAU1dnCPWJRrvA8c1Ge1UcknGeGdpD2Ld/mtMrCv97zfKhF60n81EvRfW9+9dSRsk5RdbNkLJj894bCVTvEvGWOdk1ZSqptaN7UhlZOcpQ3mlLOXbAMeNz1KFyLei2xXDSnmHO0Cbfz1L5gUm9ErTqFEjValSRevWrQuab4+bNo1uBOBwtmn/WmnOzZs3B/XSC/d1Bw8erIoWVULvxRdfVMeOHd3jwKxruBlYAAAqM2IdACAdEO+AxJbcTJQPJd3iGs9I37tqJdJ637J2Cd43oKIR6wCg8vbQC5eVvezRo4cWLVpUlCQrLCx0j0ePHh3V/oazTVtuDUFs3pAhQ9y85cuXa9WqVerbt2+5r2ElRBOe0PvLX/6imTNn6vzzz6/wnQEAoDIg1gEA0gHxDiglQVeQ2gm9f0j6P0m/l3SmpPGS6to5QdLhid45oIIR6wAgPixHlxnhGHqRGDdunIYNG6aePXuqV69emjp1qnbs2KHhw4e75UOHDlWLFi1cQw5jPes+++yzop9/+OEHLVu2TLVr11b79u3D2mbdunVd6WZbz8bAs96El1xyiUvm9enTJ+x9X7p0qT7//HP386GHHqrDDjtMcUvoWR3To446KuoXBACgsiPWAQDSAfEOCKEggnpR/vWTjPXKu8L3s/2qVtCuhqRzJN0qaWCC9w+oSMQ6AIiPzAgSeuGuF+jMM8/Uhg0bNGHCBK1du1bdu3d35ZRzc20AGrlec5mZv3yJ+/HHH4MSZ3fddZeb+vXrp1deeSWsbZq7777bbdd66O3Zs0cDBgzQ/fffH9Y+r1+/XmeddZZ7PX/JTivfedxxx2nOnDlq3LhxxMchkq+pzpgxYzRt2rSIXwgAgGRBrAMApAPiHVBGyc1IpiSTHTBuXgNJawKWbU3QPgGxQqwDgPiW3Ax3isbo0aP13XffucTaO++8o969excts6TZI488UvS4TZs28jyvxORP5oWzTVO9enVNnz5dmzZtcr33nnzyybDH7bPefNu2bdOnn37qnm/TJ598oq1bt+rSSy+NTw+9d999Vy+99JKee+451z2w+GCy9gsBAJDMiHUAgHRAvAPSs4deR0lWgKqljQ0jaaak7yQt9i0DUgmxDgBSo4deMpo/f74WLlyoTp06Fc075JBDXILwpJNOik9Cz7oGnn766VG9GAAAyYBYBwBIB8Q7IIRIe90lYQ+9EZJ2+X62cfR2S3pdUnPfMiCVEOsAID6s0124He+i7KCXdAoLC0t0iDM2z5bFJaE3a9asqF4IAIBkQawDAKQD4h2Qfj30bHc3Whkq3+Pqkv6U4H0CYolYBwDxkZmR4aZw100Hxx9/vCv9/K9//UvNm1vTKemHH37Q2LFjdcIJJ0S1zYjH0AMAAAAAAEhJBVFMSaSKpImStid6RwAAQErJjHBKB/fdd58bL8/G8zvwwAPd1LZtWzdv2rRpseuhd/jhh2vRokWqX79+WBs9+uijNXfuXLVo0UKVRmPfN1cAQGLYzY6fK+/BT4VY10RS7UTvBACksWS4QZ7s8c6GnyfWoTL+/SbTZ7O9pHxfiU0gFeNdssc6p2Zdqar1oQWAGMq3wtsVg5KbJbVs2VLvv/++G0fviy++cPNsPL3+/fsrWmEl9JYtW6YPP/xQDRo0ULjr79mzJ+qdAgAg3oh1AIB0QLwDyuFFOC6erZ9kLpY01fdvJ1/ZzUDJkpgESkOsA4D4y1QEJTeV+iU39+7dqxo1ariYdOKJJ7qpIoQ9hp7V9PS88L6pZqRJDVQAQGoh1gEA0gHxDiinqkQktzSSrOSmGeP7d1yxX9XzPX43QfsFVCRiHQDEFz30glWrVk2tWrVSQUHFflkMK6G3cuXKiDd8wAEHRLM/AAAkBLEOAJAOiHdAOdIgoTcj0TsAxBixDgDiLzNj3xTuuunguuuu07XXXqt//vOfYVe/rJCEXuvWrSvkxQAAqKyIdQCAdEC8A8pRGGHJzUjWrSR6JHoHgBgj1gFAYnrohVtyM10KPN53331asWKFmjdv7mJTrVq1gpbb+HoxK7kJAAAAAACQ0tKgh575QNKTkn6QdJukJpKel9RCUvdE7xwAAEg6lNwsafDgwapoJPQAAAAAAADSpIfeIkkTJJ0i6QtJeb752yXNlHRvgvcPAAAkH0puBsvPz1dGRoYuuOCCCh2eLrPCtgQAAAAAAJDMCqKYkszDksZLur5YK+9ukpYncL8AAEDyyojwv1RXtWpV3XnnnS6xV6HbrdCtAQAAAAAAJKvCCJN0EfbQe8I3rfE9bifpD5KO8j2+VdK7kjZKqiGpq6RLJbUJ2MZaSZMlLZFUU9KpkkZFcIPnO0mHh5hfW9K2yH4dAAAAhx56JR1//PF69dVX1aZN4De5OPfQGzZsmF577bUK2wEAACobYh0AIB0Q74AySm5GMkXAxqobLemfkv4hqaekyyV97VveSdJESfMk3SfJ8yXr/DlG+3eMpL2+8piTJD0r6a8R7EMjSatDzF/mG0MPSCXEOgCIb0Iv3CkdnHLKKbrmmmt0xRVX6F//+peeeeaZoCkuPfS2bNmi/v37q3Xr1ho+fLgLjC1aJMFXvlz6IwJAQlkP8y+T4z1I1lhnFbnrJHonACCNJVvPlmSMd82JdYj132+kJTQLIvtsnl3s8ZGSnpL0vaRjJF1SbHkzSSf48oatfOPfrfQ9p7FvnV2+nn2W3MsKYx+GSrpH0t0BrbzfljRN0liSekixeJeMsc5UqVNPGdWsny4AxI63175FVAwbL86mcNdNB3/605/cv1OmTAl5DAoKCmLfQ+/pp5/WDz/8oIsvvlhz58513QUt0/jEE09o715rIwYAQHIj1gEA0gHxDqi4MfS2+5Ic/mlPGAfXnvq0pJ2SeoRYbvPn+BJ5ljA0S329+PzJPHOc7zXDHf/Okob/J+kMSTt8P18h6TxJI/hQIMUQ6wAgPuihV1JhYWGpUzTJvKgSeqZx48YaN26cPvzwQ73zzjtq3769zjvvPDVv3lxjx47VV199FdXOAABQWRDrAADpgHgHVEzJTRuT7qCAyXq7leZzSQdKai3pal/pzI4Byx/xLbfpJUlzA3rerfeVzAzUKGBZOKxN/GW+/XhZ0vOSPvHtC5CKiHUAEHvW6S6SCYpfQs9vzZo1WrBggZuqVKmigQMH6uOPP9Yhhxyiu++24g0AACQ3Yh0AIB0Q74D9876vurx/Kl46M5Al6hb6EmlW/vLSYr3rTpe0QNKTvnUvlLQ7Bm+QJQlr+8b1qxWD7QOVDbEOAGInMyMjoimVDRw40JV89rvtttu0efPmosc//fSTy6HFJaFnZTX//e9/69RTT3X1p+fNm6fLLrtMP/74o/7+979r4cKFevzxx3XTTTdFtUMAACQasQ4AkA6Id0DFldys7RtDzz9ll5NIayupm6TrJB0q6W8By3MktZPUV9JDklZIesG3zJJvG4ttb2PAsnCHtr7d15Owl2+yn2+z8wIfCqQYYh0AxAclN3/x4osvas+eXwqw//nPf9amTZuKHufn52v58nCLpe9nQq9Zs2YaOXKkS+a9++67WrJkiS666CLl5NhXzn2OO+441atXr9xtTZ48WUcccYTq1KmjJk2aaPDgwSV+kd27d2vUqFFq2LChateurSFDhmjdunWR7jYAAGEj1gEA0kFFxTuu65BSoiy5ub8vmVfKMs83+Zf38JXKDEzqvepLIlpSLhyWRHxU0vW+noALfD//y/cvkEq4tgOAOImk3GZqd9CT53llPt4fESf0rJSm9cabPn26unfvHnIdu+BbuXJludt69dVXXbLu7bffdmU7rdXMSSedpB07bFjmfWxMvmeffdb1BLT17bVPP90KUAAAEBvEOgBAOqioeMd1HVJKYYS98yJM6N0qabGk1b7EnD1+y1dm8ztJ90r6UNL3kt7zldusIekE3/OP9SXuRkv61DcGnvW2O7+cXoGBnpI01Vfu8xDfZD9P8S0DUgnXdgAQH5nKiGhCdDK8ikwP7qcNGza4nnp2QXjMMce4OqM2cO3s2bP129/+1q3zxRdfqFOnTlq8eLH69OlT7ja3bt2qunXrasuvpJyqcfglAAChz8f5Ut3X5c7tgS3/000sY92XvtbZAIDE2Oa70U6sI9Yhif9+W0o5ETR93loo1V2tsL+HjZP0uqT1vvUtmTZKUj9JayVdLukj2w9JjSX19j2nfcA2LBl4jS8RWFPS73y97sK95dHZNz5f8R599jv8ny9RCJSFeBf7a7uag+9XRjVL5wNA7Hh7d2nn03/ar+sX/3nrrv99pBq1wrsrtWvHNl1xUteIX3f69Om68847tXbtWnXr1k3Tpk1Tr15WPDw06yR2ww036Ntvv1WHDh10++23u/Ht/DJKGcvvjjvu0JVXXul+btOmjb77zppdBVcoueYa+zYWWpUqVdw+WkwwVqHyo48+Utu2VnRdrgJl8+bNVVDgq90egUqV4vIPFNigQQP379KlS12vvf79+xetc/DBB6tVq1alBkKrTRpYn9Q+UAAAVBbEOgBAqiPWIakVxnZ96wVXmqaSHgtjGy3DXK80F/h66N0d0KvP7qLc41sGIDzEOwAoOYZeOMJdL9DcuXM1btw4zZgxQ71799bUqVM1YMAAN4SbNa4o7q233tLZZ5/tkm+nnnqqa2xhQ769//776tzZmjdJa9asCXrOCy+8oBEjRrhh3wLddNNNbqgCP0vQlcX60J1//vnKzs4uGlbOhjaoVauWexyYv0rahF5hYaEuu+wyHXXUUUUH1LKYWVlZJcZsyM3NdctCsTfoxhtvLLmgmaRqsdl3AEAY9nKUYh3rcqtKOVQtAICEqWm1T/LT+w0g1iHp/36tobQXeUIvmb6HfZUvLfKknpK6+fb5Q2/fOH0nZEh/Clj3yUpz1wiVCfEu9vGuVk4tZWZZH1wAiJ3CvEztrKBtZWZkuCncdSM1ZcoUl1QbPny4e2yJveeff14zZ84M2Vvunnvu0cknn1zU0+7mm292w77dd9997rmmaVNrTvWL//znP24M8Xbt2gXNtwRe8XXLMmzYsKDH5557bol1hg61gueRqzRfzWwsvU8++URvvPHGfm1n/PjxLlMb2EOvZUtrvwYAQGIR6wAAqY5Yh6QXZUIvmViqYUix+2gtkyQZCVQWxDsACGY5unDzdJHm8/Ly8lw1x/HjxxfNy8zMdJUdrZJjKDY/ME9krEff008/HXJ9K4NpCcK///3vJZbddtttLiFolSN///vfa+zYsapatfTU2qxZsxQrlSKhN3r0aD333HN67bXXdMABBxTNt6ynvVmbN28Oat1iB7e0jKh1Y/R3ZQQAoLIg1gEAUh2xDikhxiU3K4NZleJOEJC8iHcAUFKmIuihp4yQw6WVltvZuHGjG28uNzc3aL49trFKQ7Ge0aHWL63HtCXyrCfe6aefHjT/0ksv1eGHH+6GibMynpZUtFKd1mMwESIY6rniWS1RC4JPPfWUXnrppaJBAf169OihatWqadGiRUXzrCbqqlWr1Ldv3wTsMQAAkSHWAQBSHbEOKaXQ10sv3CkJE3oAokO8A4Dye+iFOxmrrFi3bt2iycoQJ8rMmTN1zjnnqHr16kHzrZffscceq65du7px8P7yl79o2rRp+zUO3v6omuju6TYYodUmteynPztqb16NGjXcvzYIoR00y4Dm5OTokksuccm8Pn36JHLXAQAIC7EOAJDqiHVIKZagi6QMVCTlOSuJnzxpQqH0cqG0PkROclO1BO0YUMkR7wCg7J5j4fYe86+3evVql/PxK63yYqNGjVSlShVXuTFQWZUcbX6467/++uuuI9ncuXPL3ffevXsrPz9f3377rTp27Ki0Sug98MAD7l/LcBavMXr++ee7n++++25XD3XIkCEu62l1Tu+///6E7C8AAJEi1gEAUh2xDimlIPUTeucVSCs8aUSmlGut5BO9Q0CSIN4BQOkyMjLcFA7/epbMC0zolSYrK8tVc1y0aJEGDx7s5hUWFrrHVgEyFOsUZssvu+yyonkLFiwIWfnx4Ycfdtvv1q1bufuybNkyl69q0qSJEqFqoruql8e6OE6fPt1NAAAkG2IdACDVEeuQUtIgofe6J71RVepGJg+ICPEOAEpnXyvC/WoRzVcQq+I4bNgw9ezZU7169dLUqVO1Y8cODR8+3C0fOnSoWrRoUVS2c8yYMerXr58rkTlo0CDNmTNHS5Ys0YMPPhi0XRvHb968eW694hYvXqx33nlHxx13nKswaY/Hjh2rc889V/Xr11ciMBQyAAAAAABAmjg4Q9pliUgSegAAoIJkZmS4Kdx1I3XmmWdqw4YNmjBhghu6rXv37po/f75yc3Pd8lWrVrmec35HHnmkG+7t+uuv17XXXqsOHTro6aefVufOnYO2a4k+a7Bx9tlnl3hNKwFqyydNmuSqR7Zt29Yl9Cy5mCgZXjjNS5KYZVhtLL4tv5NyqAMPAIk7H++V6j4ubdmyJazu9Igi1lWVcrgxAwAJs9WT6uYT62JybIl1iNffb3Zk36fc8/Yoqb6HvVcoXVMoTciUOmdIxW+VJMvvgcQh3sU+3jUe+ndlZtWM4SsBgFSYt1Mb/jFsv+7V+c9bD77ymWrWrhPWc3Zu36YLjz2Ee4RRoIceAAAAAABAmpTcrJchbZV0vP2uAfyd9gpoDA0AACJkne7C7XgXRQc9pF1Cr6n1kUz0TgBAGtuT6B1IA62sbkGidwIA0lihpG8SvRMpjliHWP/9RpvQS6LP5jmrpWpVpdl1pdwqIW6q1UjQjiF5EO9iLqd+LVXJrhX7FwKQ1gr2ZGhDBW0rIyPDTeGui+ikT0IPAAAAAACgvARdEva6i8QnedIHLaWOWYneEwAAkCoyI2jblCRtoColEnoAAAAAAAC+DnrFKlGWKZJ1K4ue2dLqfBJ6AACg4tBDLz5I6AEAAAAAAKRJQu+SetKYjdKV9aQuWVK1YlWvujJcCQAAiJB9nQi3kCYFN6NHQg8AAAAAAMA3NJhN4Ypk3crizLX7/r1gffCNNc/3b0H7hO0aAABIUvTQiw8SegAAAAAAAGnSQ29l60TvAQAASDWMoRcfJPQAAAAAAADSpIde62qJ3gMAAJBq6KEXv8QpAAAAAABA2iuIYkpG/9wqHfW91Hyl9N3effOmbpb+sz3RewYAAJJ5DL1wJ0SHhB4AAAAAAICvx10kybxk7KH3wBZp3EZpYE1pc+EvScl6mdLULQneOQAAkJQyMiKbEJ30KbnZQlKNRO8EAKSxXYnegTTQKq0iOwBUPvmSvkn0TqQ4Yh1i/PcbdcnNJPpsTlssPdRZGtxEuu1l3/2SmlLP7dIVSyW1SfQeotIj3sVcw4Y1VbV6zdi/EIC0lr/b09cVtK1MZbgp3HURnST5ugkAAAAAAID9tXKXdFidkvOzM6UdyVpDFAAAJFQkPe/ooRc9EnoAAAAAAABRjIuXjPmvtjWkZduk1sWqGM3fKHWqlai9AgAAySzD91+46yI6JPQAAAAAAABSPKF30zfSFa2lca2kUcul3YWSJ+ndrdK/1kmTv5X+1inRewkAAJIRPfTig4QeAAAAAACA9mMMvSRw4zfSRQdIf2gh1ciUrv9a2lkg/f4TqXm2dM9B0llNE72XAAAgGVmvu3DHxqOHXvRI6AEAAAAAAKR4Dz3rjed3TrN9kyX0thdITbISuGMAACDp0UMvPkjoAQAAAAAApHgPPVO83XzNKvsmAACA/fqOkbFvCnddRIeEHgAAAAAAgC9BVxDDhN4D3++bvt217/GhtaUJbaVTGkmb9koTv5b+t0latVtqXE0a3ES6+UCpbsDdG1t28efSyz9LtatIw5pLkw+UqmaW//oHvVUyqVfcpmMj/KUAAEDaszKa4ZbSpORm9EjoAQAAAAAAxKHk5gHZ0m3tpQ41Jc+T/r5G+s2H0ge995XE/HGPdFcH6ZBa0ne7pYu+2Dfvia6+1/OkQR9ITbOlt46Q1uyRhn4qVcuQ/ty+/Ne/sV1wchAAAKAiZGbsm8JdF9HhaxwAAAAAAEAcSm6e1jj48a3t9/XYe3uLNKKF9O9uvyw7sKZ064HSuZ9I+YX7euD97yfpsx3SwsOl3Gype519Pfiu/kqa1E7KKqeX3llNGS8PAABUPHroxUf6JPSaWXH4RO8EAKSxnYnegTTQRlJWoncCANJYXqJ3IA20I9Yhhn+/r0TfQ2/rAcGfzewq+6Yyn1sozftG2lEo9e0iqUHJdbbslXKypaoH7Xu8+GepS0Mp99Bf1hnQRLr4C+nTBtJhjUp/vYxFktpKqhHBLwiU8feC2GnaoKaq1ajFIQYQU3t3WX2AisEYevERRoV1AAAAAACA1FcQxWRaPirVnfnLNPn90l/j45+k2n+Tsh+SLnpNemqAdEiIZN7GXdLNS6ULO/0yb+1OKbdYQs7/2JaVxUp8AgAAxEJGQC+98v+LzvTp09WmTRtVr15dvXv31rvvvlvm+vPmzdPBBx/s1u/SpYv++9//Bi0///zzlZGRETSdfPLJQets2rRJ55xzjnJyclSvXj2NGDFC27dvV6KkTw89AAAAAACAGJTcXH2ulFOsh15pOtaTlp0hbcmTnvhGGvay9Oqvg5N6W/OkQS9Ih9SXJvWsmLes8KKK2Q4AAEC8x9CbO3euxo0bpxkzZrhk3tSpUzVgwAAtX75cTZo0KbH+W2+9pbPPPluTJ0/WqaeeqtmzZ2vw4MF6//331blz56L1LIE3a9asosfZ2dlB27Fk3po1a7RgwQLt3btXw4cP14UXXui2lwj00AMAAAAAANiPHnqWzAucykroZVWR2teVejSWJveWujWU7vn4l+Xb8qSTn5fqVNvXe69awLaa1pTW7Qrenv+xLQMAAEiE8HvnRddHb8qUKRo5cqRLqB1yyCEusVezZk3NnDkz5Pr33HOPS9ZdeeWV6tSpk26++WYdfvjhuu+++4LWswRe06ZNi6b69esXLfv88881f/58/e1vf3NJxKOPPlrTpk3TnDlz9OOPPyoRSOgBAAAAAAAkSKEn7Sn4pWfeSc9LWZnSMydL1YvVVeqbK328SVofkNRb8P2+JKL15gMAAEgE/xh64U6RyMvL09KlS9W/f/+ieZmZme7x4sWLQz7H5geub6xHX/H1X3nlFdfDr2PHjrr44ov1008/BW3Dymz27PlLuQTbpr32O++8o0Sg5CYAAAAAAICNMxdhyc1Ih6Ub/450SkupVW1p215p9grplR+lFwf5knnPSTvzpUcHSFv37ptM4+pSlUzppAP2Je7OWyTd0Udau0u6/l1p1KFl9woEAACI/Rh64a9rtm7dWqK3XPGSl2bjxo0qKChQbm5u0Hx7/MUXX4R8jbVr14Zc3+b7WQ++008/XW3bttXXX3+ta6+9VqeccopL5FWpUsWtW7ycZ9WqVdWgQYOg7cQTCT0AAAAAAIBiZTTDEcm6xnrWDX1JWrNTqpsldW24L5l3YkvplR+kd9bvW6/9v4Kft/L3UpucfUm9506RLn5N6vu0VKuqNKyjdNMRvH0AACBxMpWhzDC73tm6pmXLlkHzJ06cqEmTJilezjrrrKKfu3Tpoq5du+rAAw90vfZOOOEEVUYk9AAAAAAAAOKQ0Hv42NKXHdtC8i4qfxut60j/HRThCwMAAFSyHnqrV69WTk5O0fxQvfNMo0aNXI+5devWBc23xzbuXSg2P5L1Tbt27dxrrVixwiX0bN31632trXzy8/O1adOmMrcTS4yhBwAAAAAA4Cu3GekEAACQ9jIinCSXzAucSkvoZWVlqUePHlq0aFHRvMLCQve4b9++IZ9j8wPXNwsWLCh1ffP999+7MfSaNWtWtI3Nmze78fv8XnrpJffavXv3Tshbnj499FpJqp3onQCANLY90TuQBtpJqp7onQCANLY70TuQBtoQ6xDbv9+oe+jx2UQ6Id7FXIuGtZRds1bsXwhAWtuzM9LRgEuX4fsv3HUjNW7cOA0bNkw9e/ZUr169NHXqVO3YsUPDhw93y4cOHaoWLVpo8uTJ7vGYMWPUr18//eUvf9GgQYM0Z84cLVmyRA8++KBbvn37dt14440aMmSI621nY+hdddVVat++vQYMGODW6dSpkxtnb+TIkZoxY4b27t2r0aNHu1KdzZs3VyKkT0IPAAAAAAAggSU3AQAAUlKGFOYQeuHX5gxw5plnasOGDZowYYLWrl2r7t27a/78+crNzXXLV61apczMXwpSHnnkkZo9e7auv/56XXvtterQoYOefvppde7c2S23Ep4fffSR/v73v7teeJagO+mkk3TzzTcH9RR87LHHXBLPSnDa9i0BeO+99ypRSOgBAAAAAABEUUaTkpsAAADRjaEXqdGjR7splFdeeaXEvDPOOMNNodSoUUMvvvhiua/ZoEEDlxisLEjoISKr1rbUxs2NSsxvVG+jWjVdzdGME94HjiuAGJ5jf26pjTtCxLpaG9WqPrEuXngfOK4AOMcmQmGEve72N6FHvIsNjiuQ/LZuqKrdW6uUmF89p0A5jfMTsk/JgOPGMUnpjB5I6CGyJFKnM5Zr564aJZbVrLFLn8/rSFIvDngfOK4AYniO/bmlOk1Zrp17QsS67F36fFxHknpxwPvAcQXAOTYdeugR72KD4wqkRlLq0dHtlLf7l/J5fln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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Compute the initial-guess temperature field for comparison\n", "T_init_field = np.asarray(solve(x0[0], x0[1])).reshape(ny, nx)\n", @@ -507,10 +633,21 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, "id": "e337f08f8d05", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Grid: 30x30 = 900 unknowns\n", + "Sensors: 100\n", + "Simulation: 100 steps x 0.05s = 5s\n", + "True T_init range: 293.2 — 332.7 K\n" + ] + } + ], "source": [ "# --- Part 2 setup ---\n", "# Shorter simulation: 5 seconds (we want residual structure in the initial field)\n", @@ -581,10 +718,33 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "id": "c6473e7ffb35", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial loss: 4072.76\n", + "Running L-BFGS-B with 900 parameters...\n", + " iter 10: loss=54.0890, elapsed=0.3s\n", + " iter 20: loss=53.9501, elapsed=0.7s\n", + " iter 30: loss=53.9492, elapsed=1.1s\n", + " iter 40: loss=53.9492, elapsed=1.4s\n", + " iter 50: loss=53.9492, elapsed=1.8s\n", + " iter 60: loss=53.9492, elapsed=2.1s\n", + "\n", + "Optimization finished: 65 iterations, 2.6s\n", + "Loss: 4072.76 → 53.9492\n", + "T_init correlation: 0.9799\n", + "\n", + "Cost comparison per iteration:\n", + " Finite differences: 901 forward solves = ~28.2s\n", + " Reverse-mode AD: 2 solves (fwd+rev) = ~0.06s\n" + ] + } + ], "source": [ "import time\n", "\n", @@ -605,7 +765,10 @@ " return data_loss + reg_loss\n", "\n", "\n", - "value_and_grad_p2 = jax.value_and_grad(loss_fn_p2)\n", + "value_and_grad_p2 = jax.jit(jax.value_and_grad(loss_fn_p2))\n", + "\n", + "# warm up JIT\n", + "_ = value_and_grad_p2(jnp.asarray(T_init))\n", "\n", "\n", "def scipy_objective_p2(T_init_vec):\n", @@ -666,10 +829,29 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "id": "44fd35ce4a54", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/var/folders/fk/g5ssrkz179z1mjmvqn1j3q1m0000gn/T/ipykernel_73719/182219165.py:92: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n", + " plt.tight_layout()\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "fig, axes = plt.subplots(2, 3, figsize=(16, 9))\n", "\n", @@ -792,7 +974,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "id": "babc4d54e5a1", "metadata": {}, "outputs": [], @@ -804,12 +986,21 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "tesseract-core-2 (3.10.16)", "language": "python", "name": "python3" }, "language_info": { - "name": "python" + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.16" } }, "nbformat": 4, From 32d0e12c9be8be0dea9b5c75dd8fc1876cfd8684 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dion=20H=C3=A4fner?= Date: Tue, 2 Jun 2026 14:15:56 +0200 Subject: [PATCH 11/24] style(docs): tighten blog code-block and table spacing Reduce vertical whitespace in blog posts: - Code blocks: trim wrapper margin (1.5rem -> 1rem) and pre padding (1rem/1.25rem -> 0.7rem/1.1rem), and tighten the gap when a short intro line is immediately followed by a code block. Short one-line bash/python snippets no longer sit in oversized boxes. - Tables: size to content width (width:auto, capped at 100%) instead of stretching full-width, with a fit-content wrapper so the table isn't centered in an empty box, plus tighter row padding. The small 2-3 row comparison tables now waste far less horizontal and vertical space. All scoped to .blog-page so docs and landing pages are unaffected. Verified by rendering the Fortran/Enzyme post. Co-Authored-By: Claude Opus 4.8 (1M context) --- docs/static/custom.css | 39 ++++++++++++++++++++++++++++++--------- 1 file changed, 30 insertions(+), 9 deletions(-) diff --git a/docs/static/custom.css b/docs/static/custom.css index 0b683418..585d7b2f 100644 --- a/docs/static/custom.css +++ b/docs/static/custom.css @@ -624,7 +624,7 @@ body[data-theme="dark"] .ecosystem-card:focus-visible { background: var(--color-code-background); border-radius: var(--radius-md); border: 1px solid var(--color-background-border); - margin: 1.5rem 0; + margin: 1rem 0; overflow: hidden; } @@ -632,13 +632,19 @@ body[data-theme="dark"] .ecosystem-card:focus-visible { background: transparent; border-radius: 0; border: none; - padding: 1rem 1.25rem; + padding: 0.7rem 1.1rem; margin: 0; font-size: 0.85rem; - line-height: 1.6; + line-height: 1.5; overflow-x: auto; } +/* Tighten the gap when a short intro line is immediately followed by a code + block (e.g. "Building and serving it is two commands:") */ +.blog-page .content p:has(+ .highlight) { + margin-bottom: 0.6rem; +} + /* Images — center and constrain */ .blog-page .content img { display: block; @@ -778,29 +784,44 @@ body[data-theme="dark"] .ecosystem-card:focus-visible { margin: 0; } -/* Tables */ +/* Tables — size to content rather than stretching full-width, so the small + comparison tables in posts don't waste horizontal (and vertical) space. */ .blog-page .content table { - width: 100%; - margin: 2rem 0; + width: auto; + max-width: 100%; + margin: 1.25rem 0; border-collapse: separate; border-spacing: 0; font-size: 0.9rem; - line-height: 1.5; + line-height: 1.45; border-radius: var(--radius-md); overflow: hidden; border: 1px solid var(--color-background-border); } +/* Furo wraps tables in a scroll container that is itself full-width; let it + shrink so the content-width table isn't centered in a wide empty box. */ +.blog-page .content .table-wrapper { + width: fit-content; + max-width: 100%; + margin: 1.25rem 0; + overflow-x: auto; +} + +.blog-page .content .table-wrapper table { + margin: 0; +} + .blog-page .content table thead th { background: var(--color-background-secondary); font-weight: 600; text-align: left; - padding: 0.75rem 1rem; + padding: 0.45rem 0.9rem; border-bottom: 2px solid var(--color-background-border); } .blog-page .content table tbody td { - padding: 0.6rem 1rem; + padding: 0.4rem 0.9rem; border-bottom: 1px solid var(--color-background-border); } From a1808c8d796d73e5bf7f9202d5b0fc21162e08d4 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dion=20H=C3=A4fner?= Date: Tue, 2 Jun 2026 14:57:46 +0200 Subject: [PATCH 12/24] tighten prose + diagrams --- demo/enzyme_thermal_2d/figures/pipeline.png | Bin 135911 -> 143172 bytes .../generate_pipeline_diagram.py | 152 ++++++++---------- .../2026-05-15-fortran-enzyme-autodiff.md | 89 ++-------- 3 files changed, 80 insertions(+), 161 deletions(-) diff --git a/demo/enzyme_thermal_2d/figures/pipeline.png 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cy - h / 2), w, h, - boxstyle="round,pad=0.05", + boxstyle="round,pad=0.04", facecolor=bg, edgecolor=edge, linewidth=lw, @@ -36,17 +36,16 @@ def draw_box(ax, cx, cy, w, h, line1, line2, bg, edge, lw=1.5, fs=10): kw = dict(ha="center", va="center", zorder=3, parse_math=False) if line2: ax.text( - cx, cy + 0.12, line1, fontsize=fs, fontweight="bold", color="#1f2937", **kw + cx, cy + 0.13, line1, fontsize=fs, fontweight="bold", color="#1f2937", **kw ) ax.text( - cx, cy - 0.12, line2, fontsize=fs - 2, color="#6b7280", style="italic", **kw + cx, cy - 0.15, line2, fontsize=fs - 2, color="#6b7280", style="italic", **kw ) else: ax.text(cx, cy, line1, fontsize=fs, fontweight="bold", color="#1f2937", **kw) def draw_arrow(ax, x0, y0, x1, y1, rad=0.0): - style = f"arc3,rad={rad}" a = FancyArrowPatch( (x0, y0), (x1, y1), @@ -54,7 +53,9 @@ def draw_arrow(ax, x0, y0, x1, y1, rad=0.0): mutation_scale=14, color=C_ARROW, linewidth=1.8, - connectionstyle=style, + connectionstyle=f"arc3,rad={rad}", + shrinkA=0, + shrinkB=0, zorder=1, ) ax.add_patch(a) @@ -67,10 +68,10 @@ def label(ax, x, y, text): text, ha="center", va="center", - fontsize=7.5, + fontsize=8, color=C_TEXT, fontfamily="monospace", - bbox=dict(boxstyle="round,pad=0.12", fc="white", ec="#d1d5db", lw=0.5), + bbox=dict(boxstyle="round,pad=0.16", fc="white", ec="#d1d5db", lw=0.6), zorder=4, ) @@ -85,84 +86,72 @@ def badge(ax, x, y, num, color): fontsize=10, fontweight="bold", color=color, - bbox=dict(boxstyle="circle,pad=0.18", fc="white", ec=color, lw=1.3), + bbox=dict(boxstyle="circle,pad=0.3", fc="white", ec=color, lw=1.3), zorder=5, ) def main(): - fig, ax = plt.subplots(figsize=(18, 5.2)) - ax.set_xlim(-1, 20) - ax.set_ylim(-1.2, 4.0) - ax.set_aspect("equal") - ax.axis("off") + fig, ax = plt.subplots(figsize=(16, 6)) # Y lanes - Y_TOP = 2.8 - Y_BOT = 0.8 - Y_MID = 1.8 + Y_TOP = 4.6 + Y_BOT = 2.4 + Y_MID = 3.5 - # X centers — generous spacing + # X centers — each column gets >= box width + gap of clearance. + # Box width is W; column pitch is 3.4 so there is always a ~1.2 gap. X = { - "f90": 0.5, - "ll": 4.0, - "opt": 7.5, - "combined": 10.5, - "ad": 12.8, - "so": 16.0, + "f90": 0.0, + "ll": 3.4, + "opt": 6.8, + "combined": 10.2, + "ad": 13.6, + "so": 17.4, } - W, H = 2.2, 0.65 + W, H = 2.2, 0.85 + + ax.set_xlim(X["f90"] - W / 2 - 0.6, X["so"] + (W + 0.6) / 2 + 0.6) + ax.set_ylim(0.4, 6.0) + ax.axis("off") - # ── TOP TRACK: Fortran ── + # ── TOP TRACK: Fortran source path ── draw_box( ax, X["f90"], Y_TOP, W, H, "thermal_2d.f90", "Fortran source", C_FORT_BG, C_FORT ) draw_box(ax, X["ll"], Y_TOP, W, H, "thermal_2d.ll", "LLVM IR", C_IR_BG, C_IR) draw_box( - ax, - X["opt"], - Y_TOP, - W + 0.4, - H, - "thermal_2d_opt.ll", - "optimized IR", - C_IR_BG, - C_IR, + ax, X["opt"], Y_TOP, W, H, "thermal_2d_opt.ll", "optimized IR", C_IR_BG, C_IR ) draw_arrow(ax, X["f90"] + W / 2, Y_TOP, X["ll"] - W / 2, Y_TOP) - label(ax, (X["f90"] + X["ll"]) / 2, Y_TOP + 0.48, "lfortran --show-llvm") + label(ax, (X["f90"] + X["ll"]) / 2, Y_TOP - 0.62, "lfortran\n--show-llvm") - draw_arrow(ax, X["ll"] + W / 2, Y_TOP, X["opt"] - (W + 0.4) / 2, Y_TOP) - label(ax, (X["ll"] + X["opt"]) / 2, Y_TOP + 0.48, "opt -O3") + draw_arrow(ax, X["ll"] + W / 2, Y_TOP, X["opt"] - W / 2, Y_TOP) + label(ax, (X["ll"] + X["opt"]) / 2, Y_TOP + 0.62, "opt -O3") - # ── BOTTOM TRACK: C wrapper ── + # ── BOTTOM TRACK: C wrapper path ── draw_box( ax, X["f90"], Y_BOT, W, H, "wrapper.c", "Enzyme annotations", C_WRAP_BG, C_WRAP ) draw_box(ax, X["ll"], Y_BOT, W, H, "wrapper.ll", "LLVM IR", C_IR_BG, C_IR) draw_arrow(ax, X["f90"] + W / 2, Y_BOT, X["ll"] - W / 2, Y_BOT) - label(ax, (X["f90"] + X["ll"]) / 2, Y_BOT - 0.48, "clang -emit-llvm") + label(ax, (X["f90"] + X["ll"]) / 2, Y_BOT + 0.62, "clang\n-emit-llvm") - # ── MERGE ── + # ── MERGE into combined.ll ── draw_box(ax, X["combined"], Y_MID, W, H, "combined.ll", "linked IR", C_IR_BG, C_IR) - # top track -> combined + # both tracks feed llvm-link; arrows enter the left face of combined.ll draw_arrow( - ax, - X["opt"] + (W + 0.4) / 2, - Y_TOP, - X["combined"] - W / 2, - Y_MID + 0.12, - rad=-0.2, + ax, X["opt"] + W / 2, Y_TOP, X["combined"] - W / 2, Y_MID + 0.18, rad=-0.18 ) - # bottom track -> combined draw_arrow( - ax, X["ll"] + W / 2, Y_BOT, X["combined"] - W / 2, Y_MID - 0.12, rad=0.15 + ax, X["ll"] + W / 2, Y_BOT, X["combined"] - W / 2, Y_MID - 0.18, rad=0.18 ) - label(ax, (X["opt"] + X["combined"]) / 2 + 0.3, Y_MID + 0.75, "llvm-link") + # place the merge label in the open wedge to the left of combined.ll + label(ax, X["combined"] - W / 2 - 1.4, Y_MID, "llvm-link") # ── LINEAR: combined -> ad -> .so ── draw_box( @@ -170,7 +159,7 @@ def main(): X["ad"], Y_MID, W, - H + 0.1, + H, "ad.ll", "differentiated IR", C_ENZ_BG, @@ -178,52 +167,41 @@ def main(): lw=2.5, ) - W_SO, H_SO = W + 0.6, H + 0.4 + W_SO = W + 0.6 draw_box( ax, X["so"], Y_MID, W_SO, - H_SO, + H + 0.15, "libthermal_2d_ad.so", - None, + "forward / JVP / VJP", C_SO_BG, C_SO, lw=2.5, - ) - ax.text( - X["so"], - Y_MID - 0.13, - "forward / JVP / VJP", - ha="center", - va="center", - fontsize=8.5, - color="#9a3412", - fontweight="bold", - zorder=3, - parse_math=False, + fs=10, ) draw_arrow(ax, X["combined"] + W / 2, Y_MID, X["ad"] - W / 2, Y_MID) - label(ax, (X["combined"] + X["ad"]) / 2, Y_MID + 0.52, "opt -passes=enzyme") + label(ax, (X["combined"] + X["ad"]) / 2, Y_MID + 0.62, "opt\n-passes=enzyme") draw_arrow(ax, X["ad"] + W / 2, Y_MID, X["so"] - W_SO / 2, Y_MID) - label(ax, (X["ad"] + X["so"]) / 2, Y_MID + 0.52, "opt + clang -shared") - - # ── Step badges ── - badge(ax, X["f90"], Y_TOP + H / 2 + 0.32, 1, C_FORT) - badge(ax, X["ll"], Y_TOP + H / 2 + 0.32, 2, C_IR) - badge(ax, X["f90"], Y_BOT - H / 2 - 0.32, 3, C_WRAP) - badge(ax, X["combined"], Y_MID + H / 2 + 0.32, 4, C_IR) - badge(ax, X["ad"], Y_MID + (H + 0.1) / 2 + 0.32, 5, C_ENZ) - badge(ax, X["so"], Y_MID + H_SO / 2 + 0.32, 6, C_SO) - - # ── Tool labels at bottom ── - by = -0.7 + label(ax, (X["ad"] + X["so"]) / 2, Y_MID + 0.62, "opt +\nclang -shared") + + # ── Step badges, placed just above/below the box they number ── + badge(ax, X["f90"] - W / 2 + 0.1, Y_TOP + H / 2 + 0.35, 1, C_FORT) + badge(ax, X["ll"] - W / 2 + 0.1, Y_TOP + H / 2 + 0.35, 2, C_IR) + badge(ax, X["f90"] - W / 2 + 0.1, Y_BOT - H / 2 - 0.35, 3, C_WRAP) + badge(ax, X["combined"] - W / 2 + 0.1, Y_MID + H / 2 + 0.35, 4, C_IR) + badge(ax, X["ad"] - W / 2 + 0.1, Y_MID + H / 2 + 0.35, 5, C_ENZ) + badge(ax, X["so"] - W_SO / 2 + 0.1, Y_MID + (H + 0.15) / 2 + 0.35, 6, C_SO) + + # ── Tool labels at bottom, centered under the columns they cover ── + by = 0.9 for bx, txt, bg, ec in [ - (0.5, "LFortran 0.61", C_FORT_BG, C_FORT), - (7.0, "LLVM 19", C_IR_BG, C_IR), - (13.5, "Enzyme (LLVM pass)", C_ENZ_BG, C_ENZ), + ((X["f90"] + X["ll"]) / 2, "LFortran 0.61", C_FORT_BG, C_FORT), + ((X["ll"] + X["combined"]) / 2, "LLVM 19", C_IR_BG, C_IR), + ((X["ad"] + X["so"]) / 2, "Enzyme (LLVM pass)", C_ENZ_BG, C_ENZ), ]: ax.text( bx, @@ -231,20 +209,20 @@ def main(): txt, ha="center", va="center", - fontsize=8.5, + fontsize=9, color=C_TEXT, fontweight="bold", - bbox=dict(boxstyle="round,pad=0.22", fc=bg, ec=ec, lw=1), + bbox=dict(boxstyle="round,pad=0.3", fc=bg, ec=ec, lw=1), ) # Title ax.text( - 9.0, - 3.7, + (X["f90"] + X["so"]) / 2, + 5.7, "Compilation pipeline: Fortran → Enzyme AD → shared library", ha="center", va="center", - fontsize=15, + fontsize=16, fontweight="bold", color="#111827", ) diff --git a/docs/blog/2026-05-15-fortran-enzyme-autodiff.md b/docs/blog/2026-05-15-fortran-enzyme-autodiff.md index 22a77326..359fedf1 100644 --- a/docs/blog/2026-05-15-fortran-enzyme-autodiff.md +++ b/docs/blog/2026-05-15-fortran-enzyme-autodiff.md @@ -81,93 +81,38 @@ subroutine thermal_2d_solve(n, nx, ny, n_steps, & end do ``` -The stencil uses harmonic-mean conductivity at cell faces (the standard approach for flux continuity across cells with different conductivities). Boundary conditions are mixed: Dirichlet (hot wall at the bottom), convection/Robin (top), and insulated/Neumann (sides). +Boundary conditions are mixed — Dirichlet (hot wall at the bottom), convection/Robin (top), insulated/Neumann (sides) — and the faces use harmonic-mean conductivity, the standard trick for flux continuity across cells with different $k$. This is exactly where AD earns its keep: because $k(T)$ is nonlinear, the stencil coefficients depend on the current temperature field, so the Jacobian changes at every time step. Hand-coding the adjoint through that, and re-deriving it every time the forward code changes, is the kind of work AD exists to delete. -The reason AD matters here: since $k(T)$ is nonlinear, the stencil coefficients depend on the current temperature field, and the Jacobian changes at every time step. Hand-coding the adjoint through this nonlinear stencil and multi-step time loop is tremendously painful, and needs to be updated every time the forward code changes. - -This really is vanilla Fortran: no special annotations, no AD-aware constructs, explicit `do` loops, no array intrinsics. But getting to "vanilla" took some work: Our first version used local allocatable arrays for `T_cur` and `T_new`, which LFortran compiles into `_lfortran_malloc` calls, and Enzyme has no idea what to do with them, so the AD pass just crashes. The fix was to pass work arrays in from C, pre-allocated on the heap. Not a huge change, but given how unhelpful the LLVM error messages were, it took some time to figure out. We also had to disable array intrinsics and bounds checking (`--no-array-bounds-checking`) for the same reason: they emit runtime calls that Enzyme can't see through. - -This is an honest preview of what "differentiate existing Fortran" looks like today. The source stays recognizably Fortran, but you'll need to massage it, eliminating allocations and runtime calls that break the AD toolchain. For a 220-line solver, that's an afternoon; for a large legacy codebase, it's an open question. +It's vanilla Fortran — explicit `do` loops, no annotations, no AD-aware constructs — but getting to "vanilla" took some massaging. Allocatables, array intrinsics, and bounds checking all compile down to runtime calls (`_lfortran_malloc` and friends) that Enzyme can't see through, so they had to go: work arrays get passed in pre-allocated from C, and we compile with `--no-array-bounds-checking`. For a 220-line solver that's an afternoon's work; for a large legacy codebase, it's an open question. ## The pipeline -Enzyme works at the LLVM IR level, not the source level, so anything that compiles to LLVM IR (C, C++, Rust, Fortran) can be differentiated. In practice there are caveats, but the compilation chain is surprisingly straightforward, as long as you're comfortable inspecting LLVM IR when things go wrong. - -There are six steps: +Enzyme works at the LLVM IR level, not the source level, so anything that compiles to LLVM IR (C, C++, Rust, Fortran) can be differentiated. The chain is six `opt`/`clang` invocations, surprisingly straightforward as long as you're comfortable inspecting IR when things go wrong: Compilation pipeline: Fortran → Enzyme AD → shared library -**1. Fortran → LLVM IR** via LFortran: - -```bash -$ lfortran --show-llvm --no-array-bounds-checking thermal_2d.f90 > thermal_2d.ll -``` - -LFortran is a modern Fortran compiler, and the reason we reached for it is that it emits remarkably clean LLVM IR. Arrays come out as plain pointers with the usual GEP/load/store patterns, much like you'd get from C, instead of the multi-field descriptor structs and runtime library calls that Flang produces. That turns out to matter a lot, because Enzyme has to trace through every single memory access to figure out what's active, and it has a far easier time with plain pointer arithmetic than with opaque `fir.box` descriptors. The catch is that LFortran is still maturing, so not every Fortran feature is supported yet (here's the [compilation status](https://lfortran.org/progress/)) and your code has to stay within what it can handle. - -**2. Optimize the IR:** +Most of those steps are plumbing — lower the Fortran to IR, compile a thin C wrapper, `llvm-link` the two, run Enzyme, optimize, emit a `.so`. Two of them are where all the interesting failures live. -```bash -$ opt -O1 -S thermal_2d.ll -o thermal_2d_opt.ll -``` - -Notice that's `-O1`, not `-O3`! Our first pipeline used `-O3` here, and the forward pass worked perfectly, so we moved on. The VJP didn't, though. It returned NaN on certain inputs, and it took us a few hours to track down why. What was happening is that LLVM's aggressive vectorization and code-motion passes at `-O3` produce IR patterns Enzyme mishandles during reverse-mode analysis, and in our case it bit specifically when adjacent cell temperatures were equal and intermediate terms canceled out, which can turn into a division by zero once things get rearranged. We settled on keeping the pre-Enzyme optimization mild and saving `-O3` for after the AD pass instead (that's step 6). If you build something like this, our advice is to test the gradients early and often. - -**3. Compile the C wrapper to LLVM IR:** +**Why LFortran.** The first step (`lfortran --show-llvm`) is also the reason the whole thing is tractable: LFortran emits remarkably clean IR. Arrays come out as plain pointers with the usual GEP/load/store patterns, much like C, instead of the multi-field descriptor structs and runtime calls that Flang produces. That matters enormously, because Enzyme has to trace every memory access to figure out what's active, and it has a far easier time with pointer arithmetic than with opaque `fir.box` descriptors. The catch: LFortran is still maturing, so your code has to stay inside what it [supports](https://lfortran.org/progress/). -```bash -$ clang -emit-llvm -S -O1 wrapper.c -o wrapper.ll -``` +**Why `-O1`, not `-O3`.** The pre-Enzyme optimization step looks innocuous, and our first pipeline used `-O3` there. The forward pass worked perfectly, so we moved on — but the VJP returned NaN on certain inputs, and it took hours to find why. At `-O3`, LLVM's aggressive vectorization and code-motion produce IR patterns Enzyme mishandles in reverse mode; in our case it bit when adjacent cell temperatures were equal, intermediate terms cancelled, and a rearrangement turned that into a division by zero. The fix is to keep optimization mild _before_ the AD pass and save `-O3` for _after_ it. If you build something like this: test the gradients early and often. -A thin C wrapper bridges Fortran's by-pointer ABI over to a C-callable interface that Enzyme can annotate. It declares three entry points, `thermal_2d_forward`, `thermal_2d_vjp`, and `thermal_2d_jvp`, and uses Enzyme's `__enzyme_autodiff` and `__enzyme_fwddiff` intrinsics to mark which arguments should get shadow (gradient) buffers. Here's the core of the VJP entry point: +In between sits a thin C wrapper that bridges Fortran's by-pointer ABI to a C interface Enzyme can annotate. It allocates the work arrays on the heap (sidestepping the `_lfortran_malloc` issue) and marks which arguments get shadow buffers via Enzyme's intrinsics: ```c -void thermal_2d_vjp(int nx, int ny, int n_steps, - const double* T_init, double* dT_init, - const double* T_final, double* dT_final, - double k0, double* dk0, - double k1, double* dk1, - /* ... */) +void thermal_2d_vjp(/* ... nx, ny, n_steps ... */) { - double* T_cur = calloc(n, sizeof(double)); - double* dT_cur = calloc(n, sizeof(double)); + double* T_cur = calloc(n, sizeof(double)); // heap, not allocatable /* ... */ - __enzyme_autodiff((void*)thermal_2d_solve, - enzyme_const, &n_, - enzyme_const, &nx_, - enzyme_dup, (double*)T_init, dT_init, - enzyme_dup, (double*)T_final, dT_final, - enzyme_dup, &k0_, dk0, - enzyme_dup, &k1_, dk1, + enzyme_const, &nx_, // not differentiated + enzyme_dup, (double*)T_init, dT_init, // value + shadow buffer + enzyme_dup, &k0_, dk0, /* ... */); } ``` -This is also where the work arrays get allocated on the heap, sidestepping the `_lfortran_malloc` issue from earlier. - -**4. Link the IR modules:** - -```bash -$ llvm-link wrapper.ll thermal_2d_opt.ll -S -o combined.ll -``` - -**5. Run the Enzyme AD pass:** - -```bash -$ opt --load-pass-plugin=LLVMEnzyme-19.so -passes=enzyme -S combined.ll -o ad.ll -``` - -This is the step that does the real work, and where Enzyme analyzes the LLVM IR and synthesizes forward and reverse-mode derivative code. For reverse mode, it uses a store-all (tape) strategy, caching intermediate values at each time step. When it works, it's genuinely impressive — you get an adjoint of your entire time-stepping loop for free. When it doesn't, you're reading LLVM IR diffs at 2 AM wondering where your life went wrong (see [What's next](#whats-next-and-what-wed-do-differently)). - -**6. Optimize and compile to a shared library:** - -```bash -$ opt -O3 -S ad.ll -o ad_opt.ll -$ clang -shared -O3 ad_opt.ll -o libthermal_2d_ad.so -lm -``` - -Out comes a single `.so` file with three entry points you can call from Python via ctypes, one each for forward evaluation, the JVP, and the VJP. The whole pipeline runs during `tesseract build` and takes about 30 seconds end to end. +The Enzyme pass (`-passes=enzyme`) is where the real work happens: it analyzes the linked IR and synthesizes the derivative code, using a store-all tape strategy that caches intermediates at each time step. When it works, you get an adjoint of your entire time-stepping loop for free. When it doesn't, you're reading IR diffs at 2 AM (see [What's next](#whats-next-and-what-wed-do-differently)). The final `-O3 + clang -shared` step emits a single `.so` with three entry points — forward, JVP, VJP — callable from Python via ctypes. The whole pipeline runs during `tesseract build`, about 30 seconds end to end. ## Does it actually work? @@ -211,9 +156,7 @@ With that in place, it's finally time to point some real optimization problems a ### Scalar calibration: recovering 2 material parameters -For a sanity check, the setup stays simple. A steel plate is heating up, there are thermocouple readings at 9 sensor locations, and the plate's material properties are unknown. The question is whether $k_0$ (base conductivity) and $k_1$ (its temperature coefficient) can be recovered from those sparse, noisy readings. - -To keep the test honest, the "observed" data is generated synthetically: run the solver with known true values ($k_0 = 45$, $k_1 = -0.02$), sample at the sensor locations, and add 0.5 K of Gaussian noise on top. The optimizer then starts from a deliberately bad guess, 33% off on $k_0$ and the wrong sign entirely on $k_1$, and the whole thing goes to L-BFGS-B. The loss is a plain JAX function that happens to call the Fortran solver; `jax.value_and_grad` hands back both the loss and its gradient, propagating the cotangent through the HTTP boundary into Enzyme's reverse-mode pass. The optimizer is none the wiser that the gradients came from a compiled Fortran solver differentiated by an LLVM pass. +A sanity check first: a steel plate heats up, 9 thermocouples read its temperature, and the material properties are unknown. Can we recover $k_0$ (base conductivity) and $k_1$ (its temperature coefficient) from those sparse, noisy readings? To keep the test honest, the "observed" data is synthetic — the solver run at known true values ($k_0 = 45$, $k_1 = -0.02$), sampled at the sensors, plus 0.5 K of Gaussian noise — and the optimizer starts from a deliberately bad guess: 33% off on $k_0$, the wrong sign entirely on $k_1$. The loss is a plain JAX function that happens to call the Fortran solver: ```python def loss_fn(params): @@ -229,9 +172,7 @@ loss, grad = value_and_grad(jnp.array([60.0, 0.01])) Scalar calibration convergence: loss, k0, k1 -Temperature field comparison: initial guess, recovered, ground truth, error - -L-BFGS-B converges in about 20 iterations. It nails $k_0$ to within a few percent; $k_1$ lands a bit further out (the temperature field is only weakly sensitive to it, so it's poorly constrained by 9 noisy sensors), but the recovered field still matches the observations. The more interesting question is what happens once the method gets pushed a lot harder. +L-BFGS-B converges in about 20 iterations, nailing $k_0$ to within a few percent. $k_1$ lands further out — the temperature field is only weakly sensitive to it, so 9 noisy sensors barely constrain it — but the recovered field still matches the observations. The more interesting question is what happens once you push the method a lot harder. ### Thermal forensics: recovering a 900-element initial temperature field From 4186d8a40002bf8071bfab621bd3e508d962c226 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dion=20H=C3=A4fner?= Date: Tue, 2 Jun 2026 15:13:42 +0200 Subject: [PATCH 13/24] iterate on diagram --- demo/enzyme_thermal_2d/figures/pipeline.png | Bin 143172 -> 130640 bytes .../generate_pipeline_diagram.py | 90 +++++++----------- 2 files changed, 35 insertions(+), 55 deletions(-) diff --git a/demo/enzyme_thermal_2d/figures/pipeline.png b/demo/enzyme_thermal_2d/figures/pipeline.png index 3b4c84fa57e56b0f8f5d186b86d6cfed0cf7fe10..eff63a8cd36a6b1271cafef3d175227f8c8fe85a 100644 GIT binary patch literal 130640 zcmeFZcQ~7U8#msqMrkQ(RjWpA+S)~1o7zcis&4n zh`q;qxu5s_9ryG9@6RX4;YeJEtnYPw&+~JBhEOdHrCVf-WS1^ox}~BluXE`V+2c!> zuHC(P130prf0YlolXO?mch_~YcK0-QwYsEk?(Xd1nu;qpmZos(z&>4o+OWpMZZt7RAElLr)=zm*_ zbgg 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Y_MID, W, H, "ad.ll", "differentiated IR", C_ENZ_BG, C_ENZ) W_SO = W + 0.6 draw_box( @@ -178,41 +158,41 @@ def main(): "forward / JVP / VJP", C_SO_BG, C_SO, - lw=2.5, - fs=10, ) draw_arrow(ax, X["combined"] + W / 2, Y_MID, X["ad"] - W / 2, Y_MID) - label(ax, (X["combined"] + X["ad"]) / 2, Y_MID + 0.62, "opt\n-passes=enzyme") + label(ax, (X["combined"] + X["ad"]) / 2, Y_MID + 0.72, "opt\n-passes=enzyme") draw_arrow(ax, X["ad"] + W / 2, Y_MID, X["so"] - W_SO / 2, Y_MID) - label(ax, (X["ad"] + X["so"]) / 2, Y_MID + 0.62, "opt +\nclang -shared") - - # ── Step badges, placed just above/below the box they number ── - badge(ax, X["f90"] - W / 2 + 0.1, Y_TOP + H / 2 + 0.35, 1, C_FORT) - badge(ax, X["ll"] - W / 2 + 0.1, Y_TOP + H / 2 + 0.35, 2, C_IR) - badge(ax, X["f90"] - W / 2 + 0.1, Y_BOT - H / 2 - 0.35, 3, C_WRAP) - badge(ax, X["combined"] - W / 2 + 0.1, Y_MID + H / 2 + 0.35, 4, C_IR) - badge(ax, X["ad"] - W / 2 + 0.1, Y_MID + H / 2 + 0.35, 5, C_ENZ) - badge(ax, X["so"] - W_SO / 2 + 0.1, Y_MID + (H + 0.15) / 2 + 0.35, 6, C_SO) + label(ax, (X["ad"] + X["so"]) / 2, Y_MID + 0.72, "opt +\nclang -shared") # ── Tool labels at bottom, centered under the columns they cover ── - by = 0.9 - for bx, txt, bg, ec in [ - ((X["f90"] + X["ll"]) / 2, "LFortran 0.61", C_FORT_BG, C_FORT), - ((X["ll"] + X["combined"]) / 2, "LLVM 19", C_IR_BG, C_IR), - ((X["ad"] + X["so"]) / 2, "Enzyme (LLVM pass)", C_ENZ_BG, C_ENZ), + # No chip box (non-data-ink). A short tick links each label to its track so + # the eye reads the grouping without a heavy enclosure. + by = 1.0 + for x0, x1, txt, color in [ + (X["f90"], X["f90"], "LFortran 0.61", C_FORT), + (X["ll"], X["opt"], "LLVM 19", C_IR), + (X["ad"], X["so"], "Enzyme (LLVM pass)", C_ENZ), ]: + cx = (x0 + x1) / 2 + ax.plot( + [x0 - W / 2, x1 + W / 2], + [by + 0.45, by + 0.45], + color=color, + lw=1.2, + zorder=1, + solid_capstyle="round", + ) ax.text( - bx, + cx, by, txt, ha="center", va="center", fontsize=9, - color=C_TEXT, + color=color, fontweight="bold", - bbox=dict(boxstyle="round,pad=0.3", fc=bg, ec=ec, lw=1), ) # Title From 4e869db73ef7aa6613ba130f8a5f3a72c6a7276d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dion=20H=C3=A4fner?= Date: Wed, 17 Jun 2026 00:25:44 +0200 Subject: [PATCH 14/24] fine-tune blog posts --- demo/enzyme_thermal_2d/.gitignore | 3 + demo/enzyme_thermal_2d/demo.ipynb | 768 ++++++------------ .../figures/fd_convergence.png | Bin 106228 -> 0 bytes .../figures/part1_convergence.png | Bin 100650 -> 0 bytes .../figures/part1_temperature_fields.png | Bin 76630 -> 0 bytes .../figures/part2_forensics.png | Bin 222525 -> 0 bytes demo/enzyme_thermal_2d/figures/pipeline.png | Bin 130640 -> 0 bytes .../generate_blog_figures.py | 565 ------------- .../generate_pipeline_diagram.py | 259 +++--- demo/enzyme_thermal_2d/tesseract_config.yaml | 3 +- .../2025-03-10-tesseract-core-announcement.md | 13 +- docs/blog/2025-06-30-pipeline-autodiff.md | 22 +- docs/blog/2025-08-03-beginners-guide.md | 49 +- .../2025-11-28-rocket-fin-optimization.md | 23 +- docs/blog/2026-01-20-hackathon-winners.md | 22 +- .../2026-05-15-fortran-enzyme-autodiff.md | 181 +++-- .../static/blog/enzyme-analytic_benchmark.png | Bin 0 -> 77949 bytes docs/static/blog/enzyme-fd-convergence.png | Bin 106228 -> 0 bytes docs/static/blog/enzyme-part1-convergence.png | Bin 100650 -> 0 bytes .../blog/enzyme-part1-temperature-fields.png | Bin 76630 -> 0 bytes docs/static/blog/enzyme-part2-forensics.png | Bin 222525 -> 0 bytes docs/static/blog/enzyme-pipeline.png | Bin 135911 -> 157314 bytes docs/static/blog/enzyme-thermal_forensics.png | Bin 0 -> 237514 bytes docs/static/custom.css | 5 +- 24 files changed, 606 insertions(+), 1307 deletions(-) create mode 100644 demo/enzyme_thermal_2d/.gitignore delete mode 100644 demo/enzyme_thermal_2d/figures/fd_convergence.png delete mode 100644 demo/enzyme_thermal_2d/figures/part1_convergence.png delete mode 100644 demo/enzyme_thermal_2d/figures/part1_temperature_fields.png delete mode 100644 demo/enzyme_thermal_2d/figures/part2_forensics.png delete mode 100644 demo/enzyme_thermal_2d/figures/pipeline.png delete mode 100644 demo/enzyme_thermal_2d/generate_blog_figures.py create mode 100644 docs/static/blog/enzyme-analytic_benchmark.png delete mode 100644 docs/static/blog/enzyme-fd-convergence.png delete mode 100644 docs/static/blog/enzyme-part1-convergence.png delete mode 100644 docs/static/blog/enzyme-part1-temperature-fields.png delete mode 100644 docs/static/blog/enzyme-part2-forensics.png create mode 100644 docs/static/blog/enzyme-thermal_forensics.png diff --git a/demo/enzyme_thermal_2d/.gitignore b/demo/enzyme_thermal_2d/.gitignore new file mode 100644 index 00000000..214d3034 --- /dev/null +++ b/demo/enzyme_thermal_2d/.gitignore @@ -0,0 +1,3 @@ +# Generated figures (notebook + pipeline-diagram outputs). +# Regenerated on demand; copied into docs/static/blog/ by hand when publishing. +figures/ diff --git a/demo/enzyme_thermal_2d/demo.ipynb b/demo/enzyme_thermal_2d/demo.ipynb index e25df9a1..8787a641 100644 --- a/demo/enzyme_thermal_2d/demo.ipynb +++ b/demo/enzyme_thermal_2d/demo.ipynb @@ -2,31 +2,36 @@ "cells": [ { "cell_type": "markdown", - "id": "459aa200939c", + "id": "53e629d9", "metadata": {}, "source": [ "# Inverse Heat Transfer with Automatic Differentiation\n", "\n", - "A steel plate is heating up. You have thermocouple readings at a handful of\n", - "locations, but you don't know the exact material properties — or even what the\n", - "temperature distribution looked like before heating started. Can you figure it out?\n", + "A steel plate went through some unmonitored heating event. Five seconds later you\n", + "get temperature readings at a handful of sensors, and you want to reconstruct what\n", + "the temperature distribution looked like before. Can you figure it out?\n", "\n", - "This notebook solves two inverse problems of increasing ambition. The forward\n", - "model is a 2D transient heat-conduction solver written in plain **Fortran**, whose\n", - "exact derivatives are generated automatically by [Enzyme](https://enzyme.mit.edu/)\n", - "at the LLVM IR level — no manual adjoint code, no source modifications. Wrapped as\n", - "a [Tesseract](https://github.com/pasteurlabs/tesseract-core) and bridged into JAX\n", + "The forward model is a 2D transient heat-conduction solver written in plain\n", + "**Fortran**, whose exact derivatives are generated automatically by\n", + "[Enzyme](https://enzyme.mit.edu/) at the LLVM IR level: no manual adjoint code, no\n", + "source modifications. Wrapped as a\n", + "[Tesseract](https://github.com/pasteurlabs/tesseract-core) and bridged into JAX\n", "with [`tesseract-jax`](https://github.com/pasteurlabs/tesseract-jax), the Fortran\n", "solver becomes an ordinary differentiable JAX function, so `jax.grad` flows\n", "straight through it.\n", "\n", - "1. **Part 1: Scalar calibration** — recover 2 material parameters (k₀, k₁) from 9 sensors\n", - "2. **Part 2: Thermal forensics** — recover the full 900-element initial temperature\n", - " field from 100 sensors (finite differences would need 901 forward solves per\n", - " iteration; one reverse-mode pass gives all 900 gradients at once)\n", + "This notebook first checks that the gradients are actually correct, by comparing\n", + "them against an independently derived analytic gradient, then puts them to work on\n", + "a 900-parameter inverse problem:\n", "\n", - "The optimizers below only ever see a JAX function. They never know the gradients\n", - "came from a compiled Fortran solver differentiated by an LLVM pass." + "1. **Does it work?** Benchmark Enzyme's gradient against a ground-truth derivative\n", + " computed without Enzyme or finite differences.\n", + "2. **Thermal forensics** Recover the full 900-element initial temperature field\n", + " from 100 sensors. Finite differences would need 901 forward solves per\n", + " iteration; one reverse-mode pass gives all 900 gradients at once.\n", + "\n", + "The optimizer below only ever sees a JAX function. It never knows the gradients\n", + "came from a compiled Fortran solver differentiated by an LLVM pass.\n" ] }, { @@ -46,15 +51,21 @@ "cell_type": "code", "execution_count": 1, "id": "d1505e18eaec", - "metadata": {}, + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-16T21:44:36.468114Z", + "iopub.status.busy": "2026-06-16T21:44:36.467938Z", + "iopub.status.idle": "2026-06-16T21:44:39.069803Z", + "shell.execute_reply": "2026-06-16T21:44:39.069481Z" + } + }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "\u001b[2K \u001b[1;2m[\u001b[0m\u001b[34mi\u001b[0m\u001b[1;2m]\u001b[0m Building image \u001b[33m...\u001b[0m\n", - "\u001b[2K\u001b[37m⠸\u001b[0m \u001b[37mProcessing\u001b[0m\n", - "\u001b[1A\u001b[2K \u001b[1;2m[\u001b[0m\u001b[34mi\u001b[0m\u001b[1;2m]\u001b[0m Built image sh\u001b[1;92ma256:33ec\u001b[0m38a694cd, \u001b[1m[\u001b[0m\u001b[32m'enzyme-thermal-2d:1.0.0'\u001b[0m, \u001b[32m'enzyme-thermal-2d:latest'\u001b[0m\u001b[1m]\u001b[0m\n" + " [i] Building image ...\n", + " [i] Built image sha256:0172263cf380, ['enzyme-thermal-2d:1.0.0', 'enzyme-thermal-2d:latest']\n" ] }, { @@ -67,6 +78,9 @@ ], "source": [ "%%bash\n", + "# Render the build status statically instead of an animated progress\n", + "# spinner, which streams as noise in captured notebook output.\n", + "export TERM=dumb\n", "tesseract build ." ] }, @@ -74,9 +88,18 @@ "cell_type": "code", "execution_count": 2, "id": "fcc5e2141f85", - "metadata": {}, + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-16T21:44:39.071444Z", + "iopub.status.busy": "2026-06-16T21:44:39.071322Z", + "iopub.status.idle": "2026-06-16T21:44:42.871985Z", + "shell.execute_reply": "2026-06-16T21:44:42.871572Z" + } + }, "outputs": [], "source": [ + "from pathlib import Path\n", + "\n", "import jax\n", "import jax.numpy as jnp\n", "import matplotlib.pyplot as plt\n", @@ -97,7 +120,14 @@ "cell_type": "code", "execution_count": 3, "id": "2bdf1ea4fd67", - "metadata": {}, + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-16T21:44:42.873775Z", + "iopub.status.busy": "2026-06-16T21:44:42.873469Z", + "iopub.status.idle": "2026-06-16T21:44:42.877174Z", + "shell.execute_reply": "2026-06-16T21:44:42.876904Z" + } + }, "outputs": [ { "name": "stdout", @@ -126,58 +156,93 @@ "T_init = np.full(n, T_inf)\n", "Q = np.zeros(n) # no internal heating\n", "\n", + "rng = np.random.default_rng(42) # reproducible noise\n", + "\n", + "# Figures are written here (gitignored); copy into docs/static/blog/\n", + "# as enzyme-.png by hand when updating the blog post.\n", + "FIGURE_DIR = Path(\"figures\")\n", + "FIGURE_DIR.mkdir(exist_ok=True)\n", + "\n", "print(f\"Simulation: {n_steps} steps x {dt}s = {n_steps * dt:.0f}s total\")" ] }, { "cell_type": "markdown", - "id": "849d4a04755d", + "id": "aace31b0", "metadata": {}, "source": [ - "## Part 1: Scalar calibration (2 parameters)\n", + "## Does it actually work?\n", + "\n", + "Before trusting the gradients, we check them against a derivative we can compute\n", + "*independently*, without Enzyme anywhere in the loop.\n", "\n", - "### Generate synthetic data\n", + "For one regime we can do exactly that. Set the conductivity's temperature\n", + "coefficient $k_1 = 0$ and the solver becomes linear: each explicit step is an\n", + "affine map of the temperature field, $T^{s+1} = A(k_0)\\,T^s + c(k_0)$, where the\n", + "operators $A$ and $c$ encode the real stencil and the real mixed boundary\n", + "conditions, and depend affinely on $k_0$. That structure hands us the exact\n", + "derivative of the whole multi-step trajectory via the tangent recurrence\n", "\n", - "We run the solver with the **true** material properties to produce a ground-truth\n", - "temperature field, then sample it at sparse sensor locations with added noise.\n", - "In practice, these would be thermocouple readings from a real component.\n", + "$$\\frac{\\partial T^{s+1}}{\\partial k_0} = A_1\\,T^s + A(k_0)\\,\\frac{\\partial T^s}{\\partial k_0} + c_1,$$\n", "\n", - "Because the solver is now a JAX function, we build its inputs as JAX arrays. The\n", - "static grid sizes (`nx`, `ny`, `n_steps`) stay as plain integers; everything\n", - "differentiable is a JAX array." + "which we iterate in plain NumPy. We recover $A$ and $c$ by probing the solver at\n", + "two stable $k_0$ values (the map is exactly affine in $k_0$, so any two recover it\n", + "with no truncation error), confirm the reconstruction reproduces the solver's real\n", + "trajectory to roundoff, then compare the analytic gradient against Enzyme's VJP.\n", + "Finite differences, swept over step size, never get within orders of magnitude.\n" ] }, { "cell_type": "code", "execution_count": 4, - "id": "771e9a987964", - "metadata": {}, + "id": "f44eee45", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-16T21:44:42.878520Z", + "iopub.status.busy": "2026-06-16T21:44:42.878436Z", + "iopub.status.idle": "2026-06-16T21:45:06.765102Z", + "shell.execute_reply": "2026-06-16T21:45:06.764836Z" + } + }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Ground truth: k0=45.0, k1=-0.02\n", - "Temperature range: 297.61 K to 373.15 K\n" + "Recovering affine map at k0=45.0 (900 probes)...\n", + "Recovering affine map at k0=40.0 (900 probes)...\n", + "affine-model vs solver trajectory rel err = 1.13e-14\n", + "analytic gradient = 2.4101518794e+02\n", + "enzyme gradient = 2.4101518794e+02\n", + "Enzyme rel err vs analytic = 5.63e-12\n" ] + }, + { + "data": { + "image/png": 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fp/Ub/obPO7yfAYfy8Rp/55131L5PS+lAOg5SNbKbPKv9DZ+1maXsadsAtMfD/SI1ECljWsoP0hww6VS7rTH7Y6TAVKtWTb029W+HNBHYqrcPNAae29WrV9OkMGYF6Rv6XnvtNfV73bp1aX7rp27AyJEj1e/M3lOmxMleZoadjCGTvdJ/eGpBLXYEmX1wIrd07NixGT60sfPERAfkZuH8qVOnVD7erFmzcnxM7YMQ+TeZXa+1BR94Wk5uVvBG1A/MDXnO2T0+AkHcJ/JzALl7yBnCTgkf9OkfO6cPdeTtGRrw5NQ3xmwP5LPhdniOyB3r0qWL6ifkkOZF+jZq7dTaiEANO1PkVuKUGXy4Z8eYbZ5TewB9On36dJXzduHChTS5dlo/ZwUfEsWLF1fBK74s4L5+/vln6dmzZ5ovYYbSPozxwWYsBHX4EpE+4M2qMgmC3sxmoyN37P3331fBZlRUVJq/aYGGFkBWqlQpzd/xhTCn1xDyuvGhOW7cOHXK6jWA9uVmv2QKyC3El7Lcio6OVr+zew1o21B/zoAGwQJyu/Uh2MUXsexey5nBfSGgwWt08ODB6jqcb9q0aa6r1iBXNP3rDG3Rz8XMSl73mYZuBwR9EydOVF/w0+dwppdZRZ+s/pZVv+G9hNe+/pcrBIzI70TlBwST2FcglxWDF7iM/Qf6GV/qsoNAG58T+Lz98ssvVT4ncoQxaIEvpID8Vrwfcb8vvvii+o0cZuTAI+DDvgXBNPZRWiBrzP4Yny/4//TbPv3tjIXcYHw5QIyC1yPm0eB5NW/ePMNt0+9vsL/DFwbtSyq2PS6nf13jSygCZkO/+OYWA1krof/NU1/KEZj/4AMfo654I2JnkR6+3SJAQgkaBEj4jTd6Zm/YrB4zp7Zoo4uTJk2SunXrZjsykp3cPj6CUAQv+KCYOnWqCgrxHPGtEDsbQ0aDjWHK7YF+wM4MXzQ2btyo/gdfPFA+CBOdzN1GjOZkFXBjFDcrxm5zQ17PmJiFgAqjoDjCgMlH2BlixCWnPsT9Y6c7d+5cFQjjQxojtLkd6cpP+iNWGnyo4UMTI0so2YcPCgQOGJXBB44pXtPafWCCDkZ9MpP+g8jQ/ZK1wKiXqcsbZrUNDIF9MCbGYOQLQR3qh2MymqnbklN/mGKfach2QBCHIxMI4vC+RACJL1mYaKY/iSi794Ihf8tJixYt1Agqgna0SQsg8RuXcYQDwaT+UaPMaAvioN9+//13NYET+ytMHsN12n4dj7d582YVOGPgCEcWtNFePB4CUdy2Xr16Ru+PcVt8wUO/ZaZ0uoEfQ2GUFwNd+OKBwTGMEKPP0HYE7jltF2OuNzcGsjYEbxLMjsSbA6NP+odX0u88McQfGhqqdh44ZJbT6KgxtEPY+NDNy+hJbmGHgg8FpFDojxhldoglqzcWnoP2oZff2wM7dxzWxAnfpjFSgKoI2QWyed1B4Ns8Rqkw6pmbPjNmmxsKHxAYuZg/f36GoA4zhHOC1zk+UNA2pOvgOaYP0AzdbtpoZm5eE6jXipnkCCb0Hy+zyhZZwex0HP7EFxoEAfpfXNM/ljZKox1aBHxo47YYccrpOSKwMOX71lIfXunhtY39HWZgI7DIirYN8SGuvw2167S/mwIWc8C+GPtrraYv0sjymznev5lBMIQvYAj4tBFLQCCbV/r9pn/0AekGeO3rv6YxyohAHUEkTlrVF7y38OUXQad22RAYRccJ+2m8xjCY9Msvv8iQIUPU3xEQ4zniOrwOkdqAz2e8DrVAFtdpXwaM2R/j8wWVXPBFJKf3mpOR70VUIsHrESdsR8QXeI442qufdoP9jf4IOfZtCLC11ET0DS7jdgiQNTdv3lT7c/33lDn2F8yRtSHITzp9+rQazcsuMH3mmWfUiwUjATisYepRKoz44s2FMivaoTx9+uV5zEHbGeiPQuDQWGY7S7xRM1sNC4eLsHPIrDyOsaNNhm4P7LTS56KhtAxKyKQvL5bZ84DcruyFbYbnjA+azIK1nPrMmG1uTJvSb2vkg6XP08wKRixwmjdvnnpeCBpcXV0zbDdD8v/wwYIPNZS+uXz5slGvBwTPaLN+CSuUpsEHpqEy2774YMEIiT6kKaGtSBXC3zXIlc/ptYHXGg6NorQevuSa6n2b1XssP+G9hTqyCBjwG18qs4JtiG2Bbaj/vsOXIfw/vvibCr6Q4QsqjowhrQDl+Qz5kmZq5nj/ZvU4+OzRTxPC4WdTrDaFgA/BKcpr6T8PfBHGc9HvNwRhSOvAFwi8n/VHZPGFAveBfTYGFbKDtIn073/tqJv+a0e7fxxdwz5JS9PA9QiakZetP/przP4YR/Gwf8lsf4Lncv/+/Vy9F/HFWR+2LY7o4vmmzwfGXJ/0ZbtAG3xBihykX0VRG0XW7xtz7C84Imtm2DlqEzX04duZMXmRSJZGHU68+JEPpZ8ThUMW+it54IMOO0wEBRi9NeWOGfBNE8EDXsSoQYeJK8irw5sN3/DxIYIRAHNBLg/edEiUR04Sgke8yfHhlP4DGkEmaiUiDQOHG3EbjMLgGzpGBPv06aMOFeF2mAyDYAQfcNmNbOV2e2ACCnLcUMMT949+Q44Sku0xspgdtA9Q0xQBG0Z28PyNKRKOovFoDybPYYIEdlp4zjh8jXbgvCm2uaFQaxaH0bG98H5ADWN82BvzvsCoLA6VQ2Zf2LDdMMEGo2L4YMM2x3PIDD7cMIKCEXJMcsIIBD6E8d5Dvl9WsD1wuBhfIPHlUcvd1UY0DBmBwPPHl1McZkQghv/5/vvvM3yIot/xWsZj4nWMkRSMRiEgMWS74QMJzxGHKvEawP9g1ASHYHH4O6cavpnJ6j0G+nV7TQVBCwJDQK6ntrIXDp/jvYE0lexgGyLgwOsO6RzoN2wD5GujvagBbEp4jWqLPOTUNnMxx/s3M/isQfCCzx+k/uCIE15zeF0YksebHXyuYaQQh71x/0hhwOgsvuzhvZ3+/Y/AEfs8BJV4vQOeL3Js8X+GrCyFmqy4f0wKRuCLfTi2G/bpWvAGeH7IB8X9ahOhAF+OtTq16dMYDN0fY/ll1FzHQBZujxxWfFFAXIHrN2zYkDoPB+9F/C/6AAMk2Idpk7Uze02gzbg/5PniSxz2Y+jD9Dnm2Mdge2O7Y1+B9x/6V/ucxG/su5Dvq6VJ7du3T20/xCY48mbI/iLXTFoDgQwqv6VfEkcrkYPySunpl3PJ7v4yK2+zdOlS9bdhw4Zl2iv4W/oyUFm1RSsFgzIj+lDz74knnlClTVBuBO1AjUnUVM1OVvenPcf0pU60EiCoKalBiROUM0FtQ9R+RE1MlF9JX64HtfpQggllldKXJ0K9P9TjQ+1SlHVB6TKULtHKoWTVzszKGhmyPVAqZ/To0aq+KNqDUik4n74OY3Y1MtFWlGLRf56Z9SXg8dOXYkFdRNwWtQtRgxile1CSCeWbcmLoNsfjYpunh22vv/1RAgrluFCCBjU8mzdvrtu9e3eG22W1vfVrJKPOY1Y1XlG7F3VW9d8rWd0n6qyiRA5uj+eJerjjxo3LcdugtB2eM54HakXieS1fvlw9xp49e9Jsg6xK3qCMTtOmTdV9oLQYygdt2LAhQxkmwGsGpd3wOkNtTJQ6M3S7nTt3TtV4RN/jNYDXFEr5/frrrzm+FzMrC5Xdeww1fPGccpLVey09rQSVdkL5QZQNQ21LY+tRLlmyRJWPwjYsVKiQ7rnnntNdvXo1zW3w/sH7ND1tn5Rd+S0N3veoRYqSSvrlvnJTfiuz1w7aaEiJM0Pfv5kxZjvMnz9f9Qm2K0rQ4bWU1fbKbL+V1WtPv9wW7hevXdSqfvnllzMtobV27Vp1P+nLOaJEFK5HO3OCkn4o9Yf66ng+KNuG98r+/fsz3Far+4zXlX7pMZTPw+dLZn1v6P4Y94P+Qv+jHXg9oewZ6u9GRkam3i4kJESVEcQ+BG3JrhQXym3ittrnFWob4/NJ//60fkNpMdSHxXscj43PzfTP58GDB6o92C/hueA5oQSdfqm/nPYXueWEH3kLhckaYZUgfBNCSZCcEtqJbBXK0GAEFBMUspqJbyk4zIbRPYx06lcCcBTIG8YRCkwmMfVRIVuCclsYHcNoaPp8cCJr9sEHH6gRcKQ6WCIlxlDMkbVTOPyBw4bZTXogsnXIDcVhNhx+syTkqulDjixyUVG2xhGDWMBhUCx77chBLCA/FIEAUgyIyPSYI2tnMGsSuUjI60POl7XMKCYyJdRaxYgfZtjiyIP+wh6WgNm+mA2OiSBaDidy2JAr66hQRD19IXVHgoVPsC9GXizKLiFvkIhMj4GsncHEBUxoQQFulHciskeYJLZr1y41UUGbQWtJqFyACX8IXDFCjIkb+FJpiVJLZB0woQVfaPDlBkcOiMg8mCNLRERERDaJObJEREREZJMYyBIRERGRTWKObC5hOTas7Y7CwZxQRURERGQaqAyLBShQug6LDmWHgWwuIYgtXbp0bv+diIiIiLJx5coVtSJmdhjI5pK2hBs2cnbrelPab1goTYQlAzmKbVnsC+vC/rAe7Avrwb5w3P6IiopSg4Xpl8vNDAPZXNI6EUEsA1nD3wQ4YXsxkLUs9oV1YX9YD/aF9WBfWBedBT7DDXkcTvYiIiIiIpvEQJaIiIiIbBIDWSIiIiKyScyRJSIieghLDCckJEhsbCxz+S0M+Zjx8fHsCzvsDzc3N3FxcTFJuxjIEhGRw8OH9LVr1+Tu3bvqPCekWgf0xc2bNy3dDDJDfxQqVEhKliyZ5/ea0YFsu3btZMWKFVKwYMEMpRIef/xx2bJlS54aRERElN+0ILZYsWLi5eWlirAzmLWOWfLoB/aF/fRHcnKy3L9/X27cuKEu51Qn1uSB7LZt29Rhl/Ti4uJkx44deWoMERGRJdIJtCA2MDCQwZOVYCBrv/3h7e2tfiOYLV68eJ7SDAwOZI8ePZp6/t9//02NpLWdwPr169UQMRERkS3RBme0D1ciMj/t/Yb3n6enp/kD2bp166ZG4UgvSA+N+Oqrr3LdECIiIkvKaU13IrK+95vBgeyFCxfUkHL58uVl37596vCL/uyzoKAgk81AIyIiIiLKicHhcNmyZaVcuXIqSbdhw4bqsnbKa34DWc66o7el/aQDEjxmp/qNy0REROaEeGLatGnZ3uaDDz5Q8QVG7latWiUDBgxQk8qNgaPI+N/80KZNG3njjTeyfI5IyXz00UfVIXVtwnxm11E+lN86c+aMbN26VcLCwlRgq2/8+PG5uUuyAAStQxadFKRs60QkJDRGXZ43oJp0qV2EfUJEZOUQCH3yySeydu1aVXkBR0eRCoiAqn379iYN0nC/OQWfpnLy5En56KOPZPny5dKsWTNVqqlt27bqyLAxQkNDJSAgQJ2/ePGiBAcHy6FDh9RzMbd//vknTd71l19+qdpz+PBh8ff3z/I6MnMgO3fuXHn55ZelSJEiaoan/sw1nGcga32SknVyIzJBrkXEydW78XItIl6uhcfJigNh6u/abgG/0Z1TN15mIEtEZOUQmDVv3lyN5E2aNElq1aolDx48kA0bNsirr74qISEh+doeBJmY/O3qmvcS9efOnVO/e/bsmVoKzd3d3ej7QZxiKfopmNpzatCggVSqVCnb64yVkJCgUjwdldGZthMnTlTf/vAtEN8g8M1GOx08eNA8rXRghhz6j4lPkjM3Y2Trybvyw+5Q+WzdRXntx1PS6+sj0vjjfVJuzE5p9PE+efyrozL8x1Py6dqL8t2uGxIdn3Y0HfBl91xYTD49OyIi+5HfqVqvvPKKCvAwb6V3795SuXJlqVGjhrz11luyZ8+e1NtFRETIkCFDVGDl5+enJmwfOXIkzSF8jFB+//336nA4RgaffvppuXfvnvo7Dun/9ddfMn369NRJ3wiiUY4T5//44w8VjCHQ3LlzpwrOEIAWLVpUfHx8pFGjRrJp0yaDnxfa0717d3UeQbE2KSh9agFGiV9//XUZM2aMGrFF0Ir/zSq1AKOxUK9ePXU9/l8zb948qVatmnh4eEjVqlXlm2++ybaNqIPar18/9fyQ/jBlypQMt9FPLcB5jC5/99136rHxXDK7zpj+QpuDg4NVm03Rz4Cj7F988YVUrFhR9WeZMmVUzKe5cuWK9O3bV315wjZHP+O1oMFronHjxqmpEviidenSJTEno782hYeHS58+fczTGjLo0H/7agHi6uKsRlWvhcdLeExijlvO1dlJShR0l5IBKadSAe6yZN9NNVKrf6AGI7IVgrzYE0TksDCyGJuQbFStzA3H78irP57KsL+e+VwV6VSzsMH34+lm2EIMqHuLspcIMjIrG6afb4nPbFQWQsCJ4GX27Nkq7eD06dMqGAEEnwj41qxZoz7nn3rqKfnss8/U/SOAxW1r1qypDvcDgiUtgHnnnXdk8uTJajI4DuMj2OnSpYv6XwRDCNQQmJ46dUoFRjkZNWqUCrQGDhyo0iWy2x6LFy9WgfvevXtl9+7dKhhE8IS80/QQ8CPIQlCNgF8bxfzxxx/V0eSvv/5aBbkYmBs6dKjarv3798/0cUePHq2C+99++02lc7z77rtqMC+rlAWkGSDwRYCJ7Yn+wEhq+usM7a+zZ8+qIHjFihWpc5Ty2s8wduxYdeQdKQ8tWrRQaQ/ayD5G+zt37ixNmzZV6wbgSwYGNx977DFVohVfOPBFA9vu559/Vs8P29zci1kYHchiQ23cuFFeeukl87SIUk3ZcCl1pyh6vzefDM+wlfw8XB4GqR6pgaq6XNBDnQ/ycxMX57QvppolfdIEyuoxdCIjO+a8oyEislcIYiu/99+IpjHS768R3Brj7KePiJd7zpOnEcgg4MboYXYwQopgAnNatEPzCDoRzPz6668ybNiw1JG4RYsWia+vr7r8wgsvyObNm1WAg6AIQR9WPMvsUD2CW/3AEUFTnTp1Ui9//PHHsnLlSlm9erUMHz48x+eGUU4tEE+fwphe7dq1ZcKECeo8Ds8jGEW7MwtktUP9hQsXTvM88P8YUX3iiSfUZYxyol4+AsHMAtno6GiZP3++/PDDD6l5yAios1uhCo+N7Y9AU/+x019naH8hSMQXhMCHz8kU/YyRWQTU2Iba865QoYIKaGHJkiXq/zESrI2SL1y4UPUVRmJRCCAyMlK6deum/g8wym1uRgeyGG4eN26cOmyBfJwCBQqk+TuG+ck0zt+KTTNaqnFxFvm4VwUphaD14Sirn6fxOUmY0IWJXciJ/ff6fXXdkJYlpDMnehERWTVDJz3h0DICLwRv+mJjY1PzUAEjoFpwAzhcjqDIEAhg9OHxcBgbE9AwopeYmKge7/Lly2JqCGT1GdNuLUUA22Hw4MFqJFGDNmc1+Qq3RyDZpEmTNMF7lSpVJK8M7S9UjNLPwT1ign7GBLv4+PgsJwniMfAFCiPI6Vd2xWN07NhRjYh36tRJfZHo0KGDGvHFY5iT0dHPnDlz1LclDKnjpA/fmhjImk75QE91eCr9of8qxbxlQPMSJnkMBLM4Td1wSSZvuCynbjI/logcGw7vn/lfM6MOiXadflhO38hsf+0la16va9RjGwKjj2hfThO6ENwgkMCIWXbpB+kHpXDf6asSZSV9agNSA/788081IojBL4w4Pvnkk5kub59XeWm3tn0Ah9P1A1OwRFlRQ/sr/TaPNkE/57S6Fh4DudAYiU7/3tCCaozQIg5E2gtGcN9//331WkA6gtUEslgYgfLHyE5lUw79O6Uc8td+m+PQ/5MNi6pAdueZCJV3i1FeIiJHhA9pL3fDclU1ox/LfH89ulNZg1IFjIURQIx8zZw5UwUO6QMbTPxBAFO/fn01ORv5jBiNyy2kFqAigSH+/vtvNTLXq1ev1ABIf0KQpWg5sfrPAxPSSpQoIefPn5fnnnvOoPvBYXMEhMjL1XJ+kW+KXNTWrVvnqY257a/6JuhnfDlCMItUA0way+wxli5dqnKCsysVhjxjnJBvi9JpP/30k1kD2VyvD4ZvVkjcxvC7LUIyOmYsVq9eXR2aWLZsmVgb7dB/teLe4u7qpH7PH1DNLIf+yxT2kKbl/dSOVyvLRURE1re/1iCIRVCGCUyY+IMa7zg8PGPGDBVAAA7v4jwm4WB+CwLKXbt2yXvvvSf79+83+LEQHCFww//fvn0721FPBESYhITKRjgc/eyzzxo1SmouCMAQqGG08ObNmyqfEz788EP59NNP1XZDMHrs2DE1sjh16tRM7wdHpZGKgAlfW7ZskePHj6vA3RRLrua2vzqYoJ9R/eDtt99WVSCQf4t0AaSRIh8YEOij9CoeA5O9MLCJEWB8kbp69aq6jOAVk+5QqQDtwGvS3HmyRo/IxsTEyGuvvaYSmwGdjpmKuK5kyZJq9qItwLcWlMXADEN8i8FwOWZZZjb705K0Q//5oU+jorLnfJQs3X9ThrcvZfaZhkRE9iQ/99eAz17MlMdEnZEjR6p8VBzixefZt99+q26D/fi6detUQIMqALdu3VITi1q1aqVGIw2FdAFMAMLgD/Iuszs6iwBw0KBB8sgjj6jAB8FRVFSUWMPnPoJVTE5DlYKWLVuqQAyjj5jIhlq8CE4RB2AOkP4qXenhthhpRjUG5Jxi+2uBcV7ktr+cTNTPmAOF7YTtc/36dZWuoE3uxzbC9kKwiolxmByGuA85tcibxesCqS6ID+/cuaP+F/WMX3zxRTEnJ52Ry2SMGDFCHTZAEKiVXMCbCSUokNyNshW2CDMsUY6idOnSBt0eb0oMreOFmz7x2Vbdi0uUOhP2StyDZFk7oq7UK/tfQrgp4KWG7YXtxiDZstgX1oX9YVn4AMbIEUYSMSqF/tDqpZLloB/YF/bbH7F677v0+bnGxFhGj4OjlANKM6Acg/4TQU02/ZlxebV9+3b1TQe5K1mtlYzDKjjcgR0PkrRReiI3Dhw4oA7PGBrE2itfD1fpUitlxiNGZYmIiIismdGBLIarkWeSWQkLU357xf1hlBTBamYwGw5FkFH/DYdWcFskvuuX3UDaAAo4pz9huFy/qDQKEqMaA4k82SjlEMRvB29JfKLlc5qIiIiITJYji3pxqA2HnFjQglcUyNWSy00Bq0fglF0ODmq+IRcEZs2apdq1YMGC1DxdJJpnB/XSkLSM2yOXJ6fb4qTR8n20oXZ70aKivxTzd1Mrfv154o50NWG+l7at7Gl72Sr2hXVhf1h+++v/Tn89WR77wv76Q6f3vsvLe8/oQPZ///ufCjCx6gUqFmAVCJzH7Lj0dWXNBRUTkA6AhGMNZgti1h5myxkCGwmzDLEWMVa2yAlmNGJmY3rI37C3N1i3Gv4yb9ct+Xn3NWlRNm3NubzAdtJq9jH3zLLYF9aF/WFZGKTQ/zJhb/t0W8a+sN/+0D18r2HSWPoaw8ZMDjQ6kEVuLEY6sTYvZvWhvAJqiyGAxOX8gNIfyGlNPxMPl3MqDq3BhDWkJ6D0lpZ/+/3332f5HBA0I5VBfyMjpxbJyPYy2UvzfIsCKpDdcTZaHjh7ShHflNp7pnoDcLKX5bEvrAv7w7Iw6QTlmPQnsfDLtvVgX9hnfzg9fL+h6kP6yV7GPIbx65o+LAaMVTBsGQJyY+raYe1ibf1iffY4s7VyMW+pW9pHDl+Jlt8O35YhrUqa7L617WVv28wWsS+sC/vDstte/3f668nyo3/sC/vrDye9911e3nsGTfbSH+LF+exO+QF16bB0HL5B68Nl1E0j06z0BUv/YfUCIiIisk4GBbIBAQGp1QCw5B0upz9p1+fXMnMo+Ixl1DQYXcVlU044c2SP1w+UAi5OcvzafTl5/b6lm0NERESUu9QCLMGGdZ1h69atkh8wKejs2bOpl7GKCHJz0Q6sbYx8VawygioKWJ4PCzSgZJdWxYDyppB3AelQvZD8ceyOqik7oUd5blIiIiKyvUC2devWmZ43J6wN3LZt29TL2kQrBK+LFi2Svn37qpq2WEYNS8yiZizWTzZmKTbKeclaBLIrD4TJe12DxdWF+WJERERkY4EslqE1FKoAmEKbNm1yLPMwfPhwdSLzaFc1QAp5u0rYvQey/XS4tKuWMipPREREZDOBLEY7MYNMW2M3OyiLRfbBzdVZHq8XJAt2XleTvhjIEhGRvbtz545Uq1ZNLXtfrlw5cQRPP/20NGrUSEaOHCl2OdkL+annz59Xv5cvXy7BwcHyzTffyKFDh9QJ51GSC38j+/JUo5TliDccvyORsYmWbg4REenBwj76pdu002OPPWa32wl161G5qGvXrjlukwIFCqiUw0cffVSt/GlI2c1PPvlEevbsafIg9tq1a/L8889L4cKFVd1U1K1HGmVebN++Xbp37y4lSpRQz1eri59+QScEqajXGhQUpFY0PXXqVJrbvP/+++p5Y5Enuwxky5Ytm3rCyl4zZsyQF198UaUR4ITzmGz18ccfm7/FlK9qlfKRKsW8JD5RJ78fvsWtT0RkZRC0hoaGpjn9/PPPYq/mz58vr732mgrirl+/nu02uXjxovzxxx9qzs2IESOkW7dualXSrMTExKj7Hzx4sEnbHB4eLs2bN1eBNdqDFVGnTJmS52pP9+/flzp16sjMmTOzvA1WXX311Vdlz5498ueff8qDBw+kY8eO6n81NWvWVAOSP/zwg9hlIKvv2LFjakQ2PVyHjiH7gm94fR7WlF22P6UEGxERWQ8s1oMa6vonLUDCfJPXX39dxowZo6r+4G8ffPBB6v8i0MtsRBf/991336nRQyzhqw8jevpLu+O2CCzfeOMN9bgYAcWiSVolIYwEVqxYUQVwGoyMYqQQsQNGJxGM/frrrwZVNMKqnC+//LIakcXk7+y2ScmSJdXqo++++6789ttvqg1Z/Q+sW7dO/W/Tpk0ltzKb3/P555+r1UAXLlyoKi3heSOYRPCYl23SuXNnmThxovTq1SvL22AiPEapa9Sooe4Tz//y5cty4MCBNLfDyO4vv/widh/IIm8EG1p/XVycx3X4G9mfJxoEirOTyD8XouTCrVhLN4eIiIywePFi8fb2lr1798oXX3whH330kRqZAwRX+iO5SBdE8NqqVSvp06ePmveyevXq1PtCTfm1a9fKoEGDMjwGFitCXimCWgSa+P9HHnlEDh48qII2BL8Y8QTEDAiUZ82aJSdOnJA333xTHXbH6GF2li5dKlWrVpUqVaqo2yNdIKeJ4Zp27dqpQG7FihVZ3mbHjh2qTn1WsPDT22+/re4HwfnQoUNViVI8r3PnzqmA8fTp0xn+D9sQ5UKxTXB4v169ehlWSM3tNjGWlj6glVXVIMBG/6X/4mLtjF6iFhsYUXupUqVSKxSgqgG+wf3+++/maCNZWDF/d2lVOUC2nQqXZftvypjOjpH8TkSO6+77rSU5Mv9XNnT2LyqFP9lu1P+sWbNGfHx80lyHEUicAJ/VEyZMUOcrVaokX3/9tVpACHmjyDXVVsSMi4tTo61YWAijts7OzvLss8+qUUQEYIBDz6jljlFYfQjskGcJY8eOlc8++0wFtgj0AKUyv/32WxUvIIhDmuKmTZtSFzEqX7687Ny5U2bPnp1tmU8c9kdwp6UPIChDoJe+PVlBEJxdJaZLly6pfNOsYGQVpT8nTZqkglcE9U8++aRKHcCXBaRaZpZbi3lGeP4oJYp++eeff9RIORZ4QllRBI+53SbGwKgvRs6R5oB0An143hiYRElTpJLabSCLiB0d8uOPP0pISIi6DjVd8WJHJ5J96tMoSAWyv+4Pk1GdyoozhmiJiOxUcsRNSQ7PPP/S2iD/E0GSPv3RtvRlMYsXL566Wqc+jLLeu3dPjdYiiAUEopgohIlKOEyPw9LaZCp9+o+B4BijupjMpNFqvONxsdgRgkAE0voQRCHIzQomKGHEcOXKleqyq6urij8Q3BoayOZUfSk2NlY8PDyy/PuoUaNU+sTVq1dVUIjAHwN8N2/eVF8I8ByQg4r0BH24LUZkEawCnufx48fV/yKQzWmbIOZCkKxBikTLli3FWMiVxeMiQE4P6QygjZrbbSALCFiHDRtm+taQ1XqsZmHx9XCRq+Hxsud8pDxSsaClm0REZDbOBYuKWOD7OkZkc/OZjMPcWcEEI30I5NLP3kee5YYNG1SgiJxWDYIojLbikDfSA3DIG6OQhjyG/nVa8IjHRZ4r4H4QHOtLHwDqQ8CKiVr6I6YITPE/GGX29/eXnJw8eTLTeT4ajCJjdDUrd+/eVcErJpoB8k6HDBmivkwgLWPcuHHy008/qZHf9F8eqlevnuY6pGNq1Z5y2iYFCxaUJk2apF6X/jaGQN19jN6j7Tiqntlzg8DAQLH7QBYwsQvJwvq5stCjRw9TtIusjKebi3SvEyg/7b0hS/8JYyBLRHat0MS/cqybbi8QTCFvFqN8+pOPNAjUUJkIo7IdOnRQebV5gYAOwRliCEMPmSOARTCNmf4IqPUhsESVhpdeeinb+0AuKyasI/c0Kwjcs5u5j5FRpDQg3QKT2RAYol1IF8CXCbShcuXKGf4Ph/LTl7xCLq12CN+QbaL/BcMYOp1O5S1jJHvbtm1ZBvIYqUWAi2DergNZpBVgdhxeDNoiCaC94bkggn2nFyCQXXv0tvzviQri5e5i6SYRETk85Fcir1EfDrsbEpAgeOnXr5+awITRRe1+kLuppScgdRCH1DE5CUFbXiEgw/0hoMQIbYsWLVSu699//y1+fn7qUHt6CBgxUoqyWOlHXnv37q1Ga/UDWW2bICbBYX/M3MdkKpTfwvPNSqdOnVSOLx4rs9JYCFixbTVIn8Dtc4LniolvSC146qmn1Mj3nDlz1Cm320QbyT179mzqZdT7P3z4sOo75DJr6QQYJUbVBjyO1sfYjlo6gTbRLf2XBJugM1K3bt10PXv21N26dUvn4+Oj+/fff3U7duzQNW7cWLd9+3ado4iMjEQEr347iuTkZF3Tift0xd/crvv1n5u5+v/w8HD1myyLfWFd2B+WFRMTozty5Ij6jb5ISkqymf1U//791WdR+lOVKlXU31u3bq0bMWJEmv/BZzj+DxYuXJjp/+P/9L3wwgu6QoUK6eLi4jK0IbPHKFu2rO7LL79Mcx3ud+XKleo8tu+0adNUOwsUKKALDAzUderUSffXX3+l3l6/LxB7dOnSJdNtsHfvXnXf6MP028TV1VXdd4cOHXQLFixQ95cTxDOzZs3Smdrvv/+uq1mzps7d3V1XtWpV3Zw5c9L83ZBtkt7WrVsz7T+tfyGzv+OEvtfExsbq/P39dbt3787ysUz93tB/3+UlxnLCD2MCX3zDw/A8ErsRzeNbBcpg4DosbYYcEUeAEhx4/vjGhG9LjmLKhksyZcNlaVm5oCx56b9EfkPgpYbthe3mKIfsrBX7wrqwPywLE3zOnDmjZvRjoo82IYj7qf+0b99ejdhiQaT8gn6wRF8gT3X06NFqtFqb9Gbvvv32W5V6sHHjxnzrD/33nf7IsLExltE9hGF6LU8DQa22qgbyPNLnf5D90RZH2HkmQq6F21atOSIiMg4OsWu5lThE7Qiw0AImtCMn2FEUKFBAvvrqK7FFRufIou7YkSNHVLIwZtChuDJyaZDngZpnZN/KFPaQpuX9ZM/5KFlxIExe65C3pH8iIrJemPyEYBb1U3H01VGg1qojGTJkiNgqowNZFDzW1ufFLEckTqOWGWrGYdk4sn99GhVVgSwWRxjevhQPvxER2SksYUtkzYwOZDGjT4NSE1gUAbXHMLuP+USOoVudIvLeinNyNixWDl+Olnplc1cShIiIiCgvjMqRxWoVKDuBBGh9KPPAINZx+Hq4SudahdX5pfvzfwlHIiIiIqMDWSQDoy4Za8US0gvgt4O3JD4x7QoxRERERPnB6KoF7733nioIrC1lRo6pZaWCUtzfTSJiE2XTCb4WiIiIyAZyZLGeMVaRwFrHKLmFNZ71HTx40JTtIyvl4uwkTzQIkplbrqpJX13r2NaSdkRE6WFFJSKyrfeb0YEs1jQmgj4NUwLZLSfD5U50ghT2ceOGISKbgzXuUfge69wXK1ZMpdHhMud+WJalFkQg8/YH7iMhIUFCQ0PV+wzvv3wNZCdMmJCnByT7UbmYt9Qp7SNHrkTLyoO3ZEirkpZuEhGR0fBhitWFrl69KleuXEn9sCbLY1/Yb394e3tLqVKl8rx6mtGBLFH6lb4QyC795yYDWSKyWRgVwqI+qM4TEREhPj4+DGatIGi6d++eWk2UXyzsqz9cXV3VyRT9anQgm1W9WFyHNapRW3bAgAEycODAPDeOrN/j9QPlw9Xn5fi1+3Ly+n2pViJtzjQRka3A5xjSCrBaJdZ+Z/BkWdohaPaFddBZaX8YPZ47fvx4NQyMtYg//PBDdcJ5XId1mCtXriwvv/yyzJ071zwtJqtSyLuAdKheSJ3HpC8iIiKi/GL0iOzOnTtl4sSJ8tJLL6W5fvbs2bJx40ZZvny51K5dW2bMmCFDhw41ZVvJimvK/nHsjqw4ECbvdg0WVxfr+aZGRERE9svoEdkNGzZIhw4dMlzfvn179Tfo0qWLnD9/3jQtJKvXrmqABHi7Sti9B7L9dLilm0NEREQOwuhAFsvR/v777xmux3X4G9y/f18lA5NjcHN1ll71gtR5TPoiIiIissrUgnHjxqkc2K1bt0rjxo3Vdf/884+sW7dOZs2apS7/+eef0rp1a9O3lqzWU42CZMHO67Lh+B2JjE0Uf08WxCAiIiLzMjraQN5r9erV1QpfK1asUNdVqVJF/vrrL3nkkUfU5ZEjR5q+pWTVapXykSrFvOTUjRhZc/iWPNesuKWbRERERHYuV8NmzZs3VyciDUpxoKbsxDUXZOn+MAayREREZHZ5W06BSM8TDQLF2UnknwtRcuFWLLcNERERmRUDWTKZYv7u0qpygDrPmrJERERkbgxkyaT6NEqpXvDr/jBJTtZx6xIREZHZcGo5mdRjNQuLr4eLXA2Pl73nI6VZxYJm28Lrjt6WKRsuyflbsVI+0FNGdiorXWoXMdvjERERkY2PyEZGRsrdu3czXI/roqKiTNUuslGebi7SvU6gOo9JX+YMYocsOikhoTESn6hTv3EZ15vyMdpPOiDBY3aq36a8byIiIrLAiOzTTz8t3bt3l1deeSXN9UuXLpXVq1ererLk2JBe8NPeG7LmyG35pFcF8XJ3Men9I2Vh4u8X1HkteUH7PWzxSSle0F183F3Uyfvhbx8P7bzrf9d7ZHUbF9lxOkJe/C5EnB7etxYozxtQjaO+REREthrI7t27V6ZOnZrh+jZt2sh7771nqnaRDWsc7CdlC3vIpTtx8sexO9K7YUrebF7EJCSp4HLjiTuy6d+7cuveg0xvh7Tca+HxYir6gbKTk8jUjZcZyBIREdlqIBsfHy+JiYkZrn/w4IHExrLkEqXUlH2yYZBM2XBZlu6/metANiwqQf78964KXnecipC4xOTUv6HMV/q5ZBg9LR/kKTOeqSLR8YkSHZ8k9+OT1O/oOL3z2vVx2vmU26rzcUmSkJT5JDWdTuTszRh2MRERka0GsliWds6cOfLVV1+luR7L0zZo0MCUbSMbhsUREMjuPBMh1yPipURB9xz/R6fTyembMbLx+F211O3By/fS/L1UgLt0rFFYOtYsJBH3E+Wl70PUKCkCTO33u13KSb2yvnlqe0JisnScckjO3IxJHZFN/VuSTsatPCcjO5WRgl4F8vQ4RERElM+B7MSJE6VDhw5y5MgRad++vbpu8+bN8s8//8jGjRvz2ByyF2UKe0jT8n6y53yULD8QJq+1L53p7R4kJcu+81Fq1HXjibsqHUFf3dI+0rFmYRXAVivupUZ7Na4uTupQ/7mwGKkQ5CUjO5aRziaoWuDm6ixjOpdVObGpgbJemsH8HddlxcEwebtzOXmuaTFxwfAwERER5TsnHYbBjHT48GGZNGmS+u3p6Sm1a9eWsWPHSqVKlcRRoEKDv7+/quLg5+dn6eZYpZ/23JBRS8+Im4uTCghRIuulFkWkY50Ssu1USr7rlpPhEhn7X6qKu6uTtKwcIB1rFJIO1QupRRYsBVUK0gfK3h4uMmHVeTl1IyXFoHpxb/moV3l5xIxlxswBb3u8dvEa1v9yQOwPR8f3hvVgXzhuf0QZEWPlKpAlBrKGWL7/prz20+kM16fPby3sU0AFrQheW1cOMHmVA1NLTNLJd7tCZfL6SxLxMAjvVqeIjOseLKULeYgt4AeEdWF/WA/2hfVgX1gXnZUGsq6G3qF2RznViuXoJGm+2Xo1042BILZSUc+UfNcahaV+WV+bOjyPlIZBLUvI4/UDVTCLoBalxjaduCsvtS0pw9uVtvpgnIiIyB4YFMgGBARIaGioBAUFScGCBTONxBGp4/qkpCRztJNsEFbcygxSDf56u6HYukLeBeR/vSvKC82Ky/hV5+Tvs5Ey7c8rsmTfTXmvW7D0qh/Iw/ZERESWDmS3bNkihQoVUue3bt1qzvaQHUFOLBYS0M9dwVegikW9xJ5UK+EtS1+upWrmfrj6vFy5Gy/Dfzwli3eFysePl5fapfNWRYGIiIjyEMi2bt069XxwcLCULl06w0gTRmSvXLliyN2RgxjZKd3M/4e/3+qYeQUDW4b3Q5faRaRdtUIye9tVmbH5ivxzIUo6TzssTzcuKu90KSeBvm6WbiYREZFdcTb2HxDI3rp1K8P1d+/eVX8j0iCww5Ku1Yp7q2oE+D3jqTLSuVbeS2RZK48CzjLi0TKy852G8kT9QBW4/7z3pjT/3375dutVVaOWiIiILFRHVsuFTS86Olo8PGxjxjblbzCLk/6MR0dQvKC7fP18VenfvITKnz1yJVo+/v2C/LjnhnzQs7yq0kBERET5FMi+9dZb6jeC2HHjxomX1395jpjgtXfvXqlbt24em0NkXxoF+8naEXXVUr2frr2oJsD1m3dC2lUNkLZVA+SnvTfUdcgnRiqGFvQTERGRCQPZQ4cOpY6qHTt2TNzc/sv3w/k6derIqFGjDL07Iofh7OwkTzcuJl1rF1FVDeZtvyZbQsLVSYNJccgnRioGg1kiIiITB7JatYKBAwfK9OnT7aZebExMjFSrVk369OkjkydPtnRzyI75eriqRROwrO1jUw9JdPx/pepQ2QEZO1hJjIEsERGRmSZ7tWrVSgoUKCD24pNPPpGmTZtauhnkQJBG8CAp46QvTAzDcrhERERkpkD2nXfekaJFi8rgwYNl165dYsvOnDkjISEh0rlzZ0s3hRwwmM1sLTMfdxdJ0l+/l4iIiEwXyF67dk0WL14st2/fljZt2kjVqlXl888/lxs3bogpbd++Xbp37y4lSpRQE8xWrVqV4TYzZ86UcuXKqWoJTZo0kX379hn1GMjp/fTTT03YaiLDYGKXlk6g7879RDUZLDI2kZuSiIjI1IGsq6ur9OrVS3777Te1AMLQoUPlxx9/lDJlykiPHj3U9cnJea+Vef/+fTWBDMFqZpYsWaIqKUyYMEEOHjyobtupUycJCwtLvQ2qKNSsWTPD6fr166qdlStXViciS9fYrV7CW15sXVLVod0aEi5dpx2Ws0wzICIiypaTDmUI8gBltxYsWKBGaYsXLy7h4eESEBAgCxcuVCO2poAR2ZUrV8rjjz+eeh1GYBs1aiRff/21uozgGSuOvfbaayr9ISdjx46VH374QVxcXFQN3AcPHsjIkSNl/Pjxmd4+Pj5enTRRUVHq8SIiIuxm4pu5aXVk/f39M61FTCLHrkbLoIUn5XpEvPh5uMg3L1RVZbrYF/aN7w3rwb6wHuwLx+2PqKgoKViwoHq8nGIsoxdEgJs3b8r333+vgtXz58+rAHPNmjXSoUMHNZL60UcfSf/+/eXSpUtiDgkJCXLgwAEVjGqcnZ3V4+/evdug+0BKgZZWsGjRIjl+/HiWQax2+w8//DDD9djIefwu4DCwnfClARjIZq6Mr8gvg4LljWWX5eCVGJVmMLJDMRnQtIhJtxn7wrqwP6wH+8J6sC8ctz+ioqIMvq3RgSzyVjds2KAOySOtoF+/flKo0H+rFHl7e6uRzUmTJom5ID8XizBg0pk+XMbkLXNA0KwtCqE/IotvJhyRNYwW8HNENnv+/iK/Di8k7y0/Jz/vuymT/rwh5+8myRd9KqnUA1NgX1gX9of1YF9YD/aF4/aHkxH3b3QgGxQUJH/99Zc0a9Ysy9sEBgbKhQsXxFYMGDAgx9u4u7urU2Ybm6OLhtO2F7dZ9jwKuMjkvpWkeklv+eC387L8wC05fytO5g+sJsX8M74Oc4N9YV3YH9aDfWE92BeO2R9ORty/0cM78+fPzzaI1RpQtmxZMZciRYqo3FakOOjD5WLFipntcYnyE95Hg1uWlJ+G1ZSCnq5y6PI96fLlYTl8+R47goiIyNAR2RkzZhi8sV5//XWzb1gsidugQQPZvHlz6gQwTPbC5eHDh5v98YnyU8vKAbLuzboyYP6/cvpmjPT6+ohMfqqy9G4YxI4gIiKHZlAg++WXXxo8gmSqQBYJxWfPnk29jFSFw4cPq3xclPpCviomlDVs2FAaN24s06ZNUxPNsIQukb0pV8RTfh9RR4b/eEr+PHFXXvvplPwbel/e7VpOXJxZAYKIiByTQYGsJfJd9+/fL23btk29rE20QvCKKgN9+/aVW7duqUoDWIwBNWPXr1+fYQIYkb3w9XCVhQOry6T1l2T6pivy7darcir0virR5eeZqwIkREREjl1H1lGhagFm7hlS44xSsCag6fx26Ja8+ctpiXuQLBWCPGXRoOpSIcjL4P9nX1gX9of1YF9YD/aFY9eR9TcwxsrVMM7Vq1dl9erVcvnyZVXTVd/UqVNzc5dEZISe9QIlONBTBi44IefCYtVKYLP6VZM2Zlg8gYiIyFoZHchiQhWWoi1fvryq2YolXy9evKgi9fr165unlUSUQe1SPrL+zXoyeOFJ2X8xSp6fe1zGdQ+WYa1LsrwZERE5BOfcLAwwatQoOXbsmHh4eMjy5cvlypUr0rp1a+nTp495WklEmQr0dZNlr9SSZ5oUlWSdyIerL6SmHBAREdk7o0dkT548KT///HPKP7u6SmxsrPj4+KhlaXv27Ckvv/yyOdpJRFlwd3WWyU9VkuolUhZPWPpPmJy9GSvPNi0m83dck/O3YqV8oKeM7FRWutQuwu1IRESOOyKLJWi1vNjixYvLuXPn0iwdS0SWXzzh4OV7MmrpGQkJjZH4RJ36PWTRSVl3lO9RIiJy4EC2adOmsnPnTnW+S5cuMnLkSPnkk09k0KBB6m9EZPnFE9xcU2aUaiVJ8BuTTKduvMzuISIix00tQFUCLFYAH374oTq/ZMkSqVSpEisWEFnJ4gmZQaG9c2Ex+d4eIiIiqwlkUa1AP81g1qxZpm4TEeVRhUBPlU6Qvkg0cmWJiIjsRa6XA0KebFhYmCQnp50djeVjiciyMLELObFIJ9Bf8gTVDG5GJUiQbwFLNo+IiMgyObKnT5+Wli1biqenp5QtW1aCg4PVqVy5cuo3EVkeqhPMG1BNqhX3FndXJylX2EO83Zzlwu04tXjCiesp6UFEREQONSI7cOBAVXZrzZo1qmqBuZcpI6LcB7P65bYu3IqVfvNTVgJ7/KujMqlXaXm8sT83LxEROU4ge/jwYTlw4IBUrVrVPC0iIrPAkra/v15HXvwuRHacjpDhSy7JjRgnealNKX4hJSIix0gtqF69OuvFEtmogl4F5IehNeT5ZsXURLCPf78oo5eelYRErgRGREQOEMh+/vnnMmbMGNm2bZvcuXNHoqKi0pyIyLoVcHGWz3pXkLGdiouzk8hPe2/Ic3OOS/j9B5ZuGhERkXlTCzp06KB+t2/fPs31Op1OHZ5MSkoy9i6JKJ/hvfpCkyJStVSAvPLDKfn7bKR0n3FEFg+uLhWCvNgfRERkn4Hs1q1bzdMSIsp3HaoXktWv1VGTwM7fipXu04/I3AHVpHmlguwNIiKyv0C2devW5mkJEVlEtRLesu6NujJowb9y4NI9eWb2cfn0yYryXNNi7BEiIrLPBRFiYmLk8uXLamEEfbVr1zZFu4goHwX6usnSl2vJW0vOyG+HbsnopWfkbFiMvN8tWFyQSEtERGQPgeytW7dULdk//vgj078zR5bINnm6ucg3z1eRikGeMmXDZZm97ZqqPTvz+ari7e5i6eYRERHlvWrBG2+8IREREbJ37161utf69etl8eLFUqlSJVm9erWxd0dEVjYJDMvbfvNCFbUi2MYTd6XnV0fkWni8pZtGRESU9xHZLVu2yG+//SYNGzYUZ2dntUzto48+Kn5+fvLpp59K165djb1LIrIyj9cLktIBHjJwwb/y7/X70nXaIVk4qIbUK+tr6aYRERHlfkT2/v37EhQUpM4HBASoVAOoVauWHDx40Ni7IyIr1aCcn5oEVq24l4TdeyC9Zx6V1YdT3u9EREQ2GchWqVJFTp06pc7XqVNHZs+eLdeuXZNZs2ZJ8eLFzdFGIrKQUoU85LfX6qgyXXGJyfLSdyEy7c/Lqm40ERGRzaUWjBgxQkJDQ9X5CRMmyGOPPSY//vijuLm5yaJFi8zRRiKyIB8PV1k4qLp8/PsFmfPXNfnij0ty9maMdKhRWL7adFnVny0f6Klya7vULsK+IiKifOOky+PQCspwhYSESJkyZaRIEcf5EMNyvP7+/hIZGanygylneKlhe2G7YVIR2V5ffL8rVN5dcVaSklMu4z91er/nDajGYDYf+4NMj31hPdgXjtsfUUbEWEanFqTn5eUl9evXd6gglshRvfBIcflxWE3RSstq34K1YPbzPy5KUjLTDoiIyMoXRCAix9SqcoC4OjtJQlLagBWXztyMleAxf0vJAHcpXQgnD3UqU8hDShVyV7+DfN3EOYdFFtYdvS1TNlxi2gIREWWLgSwRGa1CkKeEhMakjsjqS0zWyaU7ceokEpnh76hPWzIAAa67KvFVunDK+TIPg9595yNl6OKQ1HQFPM6QRSeZtkBERBkwkCUio2FiF4JLpEkhy177Pad/Valf1k+u3I17eIqXy3fj5OrdOPX7ekS8xCfq1EgrTpnRxmrTpC04iUzdeJn5t0RElLdA9vLly1K6dOkMib5IAr5y5Yqa9EVE9g3VCTCxC8HlubAYqRDkJSM7lpHOD6sWlCjoLk3K+2f4v8QknYRGxqsg9/LDQPeq3nn8LbPpp7gOj0NERJSnQDY4OFiV39IWRdDcvXtX/S0pKcnYuyQiGw1mjS235erilJo3+0gmf09ITJb2kw/K+bDYDGkLwUU889ReIiKyP0ZXLcDIa2ZlF6Kjo8XDw8NU7SIiB+Tm6ixju5RLTSdIn3sbHZdoqaYREZEtj8i+9dZb6jeC2HHjxqmyWxqMwu7du1fq1q1rnlYSkcOmLSBN4UZkgpwNi5Xn555Q5b+83V0s3UwiIrKlQPbQoUOpI7LHjh1TK3lpcB7L1Y4aNco8rSQih05bOHLlnvT99pjsuxAlz805zmCWiIiMC2S3bt2qfg8cOFCmT5/O1ayIKN/UKe0rv7xUS56elRLMPj/3uPwwlCOzRESOzugc2YULFzKIJaJ8V7dMSjDr5+Eie8+nBLP34zm5lIjIkRkdyN6/f1/lyD7yyCNSsWJFKV++fJoTEZE5g9mfX6wlvg+D2RcYzBIROTSjy28NGTJE/vrrL3nhhRekePHimVYwICIyl3plfeWXF2vJ07OPyZ6HwSzSDLw4AYyIyOEYHcj+8ccfsnbtWmnevLl5WkREZGQwq+XMMpglInIsRqcWBAQESKFChczTGiIiI4LZn1+sqdIM1MjsvBMSw5xZIiKHYnQg+/HHH8v48eMlJobLRRKRZdUv6yc/DUsJZnefi5R+DGaJiByK0akFU6ZMkXPnzknRokWlXLlyUqBAgTR/P3jwoCnbR0SUrQblUoLZZ2Yfl10Pg9nvhtRgmgERkQMwOpB9/PHHzdMSIqI8BLNIM9CC2f7zT8hiBLNuXAGMiMieGR3ITpgwwTwtISLK68jsizXl2dnH5e+zkdJ/HoNZIiJ7Z3SOLERERMi8efNk7Nixcvfu3dSUgmvXrpm6fUREBmv4MJj1cXdJDWZjErhoAhGRvTI6kD169KhUrlxZPv/8c5k8ebIKamHFihUqsCUisnQw++Ow/4LZAfMZzBIR2SujA9m33npLBgwYIGfOnBEPD4/U67t06SLbt283dfuIiIzWKDglmPV2d5GdZxjMEhHZK6MD2X/++UdefPHFDNeXLFlSbty4Yap2ERHlOZj9KU0w+y/TDIiIHD2QdXd3l6ioqAzXnz59WgIDA03VLiIiE43M1ngYzEbIwAUMZomIHDqQ7dGjh3z00Ufy4MEDddnJyUkuX74sb7/9tvTu3dscbSQiyrXGwf6pweyO0ynBbCwngBEROWYgiwURoqOjJSgoSGJjY6V169ZSsWJF8fX1lU8++cQ8rSQiymMw+8NQ1JV1VsFst+mHpd0XByR4zE5pP+mArDt6m9uXiMgR6sj6+/vLn3/+KTt37lQVDBDU1q9fXzp06GCeFhIRmUCT8hiZrSl9Zx2Tk6H/LbEdEhojQxadlHkDqkmX2kW4rYmI7DmQ1bRo0UKdbNmFCxdk0KBBcvPmTXFxcZE9e/aIt7e3pZtFRGYMZov7u8ulO3Gp1+lUipTI1I2XGcgSEdljIDtjxgyD7/D1118XW4EyYhMnTpSWLVuqhR0wkY2I7NuNyPgM1+l0IufC/hulJSIiOwpkv/zyyzSXb926JTExMVKwYEF1GYsieHl5qbxZWwlkT5w4IQUKFFBBLBQqVMjSTSKifFA+0FOlE2AkVoMR2QpBXtz+RET2ONkLh+C1EyZ01a1bV06ePKlGMXHCeeTJfvzxxyZrGBZX6N69u5QoUUJVRli1alWG28ycOVPKlSunFmZo0qSJ7Nu3z+D7x4IOPj4+6jHQ9v/9738mazsRWa+RncqmpBOkG5Ed2bGMBVtFRET5UrVg3Lhx8tVXX0mVKlVSr8N5jNq+//77Yir379+XOnXqqGA1M0uWLFGrjE2YMEEOHjyobtupUycJCwtLvQ0C7po1a2Y4Xb9+XRITE2XHjh3yzTffyO7du9UENpyIyL5hQhcmdlUr4S3OD6PZ5hX9pTMnehER2f9kr9DQUBUEppeUlKQmTZlK586d1SkrU6dOlaFDh8rAgQPV5VmzZsnatWtlwYIF8s4776jrDh8+nOX/YyWyhg0bSunSpVOX2MXtH3300UxvHx8fr04abVEInU6nTpQzbVtxe1meo/dF51qF1Wn/xSjp+dVR+edClIRFxUugr5tF2uPo/WFN2BfWg33huP2hM+IxjA5k27dvr5aonTdvnjokDwcOHJCXX34530pwJSQkqMccO3Zs6nXOzs7q8TG6aohGjRqp0dvw8HBVUgypDJktvav59NNP5cMPP8xwfWRkJD98jHhholwbIF2ELId9kaJSgEjtkp5y9FqszNlyUYa3Kcr+cHB8b1gP9oXj9kdUJivImiyQxYhn//791WgmJksBRmhxWB/BbX64ffu2GgEuWjTthw4uh4SEGHQfrq6uKi+2VatWqnM6duwo3bp1y/L2CJqRyqC/kTGaiyDYz88vD8/GcWjfsLDNGMiyL6zFS23LyCs/nJIlB8NlZJeK4lHA6IyrPON7w3qwL6wH+8Jx+8PJiPs3OpANDAyUdevWyenTp1ODxqpVq0rlypXF1uSUvqAPpbkyK8+Fjc2gzHDa9uI2szz2RYpudQJl4pqLcj0iXlYduiXPNCnG/nBwfG9YD/aFY/aHkzkDWQ0CV0sFr0WKFFELGKTPycXlYsUs8yFERLbJ1cVJBrUoIRPXXJC5f12TpxsX5RctIiIbYXQgi0P6ixYtks2bN6sc0+Tk5DR/37Jli5ibm5ubNGjQQLXh8ccfV9ehHbg8fPhwsz8+EdmX55oVk6kbL0nIjRjZfjpCWlcJsHSTiIjIHIHsiBEjVCDbtWtXVcrKXMPLSCg+e/Zs6mXUsEVVASxcUKZMGZWvquXqNm7cWKZNm6ZKdmlVDIiIDOXv6SpPNy4mC3ZeV6OyDGSJiOw0kP3ll19k6dKlqlyVOe3fv1/atm2belmbaIXgFYF037591Qpj48ePlxs3bqiasevXr88wAYyIyBBDWpWQhX9fly0h4XLmZoxUKsqVvoiIYN3R2zJlwyU5FxYrFYI81cIyqMltDZxzc1i/YsWKYm5t2rRJU7NMOyGI1SCN4NKlS6q+6969e9XqXkREuVGuiKd0rFFYnZ+3/Ro3IhGRpASxQxadVEt7JyTp1G9cxvU2GciOHDlSpk+fztqpRGR3hrUqoX4v2x8md+8/sHRziIgsbsqGS2pJb22JArXEt5PI1I2XxSZTC3bu3Clbt26VP/74Q2rUqJFaS1azYsUKU7aPiCjfNK3gLzVLesvxa/flh92h8nqHMtz6ROTQzt+KTQ1iNSgpey4sRmxyRLZgwYLSq1cvad26tSqDhcK4+iciIluFyavDWpdU5xfuDJWExLRVWYiIHI2fZ8YxT4zIVgjyss0R2YULF5qnJUREVqBH3UD5ZM1FuRmVIL8fvi29GwZZuklERBax80yE3L6XkmalpRcgiMWI7MiO1nHEKldrMWJJ2k2bNsns2bPl3r176rrr16+nrsFLRGSr3FydZUDz4ur8nO3XOB+AiBzSzagEefWHEBW8Nq/oL9VKeIubi5NUK+4t8wdUk85WUrXA6BFZVAl47LHH5PLly6pawKOPPiq+vr7y+eefq8uzZs0yT0uJiPLJ882Ky/RNV+TY1WjZez5K5c4SETmKxCSdvPJ9iNy690CqFfeSxUNqiGcBZ4mMjFRppNa0zLxzbhZEwCIE4eHh4unpmXo98maxshYRka0r7FNA+jxMKZj9F0txEZFjmbzhkuw+Fyne7i4yu3818XJzEWtldCC7Y8cOef/991U9WX3lypWTa9e4wyci+zCkVcqkr40n7siFW7GWbg4RUb7Y/O9dmbHpijo/+alKUtFKJnWZLJBNTk6WpKSkDNdfvXpVpRgQEdkDrOzVrmqAmtQwf8d1SzeHiMjsrobHyes/nVLnMVegZ71Aq9/qRgeyHTt2lGnTpqVeRp4EJnlNmDDB7MvWEhHlp6EPS3H9su+GRMYmcuMTkd1KSEyWlxaHSHhMotQp7SMTepYXW2B0IDtlyhT5+++/pXr16hIXFyfPPvtsaloBJnwREdmLVpULStViXhKTkCw/7blh6eYQEZnNJ2suyMHL98Tf01Vm96sm7q65KmyV74xuZalSpeTIkSPy7rvvyptvvin16tWTzz77TA4dOiRBQay3SET2A0ectFzZBTuvq5m8RET2Zt3R2zJ3e0oK1bRnKkuZwh5iK1xz9U+urvL888+bvjVERFbmiQZB8um6i3ItPF7WHbutFkwgIrIXF27Fypu/nFbnX25bSjrVLCy2JFfjxqdOnZLhw4dL+/bt1QnnQ0JCTN86IiIL8yjgLP0fSVkgYa6VlOLC6En7SQckeMxO9RuXiYiMFfcgWYZ9d1LuxSVJo2A/eadLWbE1Rgeyy5cvl5o1a8qBAwekTp066nTw4EGpVauW+hsRkb3p37y4WtHmwKV7sv9ilEXbgqB1yKKTcjI0RuITdRISGqMuM5glImNNWHVOTly7L4W8XeXbF6pKARfbyIvVZ3SLx4wZI2PHjpXdu3fL1KlT1WnXrl0qZxZ/IyKyN4G+btKrQZBVjMpOWn8pzWVt7fOpGy9brE1EZHtWHAiT73ffUPuPr5+vKiUKuostMjqQDQ0NlX79+mW4Hjmz+BsRkT0a9nDS19qjt+Xq3TiLlcc5czMmw/WodXsuLOP1RESZOX3jvoxedkadf+PRMtKmSoDYKqMD2TZt2qjVvdLbuXOntGzZ0lTtIiKyKtVKeEuLSgUlGQsk7Mz/BRKSknXy2k+n1ONnpqBXAdEhoiUiykZMfJIMWxwisQnJap/2VscyYsuMrlrQo0cPefvtt1WObNOmTdV1e/bskWXLlsmHH34oq1evTnNbIiJ7Max1Sdl5JkLVlB3ZsYz4eOSq8IvREKC+8+tZ+f3wbUEKW1JySjqBftx6MypB3l52Vj7pXcEm89yIKJ/2JcvPyumbMVLUz01mPl9FXJydbHrTO+mM/Arv7OxscP3FzJaytRdRUVHi7+8vkZGR4ufnZ+nm2AS81LC9sN3w+iD2ha1JTtZJ6y8OyLmwWPno8fKpNWbN/d6Y+PsF+WbrVcHnzax+VcXZyUnlxCKdoEKQl9Qu5SNL/rmpAtuWlQvKnP7VVFFzMn1fUP5hX5jej3tuyOilZ9QX4mUv15amFfytsj+MibGM3tMlJyfnpW1ERDbL2dlJhrQsIWOXn5P5O67LwBYlzD6a8dXmKyqIhS/6VJJudVLq2HapXSTN7R6rVVhe+T5EdpyOkJ4zjsh3Q2rYVFFzIjKv49ei5f0VZ9X5tzuXMyqItWZ5Ov6EJWqJiBxJn4ZFJcDLVS7diZONJ+6Y9bG+3xUqn669qM6P6x4szzYtluVtO9YoLCuH15Hi/m7qsGHX6YctXiqMiKxDVGyivLj4pCrZ16F6IXmlbSmxF0YHskgX+Pjjj6VkyZLi4+Mj58+fV9ePGzdO5s+fb442EhFZDS93F3m+mfkXSFh1KEzlssHrHUqrFXdyUquUj6wZUVdqlvSWO9EPpM83R+W3Q7fM1kYisn46nU5GLT0jF27HSckAd5n+TGV1dMlhA9lPPvlEFi1aJF988YW4ubmlXo9FEubNm2fq9hERWZ0BzYuLq7OT7DkfJUevRpv8/jf/e1de//G0ynnFYgxvdzZ8tZ3iBd3VyGzHGoXU6MvL34fItD8vs6IBkYOav+O6rDlyWwq4OMmcftUkwLuA2BOjA9nvvvtO5syZI88995y4uLikXo8VvrhMLRE5AgSLPeoWMcuo7N7zkTJ00UlJTNZJr/qB8kmvCkZPrPB2d5H5A6vLi61TJqN98ccleePn0xKfyDkORI7k4KUo+fj3C+r8+B7BUq+sr9gbowPZa9euScWKFTOdBPbgwQNTtYuIyOpLcQEO3YdGxJvkPo9fjZZ+805IXGKyymOblodDgJiENqFnefm0d4WUGcr7w+SZWcfk7n3up4kcwd37D+TF70LkQZJOutcpIoNalBB7ZHQgW7169UwXRPj111+lXr16pmoXEZFVq13aV5qU91Mjp4v+zvuqhhdux8uzc0/IvbgkaVreT2b3M8265/2bl5Dvh9QUH3cXlQrRY8YROX8rNs/3S0TWXSpwxE+n5Fp4vAQX8ZDJfSvZbTk5o8tvjR8/Xvr3769GZjEKu2LFCjl16pRKOVizZo15WklEZKXL1u49HyU/7A6VEY+WFi+3/9KtjHEtPE4G/3BBTdDChK3FQ2qIZy7vKzNtqgbI6tfryAvzTqggtvv0wyr1wF7K7xBRWijZt/lkuHi4Oqu60r75tHiLJRj9db9nz57y+++/y6ZNm8Tb21sFtidPnlTXPfroo+ZpJRGRFepYs7CULewh4TGJ8uv+sFzdx+17CfL07BNyI+qBVAj0lJ+G1TDLh07V4t6ydkRdqVfGV7W376xjsuyfmyZ/HCKyrD3nIuXzP1LK9k18ooLUKOlj112Sq+NWLVu2lD///FPCwsIkJiZGdu7cKR07djR964iIrBjyUAe3TMk7m7sdR6l0Rtd2fHbOcTVKWty/gPz8Yk0p7PNfNRhTC/Jzk19fqaXy5ZA3N+Ln0/LFHxdZ0YDITty6l6AqlWAZ6z4Ng+SZJkXF3nFBbiKiPHi6cVHx9XBRy9ZuDQk3+P9iEpKk//wTcvzafSniU0DmPx+sajyaG1IWvn2hqrzWvrS6PO3PK/LKD6ck7gErGhDZqnVHb0v7SQek7gd75WZUgpQo6Caf9q5ot3mx+gw6fhUQEGDwxrh7925e20REZDN8PFzViluzt12TOduvSfvqhXL8n4TEZLXKDvJr/Txc5MdhNaS0T5LkF1RCGNu1nAQHesiYpWdV5YWr4XGycGB1KeJrvhFh7QN3yoZLahS6fKCnjOxUNsNyu0Rk3HtqyKKTaa67HpEg206FO8R7y6BAdtq0aann79y5IxMnTpROnTpJs2bN1HW7d++WDRs2qNW9iIgczeAWJVQ92R2nI+Tk9ftSrYR3lrdNwmzin0+nTMQo4KwmdtUs6SORkZGS355uXExKB3ioD8EDF+9Jt+lH5Lsh1aVysazbb4oPXAyLIAkjJDRGXZ43oJpDfOASmcOUDZdS31MajD1O3XjZId5XTjqsXWaE3r17S9u2bWX48OFprv/666/VBLBVq1aJI4iKihJ/f3/14ePn52fp5tgEvNSwvbDdHOFwhzVjX5geRlh/P3JbpRpMfbpyltv9nV/Pyve7b6iVwRYNri7tqhWyeH+cDYuRfnNPyMU7ceJZwFkCfQuow5O5GTHFogvRcYkSFZsk9+ISVTmxqLhEiY5Lkv+tvajuVx+ebrXi3rJpVH2xBpbuC2JfGKvc6J2SkJQxlHN3dZILX7SwyfeGMTGW0VNjMfL6+eefZ7j+sccek3feecfYuyMisgtDW5dUgeyKA2HqsH1gJofoP1t3SQWx+Az46rkqKoi1BhWDvOT3EXXl8a+PqFzfy3dTFnjQRkxfaFZMyhb2lOj4lABV+60Fqvq/sSyuMTCUci4sxkzPjMi+PUhKVpNOJV0gi31MhSAvcQRGB7KFCxeW3377TUaOHJnmelyHvxEROaKG5fykfhlfOXj5niz+O1RGPVY2zd+/2XJVvtp8RZ3/4smK0rNeoFiTwj4F1Frs+rSPRgTfxsIyub44ebqIn4er+Hi4yMFL91TA66gfuESm9tm6SxL7cKKmll6A9xS+II7sWMYhNrjRgeyHH34oQ4YMkW3btkmTJk3UdXv37pX169fL3LlzzdFGIiKbGZVF6ZvFu0JlePvSKgcWftwdKhPXpKx3/l63cvJcs+JijS5kseIXBnx61Q9S1Rn8PF3VKmH6v3E9at9i4prvw+vVKJEBk1Ic6QOXyJQ2HL8j3269qs6/0rakbDsVoY5u4Ish3lOdHSA/NleB7IABA6RatWoyY8YMtaoX4DJqyWqBLRGRI+pau4iUKOgu1yPiZeXBMHmmSTFZffiWjPn1rPr7q+1KyavtUspeWSPkxCKdIP2kESymgFSIvEKuLSZ2fbr2opy7FatGkL55oarDfOASmcrlO3Hyxs+n1flhrUvK+93Ly/vdHXP75mr5GASsP/74o+lbQ0Rkw1xdUhZI+Pj3C/Lu8rNqYhcWHgDkmb7btZxYM0zsUlUFHh6aNMchSgSznWsVlnof7JWwew+kkLf9Lp1JZA6YUPnidyclMjZRGpT1tfr9irnlag+SnJwsZ8+eVSt74by+Vq1amaptREQ2p4hvAfU7/aSnlpULWv0seG3EFGV7zHmIEtuhdZUAWbY/TLafjpCWlQNMev9E9uyj1eflyJVoCfB2lVn9qombq2OvbWV0ILtnzx559tln5dKlSxmWNcTOKSkp/4p6ExFZm1kPc9b0IX7FClrd6ljXBK+sgtn8qD2pBbJ/nQqX97oFm/3xiOwBFi9ZuDNUnf/q2Sr5shqg3QWyL730kjRs2FDWrl0rxYsXt/oRBiKi/IQVq9JjiamMMEINWKL39r0Es68oRmTrcJRk1NIz6vzrHUpbTfk+mwtkz5w5I7/++qtUrFjRPC0iIrJhWU2YYomptFBnt3oJb/n3+n3ZcSZCVUUgoszFJiTJsMUn5X58kjSr4C+jOqUt7+fInHMz0Qv5sURElPmEKa2WozhgTUdj0wvgr1MRlm4KkVV7b8U5ORkao1bdQ6UPTCylXI7Ivvbaa2oxhBs3bkitWrWkQIGUiQ2a2rVrG3uXRER2I78mTNmD1lUKqjqY20+FqzkXTFUjymjJvpvyy76bqp7zN89XlaJ+TMPJUyDbu3dv9XvQoEGp12Hno+2EONmLiBxdfk2YsnWNg/3Fw9VZbkQlyOmbMVKlmLelm0RkVUJC78vY5SlHwbFaYPNKKbnllIdA9sKFlNVpiIiI8gIrnzWp4KdSC7afimAgS6QnOi5Rhi4+KXEPkqVNlQB5vb31LqZiU4Fs2bJMMCYiItPlySKQRRkuLPFLRMir18noZWflXFisFPd3UyvrOWey7DMZGMiuXr1aOnfurPJhcT47PXr04HYlIiKDtFaLIVyQXeci1YpF7g5e3J0Ivt99Q9WMdXV2UoseFPZJOx+JjAxkH3/8cTW5KygoSJ3PCnNkiYjIGFWLe0mQbwG1XO0/F6KkBXMAycEdvXJPxq88p86/262cNAr2s3STrJpBX32xDC2CWO18VidO9CIiImNgAKTVwzJcqF5A5MgiYxNl2OIQSUjSSaeaheVFptvkyKGP4Xz55ZdSo0YNqV69urz++usZltwlIqL8Si8Q+es068mS40IM8ubPp+Xy3TgpU8hDvny6EkvSGcBhA9lbt27J119/LQcOHJBjx46p33v27LF0s4iIHHa52mNXo+VOdIKlm0NkEXP+uibrj98RNxcnmdO/qhT0Yl6sIRw2kIXExESJi4uTBw8eqJOWPkFERPknyM9NqhdPqSGL5WqJHA3ywz9Zc1Gd//Dx8lK7tK+lm2QzrDaQ3b59u3Tv3l1KlCihhtZXrVqV4TYzZ86UcuXKiYeHh1o6d9++fQbff2BgoIwaNUrKlCmjHqNDhw5SoUIFEz8LIiIyRKsqKaOyXK6WHM2d6Afy0vcnJTFZJz3rBUq/R4pbukk2xWoD2fv370udOnVUsJqZJUuWyFtvvSUTJkyQgwcPqtt26tRJwsLCUm9Tt25dqVmzZobT9evXJTw8XNasWSMXL16Ua9euya5du1TwTERElqknC9pytUSOIDlZJ6//dEpCIxKkfKCnTOpTkXmx5l4QIb+gbi1OWZk6daoMHTpUBg4cqC7PmjVL1q5dKwsWLJB33nlHXXf48OEs/3/ZsmVSsWJFKVSokLrctWtXlSPbqlWrTG8fHx+vTpqoqCj1Gztc7nQNo20rbi/LY19YF/aHSKNgX3F3dZLQyAQ5fSNGKhfzYl84OEd4X8zYfEW2hoSrVe6QF+vt7mK1z1eXj/1hzGOYLJDFofnz58+rk7klJCSoyVljx45Nvc7Z2Vm1Yffu3QbdR+nSpdUoLHJksdDDtm3bZNiwYVne/tNPP5UPP/www/WRkZFW+6KzNthO0dHR6jzSRYh9QXxv6GtQxlt2nY+WjUdDpahnEYu8PLifsh723hd7L0TL5PWX1PlxnUtICa9EFVNYK10+9oc2WJivgSwWSrhz547kh9u3b6uatUWLFk1zPS6HhIQYdB9NmzaVLl26SL169VQQ3L59+2xXJUPQjFQG/Y2MYNjf31/8/Fis2BBawI9tZo87JVvCvrAu7I8U7asXUYHs3stxMryjP/vCwdnz+yIsKkHGrAqRZJ1I30ZBMqB1ObF2unzsD2Pu32SB7PDhw8XWfPLJJ+pkCHd3d3XKbGPb2xvMnLTtxW1meewL68L+EGldtZB8vOai7D4XqQrCW2q5WvaF9bDHvkhM0smrP5ySW/ceSNViXvJJb9vJi3XKp/4w5v7zvJfAyCQqCpw8eVLyS5EiRcTFxUVu3ryZ5npcLlasWL61g4iITKdacS8J9C0gsQnJsv+C4YcWiWzJlA2XZNe5SJUPO2dANfFyc7F0k2ya0YHsU089pRYSgNjYWGnYsKG6rnbt2rJ8+XLJD25ubtKgQQPZvHlz6nVYIheXmzVrli9tICIiMyxX+3CVr+1c5YvsyLqjt6X9pANSdvROmb7pirpu8lOVpGKQZSY1OnQgixJVLVu2VOdXrlypciYiIiJkxowZMnHiRJM1DAnFqDqgVR64cOGCOn/58mV1Gfmqc+fOlcWLF6vR4JdfflmV7NKqGBARke1pnVpPNtzSTSEyWRA7ZNFJCQmNkQdJ/00OL+BiG+kEdhfIYkadVrJq/fr10rt3b/Hy8lLlq86cOWOyhu3fv19NxMJJC1xxfvz48epy3759ZfLkyeoy6sUiyEV70k8AIyIi29Hy4YjssWtYrvaBpZtDZJJUAoSs+vWNkAI6dWPKwBzljdGTvTBTHyWuEMwicPzll1/U9VhgACtsmUqbNm1yLGuFCWa2OMmMiIgyV9TPTeXKngyNkZ1nItRKR0S27Pyt2DRBLCC8ORcWY6EWOfiI7BtvvCHPPfeclCpVSi3tioBTSzmoVauWOdpIREQOpNXDVb6YXkD2INDXLcN1GJGtwPxYywSyr7zyihqRxQpaO3fuVDVYoXz58ibNkSUiIsdervav01yulmzbpTuxGVJkEMRiRHZkxzIWa5dDpxYgeG3RooWqVqAPObJERER51STYL2W52ogEORsWK5WKcmY32Z64B8kybHGIxD5IlvKBHqouMtIMMBKLILZzbcusXieOHsi2a9dOSpYsKc8++6w61ahRwzwtIyIih+Tp5iKNy/vLjtMRKr2AgSzZog9/Oy/HrkZLgLerLHmptpQMyLioElkgteD69esycuRI2bZtm8qJRcWASZMmydWrV03QHCIiIpHWrCdLNmzlwTBZvCtUpRF8/WwVBrHWFMhiVS1UCvj777/l3Llz0qdPH1XLtVy5cmq0loiIyFT1ZP8+GyHxicncoGQzztyMkdFLU8qRjuhQWtpWSylZSuaRpyVqg4OD5Z133pHPPvtMjc7+9ddfpmsZERE5rGrFvaWIT8pytQcucrlasg0xCUny4uKTEpOQLM0r+svITmUt3SS7l+tAFiOyqGBQvHhxlStbs2ZNWbt2rWlbR0REDsnZGcvVpozKcrlashXvLj8nITdiJNC3gMx8vqq4OHP1LqsLZMeOHatGYpFGgOVip0+fLjdu3JDvv/9eHnvsMfO0koiIHLcMF5erJRvwy74bsvSfm4LY9dsXqkqQX8b6sWQFVQuw8MHo0aPlqaeeUvmyRERE5lwY4ejVaLl7/4EU8i7ADU1W6d/r9+XdX8+p82M6l5VHKqYcTSArDGSRUkBERJQfy9VWLealDtViudoedblcLVmfe3GJMmzxSYlLTJa2VQNkeLvSlm6SQ8nTZC8iIiJHSi9Yd/S2tJ90QILH7FS/cZkcl06nUxUKsNBB8YJuMuPZKiq/m/IPA1kiIrKBQDZCBQ2WhKB1yKKTEhIaI/GJOvUblxnMOi7Uil19+La4OjvJrBeqSWEfpr/kNwayRERktRqX9xM3Fye5HhGvlqu1pCkbLqnfWjiN3yh4P3XjZYu2iyzjyJV78sGq8+r8e93KSaNgP3aFtQeySUlJarJXRESE+VpERET0kNfD5Wph+2nLphecu5UxkMYg8bmwGIu0hywnIuaByotNSNLJYzULy7DWJdkdthDIuri4SMeOHSU83DpylYiIyHFW+UJ6gSX5uLtk+bejV+7la1vIcpDi8uYvZ+TK3XgpU8hDvnymsjhhaJ5sI7UACx+cP58ylE5ERJRfebK7zkZIgoWWq718J06iYhPVeS1k0X4jX7br9MPyxR8XLdY+yj+z/7omG47fUSkvc/pXFX9PowtAkSUD2YkTJ8qoUaNkzZo1EhoaKlFRUWlOREREplS9uLeaRBNjweVqP113URCjVivuJdVKeIu7q5P6Pe3pytKjbhFJShaZ9ucV6TLtsJy4Fm2RNpL57bsQKZ+suaDOf/h4eald2peb3cKM/hrRpUsX9btHjx5phtIx1I7LyKMlIiIy9XK1Kw/eUsvVNsvnYvOHLt2T3w7dUhO7pj9bRWqW9Enz96caF5WutW/JO8vPqsL4CGbf7FhGXm1XSgq4cE61vbgTnSAvfxeivrT0rBco/R4pbukmUW4C2a1bt3LDERFRvqcXIJBFPdm3u5TLt8fFIM1Hv6ek0/VpGJQhiNV0rxsoTSv4y9vLzsr643fkiz8uyfpjd2T6s5WlSjHvfGsvmUdysk5e+/G0hEYmSIUgT5nUpyLzYm01kG3durV5WkJERJQFjMjCkXxerhZB6d7zUeLh6ixjOmcfQAf6usn8gdVUwP3+inNqad1OUw7J6M5l5aU2pcSFhfJt1ozNV2TbqXDxKOAsc/pVEx8P5sVai1wd80D5rSlTpsiQIUPU6csvv5TIyEjTt46IiEhEivm7S5ViXqrc1d9n8qd6wYOkZPlkzUV1/sU2JaVEQfcc/wcpdk80CJItY+pLh+qFVHkm3MfjXx2RsyzTZZOwPPLk9Sk1hD/tXVHlRpMNB7L79++XChUqqOD17t276jR16lR13cGDB83TSiIicnj6q3zlhx9231BLj2Ki2SvtShkdeC8eXF2mPl1JfD1c5MCle9Jx8iGZ89c1dZiabMPNqAR59YcQQZf1bVxUncjGA9k333xTTfS6ePGirFixQp0uXLgg3bp1kzfeeMM8rSQiIofX+mF6wV+nw82+XC1KbWkreY3qVEZ8c3EoGaOzTzcuJltGN1C1cOMSk+WD385L72+OysXbll2ljHKWmKSTV74PkVv3HkjVYl7yyRMVuNnsZUT27bffFlfX/97UOD9mzBj1NyIiInNoUsFf1e68Fh6f6SpbpjRzy1W5ez9RKgZ5yrNNi+XpvkoGuMtPw2rK509WFC83Z5Vz237yQVm48zpHZ63Y5A2XZPe5SPF2d5E5A6qpVebIDgJZPz8/uXw547rSV65cEV9f1lMjIiJzLlebsp79djOmF1yPTJB526+r8+91CzZJCS2Mzr7wSHE1OvtIBX+JTUiW91ack6dnH5Mrd+NM0GoypS0n78qMTVfU+clPVZKKQV7cwFbK6Hdn3759ZfDgwbJkyRIVvOL0yy+/qElfzzzzjHlaSUREpKoXPMyTPW2+pdJnbL2p0gCaVfCXjjUKmfS+yxT2kKUv15KJvSqIp5uz7DwTKe0mHZQfd4eaPV2CDIMR/9d+PKXO929eXNWMJetldNLP5MmT1TfLfv36SWJiynJ9BQoUkJdfflk+++wzc7SRiIgodcLX/9ZelF1nI9VysG6upl1w4NjVaFl9NGW0d3yPYLPUCsUCD4NalpC2VQPkjV9Oyz8XomT0srOy6O9Q9Zwu342T8oGeMrJTWelSu4jJH58yWnf0tsqJxuQ+ZycniX2QLLVL+cgHPctzc1k5o/YAWLVrz5498sEHH0h4eLgcPnxYnVC5AFUM3N1zLk1CRESUWzVKpCxXez8+SQ5eumeGxQ9Slh/tVS9Q6ph5+dHgQE9Z8WptmdAjWBCPn7h+X86ExUp8ok5CQmNkyKKTKsAi88I2xrbGNse2RxALzzQpKu4m/qJEpmdUD7m4uEjHjh1VHVkvLy+pVauWOuE8ERGRuWE0s2WllOoF202cXrD5ZLga6cWEsre7lJX8gEUSXmxTSsoW9kxzPZIMMBg8dWPGOSlkWhiJxbi7fmIHLn+/+wY3tQ0w+qtGzZo15fz5lOX6iIiI7KGeLEotffxwKdoXmhSW0oU8JD9dDc844Qsps+e4iILZIZ0gfXYyLnPb22kgO3HiRBk1apSsWbNGQkNDJSoqKs2JiIgoP5arPXzlnoTff2CS+/xl3w05czNWArxcZWiLIMlvyIlNn42LyxU4W97sUB4tPYyGc9vbaSDbpUsXOXLkiFoUoVSpUhIQEKBOBQsWVL+JiIjMqXhBd6lc9OFytWfzPiobHZcokx4uQfpmxzLi55H/9UIxsUtLJ9Dg8nAjVxQj41yPiFf1gvWhD/DaGtmxDDenPVYt2Lp1q3laQkREZCCslHX6ZoxKL+hWJ2/lkb7ZelWt3hRcxENeaFZMYu+bdhKZIVCdYN6AaionFoe0k5JFEpN1ql1kHhExD+S5OcclIiZRivm5ib+Xq1pxDSOxCGI7s2KE/QWyDx48kI8++khmzZollSpVMl+riIiIcsiTnbv9uvx1KmW52tyWyQqNiJdZ266p8+92DVblvCy1eCyCWa3cFurKoiTXV5uvyHNNi4mXO1eVMqXYhCQZMP9fOXUjRgWxq1+vI6XyOS+aLJBagHqxR48eNdFDExER5U7T8inL1V4Nj1eTdXILKQVxD5KlYTk/6VK7sNV0x1ONi0rZwh5yO/qBLNiZssoYmUZSsk5e/eGU7LsQpdJIfhxWk0GsI+XIPv/88zJ//nzztIaIiMgAGKFsFPxwudrTucuT/ff6fVnyz011foKZFj/ILSyL+9bDHM1vt16Ve3Fp8zgpdzB6/+7ys7L++B1xd3WShYOqS7US3tycjpQji9W8FixYIJs2bZIGDRqIt3faF8DUqVNN2T4iIqJMtaoSIH+fjVTpBQNblDB6K038/YKa1NO9bhFpUC4lKLYmTzQIUqkFZ8NiZe5f1+StTvlT29aefbnxsqoPi+8sXz9XVZpVTKmAQQ40Inv8+HGpX7+++Pr6yunTp+XQoUOpJ6zyRURElJ/1ZBHMPsDsKCNsCwmXbafCpYCLk7zbtZxYIyyWgGoGMPuvayYrNeaokHc8eUPKAhOfPFFButbh8r/2gFULiIjIJtUs4S2FvF1V+SQsV9ukvL/BOZLa4gcYyU2/qpY16V6niMzY5CUnQ2NUMPtOF+sMuq0dUgne/vWsOv/Go6VlQHPjR/DJOuV6EeGzZ8/Khg0bJDY2NjXvhIiIKF+Xq62srfJl+HK1y/bfVIGhv6erjOhQWqz9OY56LGVUdt72a3InOsHSTbI5+y5EyivfhUiyTuSZJkVl9MPtSQ4ayN65c0fat28vlStXVosjYHUvGDx4sIwcOdIcbSQiIsqynixsN3C52pj4JPliXcriByMeLS0B3gWsfss+VrOw1C7lIzEJyfL1lquWbo5NOXXjvgyY96/EJSZLh+qF5PMnK1nVpD6yQCD75ptvqjJcly9fFi8vr9Tr+/btK+vXrzdBk4iIiAzT6uGILJarRYH7nODw/I2oBCldyD1XE8QsAYHXmM4po4iLd4bKzSiOyhq6atezWPAgNlEalPWVWf2qiqsLg1hx9EB248aN8vnnn6vlafVhgYRLl1K+5RIREeWHEgXdpVJRT3XY+O8zkdneNiwqQWZuuZK6+IG7a66z6/Jd26oBqtYtRhZnbEqZsEQ5r9oVGpEgFYM8ZfGQGuLlxkUl7JHR7+L79++nGYnV3L17V9zd3U3VLiIiIoO0NjBPdsqGS+rwfL0yvtKjrm3NWNcflf1x9w25Gh5n6SbZzKpdPw2rKYVsIIWE8imQbdmypXz33Xdp3lzJycnyxRdfSNu2bXPZDCIioryV4UI5rawmHp++cV9+3HNDnR9vZYsfGKpFpYLSvKK/JCTpZPqfKSPLlBZX7XI8RpffQsCKyV779++XhIQEGTNmjJw4cUKNyP7999/maSUREVEWmlXwV/VgsVzthdtxUj4wYzmtiWsuqvSDzrUKG1ymyxqN7lxW/v7qqCzZd1NebVdKyhWx3tJh+Y2rdjkmo0dka9asqRZCaNGihfTs2VOlGjzxxBNqQYQKFSqYp5VERETZLVf7cGWu7aczphfsPBMhm/69K67O1rv4gaEaB/urfNnEZJ1apYr+w1W7HJPRI7Lg7+8v7733nulbQ0RElMv0gl3nsFxtRJpi98nJOvlodcriBy88UkwqBGWc42FrUAd1a0i4LD8QJsPbl5ZKRW3/OZly1a7/cdUuh2I7UzaJiIhyqCf795mINMvVrjx4S45fuy++Hi7yVscydrH96pbxlY41CqlUiakclc2wald/rtrlUBjIEhGRzatZ0kcCvF0lOj5JLVerzV7/dN1FdR4jl4V93MReaKtT/Xbolpy8fl8cFVftIocIZHv16iUBAQHy5JNPZvjbmjVrpEqVKqoO7rx58yzSPiIiMsFytZUervJ1OmWVr3k7rqui+Kg1O6SlbSx+YKgaJX2ke52UEmKTNzhmDXeu2kUOE8iOGDEiTckwTWJiorz11luyZcsWNVlt0qRJagleIiKy3TJc20+Fy53oBPl6c0qJqrFdyomnHRbDH/VYWXF2Evnj2B05eiVlFNohV+0qx1W7HFmuAlkEgJs2bZLZs2fLvXspb57r169LdHS0WKM2bdqIr69vhuv37dsnNWrUkJIlS4qPj4907txZrVxGRES2u1ztocv35IPfLsi9uCSpVcpHetUPFHuESV696gep85PWX3LcVbsGc9UuR2Z0IItlaGvVqqVKb7366qty69YtdT2WrR01apTRDdi+fbt0795dSpQooQpUr1q1KsNtZs6cKeXKlRMPDw9p0qSJCkBNAcE3glgNzl+7ds0k901ERPmrZIC7WskJk6Awox861Sik0g7sFSawuTiLbD4ZLvsvRok9W3f0trT74oDUGLdHrdpV0NNVfnqRq3Y5OufcHKZv2LChhIeHi6enZ5o81M2bNxvdANShrVOnjgpWM7NkyRJ1+H/ChAly8OBBddtOnTpJWFjKTgrq1q2r6tumPyFQJSIix4BA50ZUQprrUJIJ19ur4EBPeapRUXX+iz/sd1R27ZFbMmTRSQm5ESPa4m1IKzh6xTqPBJMV15HdsWOH7Nq1S9zc0s7+xIhpbkYzcTgfp6xMnTpVhg4dKgMHDlSXZ82aJWvXrpUFCxbIO++8o647fPiw5AZGgfXbjPONGzfO1X0REZFlTdlwSTD2qr9ILVaiRYmqLrVTJkbZozcfLSO/7g9TCz/sOhshj1RMmfRmyxISk+X4tWjZcfK2HL9xXTYczzh/xRH6lswQyCYnJ0tSUlKG669evZppHmpeYAncAwcOyNixY1Ovc3Z2lg4dOsju3bvzfP8IWo8fP64CWCzy8Mcff8i4ceMyvW18fLw6aaKiolKXxMtqbW9KS9tW3F6Wx76wLuwP0zh/KzZNEJuybUXOhcUYvJ+2xb5ASsWzTYrJ4l2halR2xat+KlXPltyJfiAHLkbJ/ov3ZP+lKDlyOVriEv+rB5wZY/uW8iY/3xvGPIbRgWzHjh1l2rRpMmfOHHUZbxZM8sKh/y5duogp3b59WwXNRYumHDbR4HJISIjB94PA98iRIyqNoVSpUrJs2TJp1qyZuLq6ypQpU6Rt27YqQB8zZowULlw40/v49NNP5cMPP8xwfWRkJN9ERrwwtQmBtraTtTfsC+vC/jCNsoXc5UxYXNoRWRwxLOyu9tX23BcDm/jLL/tuyL4LUbLu4DVpUdG0A0umlKzTyblb8XLoSowcvnpf/b50N21KCBT0dJFaxd2kQTk/WX4oXK6GJ+Spbylv8vO9oQ0WmiWQReCHHNXq1atLXFycPPvss3LmzBkpUqSI/Pzzz2KNUGEhKz169FCnnGBUGLm6+hu5dOnSaiTXzy9ljW8y7BsWtpktfUDYI/aFdWF/mMbozuVk6OIQdcgZuxvtN67Hfsee+wJPr98jUTJ3+3X5Zsdt6VK/ZL63H7nIONSPkfHygZ5qIhoO+0fHJcrBy9EPR1yj1IIVUXEZj+xWKeYlDcv5SoOyftIw2E+CC7urz1r0RY3Sd/Lct5Q3+fneMOb+jQ5kMaKJ0c1ffvlFjh49qqLzwYMHy3PPPZdm8pcpIDh2cXGRmzdvprkel4sVKyb5yd3dXZ0y29i2tLOzNG17cZtZHvvCurA/8q5rnUCZN8BJBVM45FwhyEtGdiwjnY3MobTVvnitfWn5Yc8NOXwlWv78N1w61cz8CKO5glgVaD7MUQ4JjVGXSwW4q5qvqCShz8vNWeqX9ZWG5fzUCecLehXIEDhp/WCqvqW8ya/3hlkDWYzCogzW888/L+aGCWUNGjRQ1RAef/xxdR1SAHB5+PDhZn98IiKyLRgBdNTJP0V83WRwixLy9Zarqq7so9Xzr/RY+ol22u+r4SlzS0oXck8NWnGqVtxbXF2Ma5sj9y2ZMJANCgpSpbYQyLZv315NvsoLjOiePXs29fKFCxdUFYJChQpJmTJl1OH8/v37q5JfmJyF/FzkumpVDIiIiCjFy21LqUlf/16/L2uP3pbudQPzZalYVRYrk7+5OjvJvnGNpJh/xiOaRKZgdBS6ePFiiYmJUQsiYAGBN954Q/bv35/rBuB/69Wrp06AwBXnx48fry737dtXJk+erC6jXiyC3PXr12eYAEZEROToArwLyNBWKQv9TN5wSZLSH9M3ocjYRJmw6px0mHwwtbarPhwdrlzMi0EsmZWTLpd1FLA07a+//qomeG3ZskXKly+vRmm1ANTeaQnomC3JyV6GwUsN28vWJlHYI/aFdWF/WA976Iuo2ERpOvEftWDAV89Wkd4NU5axNZXkZJ0s+eemfLr2otyOfqCuq1vaR+Xmpp+MNX9AtVznsdpDX9gTXT72hzExVq7zAlAzFof3N27cqCZ9eXt7Z1qeioiIiPKPn6erSjGAqRsvyYOk7OuxGuPgpSjpNv2wjFxyRgWxFYI81TKx696sJ/MGVFO5r+6uTup3XoJYIrPlyOpP+lq9erX89NNPqYf6R48endu7IyIiIhMZ1LKEzNl+TS7cjpNl/4TJs03zVunn1r0E+WTNRVn6T0oVIR93F3mrUxkZ1KKEuLmmjIlxMhbZRCC7YcMGFbyuWrVKLSjw5JNPqlHZVq1amaeFREREZBRvdxcZ3q6UfLj6gnz552WVXuD+MOA0BkZzF+4MVVUJ7j2s/fpUoyAZ2zVYivqlXaqeyCYCWVQs6Natm3z33XdqJa8CBdLWfSMiIiLL6/dIcZm17ZpcC4+Xn/fekAHNSxj1/9tPh8u4lefkzM1Ydbl2KR+Z+EQFVT6LyGYDWSxGgPxYIiIisl6ebi7yeofS8t6KczLjzyvSt1FRdV1OrtyNkw9+Oy9/HLujLhfydlUjsM80LppvdWmJTBrIYvaYNmsMs9ayWwOXM/iJiIisA3Jjv9l6VY3Kfr/7hgxrnVKaKzMxCUkyc8tV+XbLVYlLTBYXZ1GjuCM7lcmw6haRTQWyAQEBEhoaqhZDKFiwYKZlF7Sl5JKSMq6fTERERPkPebFvPFpGRi89I19vviLPNy0mXu4uGT6/1x29Ix+sPq8CXmhe0V8+7lVBqhb3ZreR7QeyqBOLlbZg69at5m4TERERmQgmZ83cfEUu3omTBTuvy/D2pdOsyjVu5XnZeSZCXS5R0F0m9AiWbnWKsHYr2U8g27p169TzwcHBUrp06QwvcHyju3LliulbSERERLlWwMVZlcp6/afT8tm6i2rFr+AinlIqwF22nQoXlJlF7ddX2pWWV9uVEi8D8miJbHayFwJZLc1A3927d9XfmFpARERkXTwKpJTewoq1CYk6OXUjRp3gsZqF5YOe5aVMYQ8Lt5IoHwJZLRc2vejoaPHw4JuAiIjI2ny58bLgkzv9mvQIXhcMqm6hVhHlYyD71ltvqd8IYseNGydeXl6pf8Mo7N69e6Vu3bomaBIRERGZ0vlbsRmCWLgZmTK5i8juA9lDhw6ljsgeO3ZM3Nz+W9ED5+vUqSOjRo0yTyuJiIgo18oHekpIaEyaYBYHVysE/TcoRWTXgaxWrWDgwIEyffp01oslIiKyESM7lZUhi06q4FWnk9TfIzuWsXTTiPLE6IWXFy5cyCCWiIjIhnSpXUTmDagm1Yp7qwoF+D1/QDXpXLuIpZtGlL+TvWD//v2ydOlSuXz5siQkJKT524oVK/LWIiIiIjJLMIsTkUOPyP7yyy/yyCOPyMmTJ2XlypXy4MEDOXHihFo0wd/f3zytJCIiIiLKayD7v//9T7788kv5/fff1SQv5MuGhITIU089JWXKMNeGiIiIiKw0kD137px07dpVnUcge//+fVWS680335Q5c+aYo41ERERERHkPZAMCAuTevXvqfMmSJeX48ePqfEREhMTEpKwSQkRERERkdZO9WrVqJX/++afUqlVL+vTpIyNGjFD5sbiuffv25mklEREREVFeA9mvv/5a4uLi1Pn33ntPChQoILt27ZLevXvL+++/b+zdERERERHlTyBbqFCh1PPOzs7yzjvv5O6RiYiIiIjMHchGRUUZfId+fn55aQ8RERERkekC2YIFC6rKBNnR6XTqNklJSYY9MhERERGRuQPZrVu35uUxiIiIiIgsE8i2bt3a9I9MRERERJSfdWRhx44d8vzzz6ulaq9du6au+/7772Xnzp3sDCIiIiKyzkB2+fLl0qlTJ/H09JSDBw9KfHy8uj4yMlItX0tEREREZJWB7MSJE2XWrFkyd+5cVUNW07x5cxXYEhERERFZZSB76tQptbpXev7+/mqZWiIiIiIiqwxkixUrJmfPns1wPfJjy5cvb6p2ERERERGZdmWvoUOHyogRI2TBggWqbuz169dl9+7dMmrUKBk3bpw4mtuj6ku8m4ulm2EbdCLJumS57eQskn1ZYmJfOBa+N6wH+8J6sC8ctj/uJSSZL5DFkrTJycnSvn17iYmJUWkG7u7uKpB97bXXxNEkh9+Q5AKMyozaZmbrDTIW+8K6sD+sB/vCerAvHK8/kh/oDL6tkw5LcuVCQkKCSjGIjo6W6tWri4+Pj8TGxqpqBo4Ay/YiL/jc0AriyxFZo77NOXNE1vLYF9aF/WE92BfWg33hsP1xLyFJKsw9pypi+fn5mSeQ1YcSXDNnzpQvvvhCbty4IY4UyBqykSkFXmrYXthuOS15TObFvrAu7A/rwb6wHuwLx+2PKCNiLGdjgtWxY8dKw4YN1UIIq1atUtcvXLhQgoOD5csvv5Q333wz760nIiIiIjJljuz48eNl9uzZ0qFDB9m1a5f06dNHBg4cKHv27JGpU6eqyy4unPRERERERFYWyC5btky+++476dGjhxw/flxq164tiYmJcuTIER4mJiIiIqJ8Z3BqwdWrV6VBgwbqfM2aNVWlAqQSMNeRiIiIiKw6kE1KShI3N7fUy66urqpSARERERGRVacWYLbagAED1EgsxMXFyUsvvSTe3t5pbrdixQrTt5KIiIiIKLeBbP/+/dNcfv755w39VyIiIiIiywWyKLNFRERERGRzObJERERERNaEgSwRERER2SQGskRERERkkxjIEhEREZF9T/aijOXIICoqipvGiG2G7YVFNLiQhmWxL6wL+8N6sC+sB/vCcfsj6mFspcVa2WEgm0v37t1Tv0uXLp3buyAiIiKibGItf39/yY6TzpBwlzJITk6W69evi6+vL0cXjfiGhcD/ypUr4ufnx1eVBbEvrAv7w3qwL6wH+8Jx+0On06kgtkSJEuLsnH0WLEdkcwkbtlSpUrn9d4eGNwADWevAvrAu7A/rwb6wHuwLx+wP/xxGYjWc7EVERERENomBLBERERHZJAaylG/c3d1lwoQJ6jdZFvvCurA/rAf7wnqwL6yLu5V+hnOyFxERERHZJI7IEhEREZFNYiBLRERERDaJgSwRERER2SQGskRERERkkxjIktXo1auXBAQEyJNPPmnU38j8Jk+eLDVq1JCaNWvKDz/8wE1uIadOnZK6deumnjw9PWXVqlXsDwspV66c1K5dW/VF27Zt2Q8WFBERIQ0bNlR9gf3U3Llz2R8WlJ+f2axaQFZj27Ztakm6xYsXy6+//mrw38i8jh07Jv3795ddu3apZQPxgb1+/XopWLAgN70FRUdHq0Dq0qVL4u3tzb6wAGz/48ePi4+PD7e/hSUlJUl8fLx4eXnJ/fv3VTC7f/9+KVy4sKWb5pC25eNnNkdkyWq0adNGfH19jf4bmdfJkyelWbNm4uHhoUYA69SpowJZsqzVq1dL+/btGcQSiYiLi4sKYgEBLb5040SWkZ+f2QxkySDbt2+X7t27S4kSJcTJySnTw5kzZ85UIxQIeJo0aSL79u3j1rWDvsHIBr5d49BdeHi4On/t2jUTPwv7kJ/vk6VLl0rfvn1N0Gr7lB99gftt3bq1NGrUSH788UcTtt7+5Ed/YB+FL9qlSpWS0aNHS5EiRUz4DOzHdjv7PHe1dAPINuBQDXYQgwYNkieeeCLD35csWSJvvfWWzJo1S73op02bJp06dVI5fUFBQeo2yF1KTEzM8L8bN25Ubyiyzr6pXr26vP7669KuXTvx9/eXpk2bqtEPstz7JCoqSqV6/PLLL+wGC/bFzp07pWTJkhIaGiodOnSQWrVqqZxZskx/IN3pyJEjcvPmTfUYyM8sWrQou8PeP891REbCy2blypVprmvcuLHu1VdfTb2clJSkK1GihO7TTz816r63bt2q6927t9F/I/P3jWbw4MG6NWvWcJNbsC++++473XPPPcc+sKL3xahRo3QLFy5kn1hJf7z88su6ZcuWsT+s9PPclJhaQHmWkJAgBw4cUCMSGmdnZ3V59+7d3MJ20DdhYWHqN76R4xATvp2TZfoCmFZg+b7AqBYms2gT77Zs2aIqe5Bl+gOjsFp/REZGqsPnVapUYXc4wOc5Uwsoz27fvq1mjKY/hIPLISEhBt8P3ig4LIQPCOQ4LVu2TE0yyulvZP6+6dmzp/pwwOz4hQsXiqsrdx2W6gv0A75MLF++3Og2kOn6AoETSgwB7mvo0KEqV5Ys0x+o3jFs2LDUSV6vvfaaSvUg6/s8NzV+GpHV2LRpU67+RuZnrd/EHRHylBFEkWWVL19efVCTdWjcuLEcPnzY0s0gC3xmM7WA8gwzQzH5J/2HKy4XK1aMW9iC2DfWg31hPdgX1oX9YT2K2ODnOQNZyjM3Nzdp0KCBbN68OfW65ORkdZmH/y2LfWM92BfWg31hXdgf1sPNBj/PmVpABsFkhrNnz6ZevnDhgjqMU6hQISlTpowq1YHVn7BEIA7xoFwHcmMGDhzILWxm7Bvrwb6wHuwL68L+sB7R9vZ5bva6CGQXUEYDL5f0p/79+6fe5quvvtKVKVNG5+bmpsp37Nmzx6JtdhTsG+vBvrAe7Avrwv6wHlvt7PPcCT8sHUwTERERERmLObJEREREZJMYyBIRERGRTWIgS0REREQ2iYEsEREREdkkBrJEREREZJMYyBIRERGRTWIgS0REREQ2iYEsEREREdkkBrJEREREZJMYyBIRERGRTWIgS0REREQ2iYEsEVmNNm3ayBtvvGH2/8mt9I+V/rJOp5Nhw4ZJoUKFxMnJSQ4fPpzpdWQZ+flaIaL84aTDXpaIKJ8MGDBAFi9enOH6M2fOqGCvQIEC4uvra/D93b17N83/IFipW7euTJs2zaTtzuy+0z/2H3/8IT179pRt27ZJ+fLlpUiRIvLnn39muM7V1VUchTn7w1jp+4uIbJ/j7E2JyGo89thjsnDhwjTXBQYGiouLi9H3heDXUtI/9rlz56R48eLyyCOPZHudsRISEsTNzS1PbSXLvlaIyDyYWkBE+c7d3V2KFSuW5oQgNrND96+//rqMGTNGBSG43QcffJDmvvT/B6O9f/31l0yfPl0dxsfp4sWLkpycLJ9++qkEBweLp6en1KlTR3799dds23j//n3p16+f+Pj4qEB0ypQpGW6T/rFfe+01uXz5snrccuXKZXod5NQe3O/w4cPVfWMEt1OnTgb9nyHbDPfxxRdfSMWKFVU/lClTRj755JM0fzd2W+HvtWrVUrcvXLiwdOjQQW2/rPrDmG2Ak7+/v9oO48aNU6kaxrYjfX+hDVp79E/4e162A8ybN09q166t/gftbteuXY7/Q0R5gNQCIqL80r9/f13Pnj0z/Vvr1q11I0aMSHPZz89P98EHH+hOnz6tW7x4sc7JyUm3cePGTP8nIiJC16xZM93QoUN1oaGh6pSYmKibOHGirmrVqrr169frzp07p1u4cKHO3d1dt23btizb+fLLL+vKlCmj27Rpk+7o0aO6bt266Xx9fTO0T/+xP/roI12pUqXU44aFhWV6HeTUHtyvj4+PbvTo0bqQkBB1MuT/DNlmY8aM0QUEBOgWLVqkO3v2rG7Hjh26uXPnpv6/sdvq+vXrOldXV93UqVN1Fy5cUNtq5syZunv37mXZH8ZsA2xfPP8ffvhB5+XlpZszZ47R7UjfX2iD1h6cDh06pCtcuLBu3Lhxud4OsHz5crVtly5dqrt06ZLu+PHjujVr1mR5eyLKOwayRJTvgayLi4vO29s79fTkk09mGci2aNEizf83atRI9/bbb6e5TVbBJcTFxakAaNeuXWnuZ/Dgwbpnnnkm0zYi+HFzc1MBiebOnTs6T0/PbB/ryy+/1JUtWzbNfaW/zpD24H7r1auX5u+GPo/stllUVJQKxvQD19w8hr4DBw5giFR38eLFTP+efhsZsw2qVaumS05OTv07ngOuy007smpLbGysrkmTJuqLSlJSUq63A/zvf//T1a1bVxceHp7lbYjItJgjS0T5rm3btvLtt9+mXvb29s7ytjhMqw+H+cPCwgx+rLNnz0pMTIw8+uijGfJO69Wrl+n/IK8Vf2/SpEnqdThMX6VKFYMfN6/tadCgQa6fR1bb7OTJkxIfHy/t27fPU9v04ZA77g+H9JEC0bFjR3nyySclICAgz9ugadOm6pC/plmzZirFIykpKUM+dW7aAYMGDZJ79+6pSXnOzs653g4wdOhQWbJkiXqteHl5ybFjx1RqAhGZDwNZIsp3CFyRo2kIzDLXh8AG+YuGio6OVr/Xrl0rJUuWTPM35IjmN0Pbkz64N+Z5ZLXNkLdpirbpQ0CJIHDXrl2yceNG+eqrr+S9996TvXv3ZhnEmaNPctOOiRMnyoYNG2Tfvn1pKhnkpn0PHjyQp59+Wk3qmz9/vsqP1XKiich8GMgSkV3B7H6M2GmqV6+ugg9MuGrdurVB91GhQgUVDCIIwmQoCA8Pl9OnTxt8H1nJTXvy8n/6KlWqpILZzZs3y5AhQ0z2GAiUmzdvrk7jx4+XsmXLysqVK+Wtt97K0B/GPA62v749e/ao55BVdYvs2pHe8uXL5aOPPlIl09Dfed0OeByM5G7atMmg2xORaTCQJSK7glEwBECYmY6KAzjMO2rUKHnzzTfVqGSLFi0kMjJS/v77b/Hz85P+/ftnuA/83+DBg2X06NFq9ntQUJAa3dMOPecFRv6MbU9e/k+fh4eHvP3226qiAQJMBHy3bt2SEydOqOebm8fAtkZgjEP52E64jPusVq1alv1h6OMgkEQQ+uKLL8rBgwfVKGtm1SMMaYe+48ePq4oU2BY1atSQGzduqOuxTYxpX/q0g9DQUPn++++lZcuWalQXt8d2daS6wUT5je8uIrIrCEAQaGBULTY2Vi5cuCAff/yxqlOLckrnz5+XggULSv369eXdd9/N8n4mTZqkgpHu3burwGbkyJEqmDGF3LQnL/+nDyWsEFhhxPL69esqf/all17K9WMgsNu+fbta8CAqKkqNgiLY7Ny5c5b9geDWkMdBsIn/ady4sRqFHTFihFolLTft0Ld//36VA4vUApw0GH3FwhW52Q5IKzh06JD6+82bN1VAjJxdBOFEZD5c2YuIiKyONa0IRkTWiwsiEBEREZFNYiBLRERERDaJqQVEREREZJM4IktERERENomBLBERERHZJAayRERERGSTGMgSERERkU1iIEtERERENomBLBERERHZJAayRERERGSTGMgSERERkU1iIEtERERENomBLBERERHZJAayRERERCS26P+CDuKAFdN4mQAAAABJRU5ErkJggg==", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ - "# True material properties (what we want to recover)\n", - "k0_true = 45.0 # base conductivity [W/(m*K)]\n", - "k1_true = -0.02 # temperature coefficient [W/(m*K^2)]\n", + "# --- Independent analytic-gradient benchmark (linear regime, k1 = 0) ---\n", + "k0_bench = 45.0 # CFL r ~ 0.26; both probe values must keep r < 0.5\n", + "coef = dt / (rho * cp)\n", "\n", "\n", - "def make_inputs(k0, k1):\n", - " \"\"\"Build a full input dict (JAX arrays) for the Tesseract.\"\"\"\n", + "def _bench_inputs(k0, n_steps_, field):\n", " return {\n", - " \"T_init\": jnp.asarray(T_init),\n", + " \"T_init\": jnp.asarray(field),\n", " \"Q\": jnp.asarray(Q),\n", " \"nx\": nx,\n", " \"ny\": ny,\n", - " \"n_steps\": n_steps,\n", - " \"k0\": jnp.asarray(k0, dtype=jnp.float64),\n", - " \"k1\": jnp.asarray(k1, dtype=jnp.float64),\n", + " \"n_steps\": n_steps_,\n", + " \"k0\": jnp.float64(k0),\n", + " \"k1\": jnp.float64(0.0), # linear regime\n", " \"rho\": jnp.float64(rho),\n", " \"cp\": jnp.float64(cp),\n", " \"h_conv\": jnp.float64(h_conv),\n", @@ -189,414 +254,105 @@ " }\n", "\n", "\n", - "def solve(k0, k1):\n", - " \"\"\"Forward solve through the Fortran solver, returns T_final as a JAX array.\"\"\"\n", - " return apply_tesseract(enzyme_tess, make_inputs(k0, k1))[\"T_final\"]\n", - "\n", - "\n", - "# Run the ground-truth simulation\n", - "T_true = np.asarray(solve(k0_true, k1_true)).reshape(ny, nx)\n", - "\n", - "print(f\"Ground truth: k0={k0_true}, k1={k1_true}\")\n", - "print(f\"Temperature range: {T_true.min():.2f} K to {T_true.max():.2f} K\")" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "7e544cbd0338", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Number of sensors: 9\n", - "Noise std: 0.5 K\n", - "Observed temperatures: [341.04 340.36 341.26 314.51 313.06 313.39 301.68 301.46 301.61]\n" - ] - } - ], - "source": [ - "# Place sensors on a regular grid in the interior (away from BCs)\n", - "# This mimics a realistic thermocouple layout\n", - "sensor_ix = [7, 15, 22] # x positions\n", - "sensor_jy = [7, 15, 22] # y positions\n", - "sensor_indices = []\n", - "sensor_coords = []\n", - "\n", - "for jy in sensor_jy:\n", - " for ix in sensor_ix:\n", - " sensor_indices.append(jy * nx + ix)\n", - " sensor_coords.append((ix, jy))\n", - "\n", - "sensor_indices = np.array(sensor_indices)\n", - "n_sensors = len(sensor_indices)\n", - "\n", - "# Extract true temperatures at sensor locations and add noise\n", - "rng = np.random.default_rng(42)\n", - "noise_std = 0.5 # K — realistic thermocouple noise\n", - "T_true_flat = T_true.flatten()\n", - "T_obs = T_true_flat[sensor_indices] + rng.normal(0, noise_std, n_sensors)\n", - "\n", - "print(f\"Number of sensors: {n_sensors}\")\n", - "print(f\"Noise std: {noise_std} K\")\n", - "print(f\"Observed temperatures: {T_obs.round(2)}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "904587d15cc3", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Visualize the ground truth and sensor locations\n", - "fig, ax = plt.subplots(1, 1, figsize=(8, 4))\n", - "im = ax.imshow(\n", - " T_true, origin=\"lower\", cmap=\"hot\", extent=[0, Lx * 1e3, 0, Ly * 1e3], aspect=\"auto\"\n", + "def _step(field, k0):\n", + " \"\"\"One explicit solver step from `field` at conductivity k0.\"\"\"\n", + " out = apply_tesseract(enzyme_tess, _bench_inputs(k0, 1, field))[\"T_final\"]\n", + " return np.asarray(out, dtype=np.float64)\n", + "\n", + "\n", + "def _affine_map(k0):\n", + " \"\"\"Recover U(T;k0) = A T + c via unit probes (n+1 solver calls).\"\"\"\n", + " c = _step(np.zeros(n), k0)\n", + " A = np.zeros((n, n))\n", + " for j in range(n):\n", + " e = np.zeros(n)\n", + " e[j] = 1.0\n", + " A[:, j] = _step(e, k0) - c\n", + " return A, c\n", + "\n", + "\n", + "# Non-uniform initial field so the gradient is non-degenerate.\n", + "xb, yb = np.linspace(0, Lx, nx), np.linspace(0, Ly, ny)\n", + "XXb, YYb = np.meshgrid(xb, yb)\n", + "T_init_bench = (\n", + " T_inf + 40.0 * np.sin(np.pi * XXb / Lx) * np.sin(np.pi * YYb / Ly)\n", + ").ravel()\n", + "\n", + "ka, kb = 45.0, 40.0\n", + "print(f\"Recovering affine map at k0={ka} ({n} probes)...\")\n", + "Aa, ca = _affine_map(ka)\n", + "print(f\"Recovering affine map at k0={kb} ({n} probes)...\")\n", + "Ab, cb = _affine_map(kb)\n", + "\n", + "A1 = (Aa - Ab) / (ka - kb)\n", + "A0 = Aa - ka * A1\n", + "c1 = (ca - cb) / (ka - kb)\n", + "c0 = ca - ka * c1\n", + "A = A0 + k0_bench * A1\n", + "c = c0 + k0_bench * c1\n", + "\n", + "# Exact tangent recurrence over the full 500-step trajectory (pure NumPy).\n", + "T = T_init_bench.copy()\n", + "dT = np.zeros(n)\n", + "for _ in range(n_steps):\n", + " dT = A1 @ T + A @ dT + c1\n", + " T = A @ T + c\n", + "analytic = float(np.sum(dT))\n", + "\n", + "# Consistency check: does the affine model match the solver's real trajectory?\n", + "T_solver = np.asarray(\n", + " apply_tesseract(enzyme_tess, _bench_inputs(k0_bench, n_steps, T_init_bench))[\n", + " \"T_final\"\n", + " ],\n", + " dtype=np.float64,\n", ")\n", - "plt.colorbar(im, ax=ax, label=\"Temperature [K]\")\n", - "\n", - "# Plot sensor locations\n", - "for ix, jy in sensor_coords:\n", - " x_mm = ix / (nx - 1) * Lx * 1e3\n", - " y_mm = jy / (ny - 1) * Ly * 1e3\n", - " ax.plot(x_mm, y_mm, \"ws\", markersize=8, markeredgecolor=\"blue\", markeredgewidth=1.5)\n", - "\n", - "ax.set_xlabel(\"x [mm]\")\n", - "ax.set_ylabel(\"y [mm]\")\n", - "ax.set_title(\n", - " f\"Ground truth temperature field (k₀={k0_true}, k₁={k1_true})\\n□ = sensor locations\"\n", + "traj_rel = np.linalg.norm(T - T_solver) / np.linalg.norm(T_solver)\n", + "print(f\"affine-model vs solver trajectory rel err = {traj_rel:.2e}\")\n", + "\n", + "# Enzyme VJP of the same scalar (cotangent = ones).\n", + "vjp = enzyme_tess.vector_jacobian_product(\n", + " inputs=_bench_inputs(k0_bench, n_steps, T_init_bench),\n", + " vjp_inputs=[\"k0\"],\n", + " vjp_outputs=[\"T_final\"],\n", + " cotangent_vector={\"T_final\": np.ones(n)},\n", ")\n", - "plt.tight_layout()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "c6386c40c0f5", - "metadata": {}, - "source": [ - "### Define the inverse problem\n", - "\n", - "Minimize the misfit between predicted and observed sensor temperatures:\n", - "\n", - "$$\n", - "J(k_0, k_1) = \\frac{1}{2} \\sum_{i=1}^{N_\\text{sensors}} \\left( T_\\text{pred}(\\mathbf{x}_i; k_0, k_1) - T_\\text{obs}(\\mathbf{x}_i) \\right)^2\n", - "$$\n", - "\n", - "`loss_fn` is a plain JAX function that happens to call the Fortran solver through\n", - "`apply_tesseract`. We hand it to `jax.value_and_grad`, and JAX propagates the\n", - "cotangent through the HTTP boundary into Enzyme's reverse-mode pass — one reverse\n", - "sweep returns $\\partial J / \\partial k_0$ and $\\partial J / \\partial k_1$ at once.\n", - "Finite differences would need a separate forward solve per parameter." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "43111e1b97b5", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Initial loss = 409.1875\n", - "Gradient via Enzyme: dJ/dk0 = 27.526953, dJ/dk1 = 9510.217207\n" - ] - } - ], - "source": [ - "T_obs_jax = jnp.asarray(T_obs)\n", - "\n", - "\n", - "def loss_fn(params):\n", - " \"\"\"Sensor-misfit loss as a function of [k0, k1]. Pure JAX.\"\"\"\n", - " k0, k1 = params\n", - " T_pred = solve(k0, k1)\n", - " residuals = T_pred[sensor_indices] - T_obs_jax\n", - " return 0.5 * jnp.sum(residuals**2)\n", - "\n", - "\n", - "# jax.value_and_grad differentiates straight through the Fortran solver.\n", - "value_and_grad = jax.value_and_grad(loss_fn)\n", - "\n", - "# Sanity check: gradient at the initial guess.\n", - "loss0, grad0 = value_and_grad(jnp.array([60.0, 0.01]))\n", - "print(f\"Initial loss = {loss0:.4f}\")\n", - "print(f\"Gradient via Enzyme: dJ/dk0 = {grad0[0]:.6f}, dJ/dk1 = {grad0[1]:.6f}\")" - ] - }, - { - "cell_type": "markdown", - "id": "b1e034157040", - "metadata": {}, - "source": [ - "### Run the optimization\n", - "\n", - "We start from a deliberately wrong initial guess (33% off on k₀, wrong sign on k₁)\n", - "and let `scipy.optimize.minimize` drive L-BFGS-B, with `jax.value_and_grad`\n", - "supplying both the loss and its gradient. The bounds keep the parameters physically\n", - "plausible and the time stepping CFL-safe." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "81fa6219dfdb", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Initial guess: k0=60.00, k1=0.0100, loss=409.1875\n", - " k0=49.5370, k1=-0.024209, loss=10.623775\n", - " k0=46.9414, k1=-0.032678, loss=4.835226\n", - " k0=48.0019, k1=-0.029202, loss=0.989078\n", - " k0=47.9192, k1=-0.029457, loss=0.961049\n", - " k0=47.9118, k1=-0.029464, loss=0.960913\n", - " k0=47.9059, k1=-0.029456, loss=0.960832\n", - " k0=47.8638, k1=-0.029372, loss=0.960316\n", - " k0=47.7726, k1=-0.029154, loss=0.959282\n", - " k0=47.5080, k1=-0.028466, loss=0.956421\n", - " k0=46.8954, k1=-0.026791, loss=0.950077\n", - " k0=45.6409, k1=-0.023246, loss=0.937793\n", - " k0=43.9279, k1=-0.018262, loss=0.922245\n", - " k0=42.8393, k1=-0.014951, loss=0.912410\n", - " k0=42.8101, k1=-0.014745, loss=0.910273\n", - " k0=42.9610, k1=-0.015156, loss=0.910138\n", - " k0=42.9937, k1=-0.015250, loss=0.910135\n", - " k0=42.9956, k1=-0.015255, loss=0.910135\n", - " k0=42.9956, k1=-0.015255, loss=0.910135\n", - " k0=42.9956, k1=-0.015255, loss=0.910135\n", - "\n", - "Optimization finished in 19 iterations\n", - " True: k0=45.0000, k1=-0.020000\n", - " Recovered: k0=42.9956, k1=-0.015255\n", - " Error: k0: 4.45%, k1: 23.72%\n" - ] - } - ], - "source": [ - "from scipy.optimize import minimize\n", - "\n", - "# Initial guess: 33% off on k0, wrong sign on k1\n", - "x0 = np.array([60.0, 0.01])\n", - "\n", - "# Track optimization history\n", - "history = {\"k0\": [x0[0]], \"k1\": [x0[1]], \"loss\": []}\n", - "\n", - "\n", - "def scipy_objective(params):\n", - " loss, grad = value_and_grad(jnp.asarray(params))\n", - " return float(loss), np.asarray(grad, dtype=np.float64)\n", - "\n", - "\n", - "def callback(params):\n", - " loss, _ = scipy_objective(params)\n", - " history[\"k0\"].append(params[0])\n", - " history[\"k1\"].append(params[1])\n", - " history[\"loss\"].append(loss)\n", - " print(f\" k0={params[0]:.4f}, k1={params[1]:.6f}, loss={loss:.6f}\")\n", - "\n", - "\n", - "history[\"loss\"].append(scipy_objective(x0)[0])\n", - "print(f\"Initial guess: k0={x0[0]:.2f}, k1={x0[1]:.4f}, loss={history['loss'][0]:.4f}\")\n", - "\n", - "result = minimize(\n", - " fun=scipy_objective,\n", - " x0=x0,\n", - " method=\"L-BFGS-B\",\n", - " jac=True, # scipy_objective returns (loss, grad)\n", - " bounds=[(5.0, 80.0), (-0.08, 0.08)], # stay CFL-safe\n", - " callback=callback,\n", - " options={\"maxiter\": 50, \"ftol\": 1e-12, \"gtol\": 1e-8},\n", - ")\n", - "\n", - "k0_opt, k1_opt = result.x\n", - "T_opt = np.asarray(solve(k0_opt, k1_opt)).reshape(ny, nx)\n", - "\n", - "print(f\"\\nOptimization finished in {result.nit} iterations\")\n", - "print(f\" True: k0={k0_true:.4f}, k1={k1_true:.6f}\")\n", - "print(f\" Recovered: k0={k0_opt:.4f}, k1={k1_opt:.6f}\")\n", - "print(\n", - " f\" Error: k0: {abs(k0_opt - k0_true) / k0_true * 100:.2f}%, \"\n", - " f\"k1: {abs(k1_opt - k1_true) / abs(k1_true) * 100:.2f}%\"\n", - ")" - ] - }, - { - "cell_type": "markdown", - "id": "72a435fe434e", - "metadata": {}, - "source": [ - "### Visualize results\n", - "\n", - "#### Convergence" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "e08c0b018c43", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, axes = plt.subplots(1, 3, figsize=(14, 4))\n", - "\n", - "# Loss convergence\n", - "axes[0].semilogy(history[\"loss\"], \"k.-\", linewidth=1.5)\n", - "axes[0].set_xlabel(\"Iteration\")\n", - "axes[0].set_ylabel(\"Loss (sum of squared residuals)\")\n", - "axes[0].set_title(\"Convergence\")\n", - "axes[0].grid(True, alpha=0.3)\n", - "\n", - "# k0 convergence\n", - "axes[1].plot(history[\"k0\"], \"b.-\", linewidth=1.5, label=\"k₀ estimate\")\n", - "axes[1].axhline(\n", - " k0_true, color=\"b\", linestyle=\"--\", alpha=0.5, label=f\"k₀ true = {k0_true}\"\n", - ")\n", - "axes[1].set_xlabel(\"Iteration\")\n", - "axes[1].set_ylabel(\"k₀ [W/(m·K)]\")\n", - "axes[1].set_title(\"Base conductivity\")\n", - "axes[1].legend()\n", - "axes[1].grid(True, alpha=0.3)\n", - "\n", - "# k1 convergence\n", - "axes[2].plot(history[\"k1\"], \"r.-\", linewidth=1.5, label=\"k₁ estimate\")\n", - "axes[2].axhline(\n", - " k1_true, color=\"r\", linestyle=\"--\", alpha=0.5, label=f\"k₁ true = {k1_true}\"\n", - ")\n", - "axes[2].set_xlabel(\"Iteration\")\n", - "axes[2].set_ylabel(\"k₁ [W/(m·K²)]\")\n", - "axes[2].set_title(\"Temperature coefficient\")\n", - "axes[2].legend()\n", - "axes[2].grid(True, alpha=0.3)\n", - "\n", - "plt.tight_layout()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "5152dd0af3b7", - "metadata": {}, - "source": [ - "#### Temperature fields: initial guess vs. optimized vs. ground truth" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "977f62064249", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/fk/g5ssrkz179z1mjmvqn1j3q1m0000gn/T/ipykernel_73719/639399457.py:61: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n", - " plt.tight_layout()\n" - ] - }, - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Compute the initial-guess temperature field for comparison\n", - "T_init_field = np.asarray(solve(x0[0], x0[1])).reshape(ny, nx)\n", - "\n", - "# Common color range\n", - "vmin = min(T_true.min(), T_opt.min(), T_init_field.min())\n", - "vmax = max(T_true.max(), T_opt.max(), T_init_field.max())\n", - "\n", - "fig, axes = plt.subplots(1, 4, figsize=(18, 4))\n", - "extent = [0, Lx * 1e3, 0, Ly * 1e3]\n", - "\n", - "axes[0].imshow(\n", - " T_init_field,\n", - " origin=\"lower\",\n", - " cmap=\"hot\",\n", - " extent=extent,\n", - " aspect=\"auto\",\n", - " vmin=vmin,\n", - " vmax=vmax,\n", + "enzyme_grad = float(vjp[\"k0\"])\n", + "enzyme_err = abs(enzyme_grad - analytic) / (abs(analytic) + 1e-30)\n", + "print(f\"analytic gradient = {analytic:.10e}\")\n", + "print(f\"enzyme gradient = {enzyme_grad:.10e}\")\n", + "print(f\"Enzyme rel err vs analytic = {enzyme_err:.2e}\")\n", + "\n", + "# Central finite differences vs the same analytic reference, swept over step size.\n", + "epsilons = np.logspace(-1, -12, 24)\n", + "fd_err = []\n", + "for eps in epsilons:\n", + " Tp = np.asarray(\n", + " apply_tesseract(\n", + " enzyme_tess, _bench_inputs(k0_bench + eps, n_steps, T_init_bench)\n", + " )[\"T_final\"]\n", + " )\n", + " Tm = np.asarray(\n", + " apply_tesseract(\n", + " enzyme_tess, _bench_inputs(k0_bench - eps, n_steps, T_init_bench)\n", + " )[\"T_final\"]\n", + " )\n", + " fd = np.sum(Tp - Tm) / (2 * eps)\n", + " fd_err.append(abs(fd - analytic) / (abs(analytic) + 1e-30))\n", + "\n", + "fig, ax = plt.subplots(1, 1, figsize=(7, 4.5))\n", + "ax.loglog(\n", + " epsilons, fd_err, \"o-\", ms=4, color=\"#1971c2\", label=\"Central finite differences\"\n", ")\n", - "axes[0].set_title(f\"Initial guess\\nk₀={x0[0]}, k₁={x0[1]}\")\n", - "\n", - "axes[1].imshow(\n", - " T_opt,\n", - " origin=\"lower\",\n", - " cmap=\"hot\",\n", - " extent=extent,\n", - " aspect=\"auto\",\n", - " vmin=vmin,\n", - " vmax=vmax,\n", + "ax.axhline(\n", + " enzyme_err, color=\"#e8590c\", lw=2, label=f\"Enzyme AD ($\\\\approx${enzyme_err:.0e})\"\n", ")\n", - "axes[1].set_title(f\"Recovered\\nk₀={k0_opt:.2f}, k₁={k1_opt:.4f}\")\n", - "\n", - "im2 = axes[2].imshow(\n", - " T_true,\n", - " origin=\"lower\",\n", - " cmap=\"hot\",\n", - " extent=extent,\n", - " aspect=\"auto\",\n", - " vmin=vmin,\n", - " vmax=vmax,\n", - ")\n", - "axes[2].set_title(f\"Ground truth\\nk₀={k0_true}, k₁={k1_true}\")\n", - "\n", - "# Error field\n", - "error = np.abs(T_opt - T_true)\n", - "im3 = axes[3].imshow(error, origin=\"lower\", cmap=\"Blues\", extent=extent, aspect=\"auto\")\n", - "axes[3].set_title(f\"|Recovered - Truth|\\nmax error: {error.max():.3f} K\")\n", - "\n", - "for ax in axes:\n", - " ax.set_xlabel(\"x [mm]\")\n", - " ax.set_ylabel(\"y [mm]\")\n", - " for ix, jy in sensor_coords:\n", - " x_mm = ix / (nx - 1) * Lx * 1e3\n", - " y_mm = jy / (ny - 1) * Ly * 1e3\n", - " ax.plot(\n", - " x_mm, y_mm, \"ws\", markersize=5, markeredgecolor=\"blue\", markeredgewidth=1\n", - " )\n", - "\n", - "plt.colorbar(im2, ax=axes[:3].tolist(), label=\"Temperature [K]\", shrink=0.9)\n", - "plt.colorbar(im3, ax=axes[3], label=\"Error [K]\", shrink=0.9)\n", + "ax.set_xlabel(\"Finite difference step size $\\\\epsilon$\")\n", + "ax.set_ylabel(\"Relative error vs. independent analytic gradient\")\n", + "ax.set_title(\"Enzyme matches the analytic gradient; FD only in a narrow sweet spot\")\n", + "ax.legend(framealpha=0.9)\n", + "ax.grid(True, alpha=0.2)\n", "plt.tight_layout()\n", + "fig.savefig(FIGURE_DIR / \"analytic_benchmark.png\", dpi=180, bbox_inches=\"tight\")\n", "plt.show()" ] }, @@ -605,7 +361,7 @@ "id": "8be059a8e35b", "metadata": {}, "source": [ - "## Part 2: Thermal forensics — recovering a hidden heat signature (900 parameters)\n", + "## Thermal forensics: recovering a hidden heat signature (900 parameters)\n", "\n", "A steel plate was subjected to an unmonitored heating event — say, a laser pulse\n", "or a localized defect generating heat. Five seconds later, you measure temperatures\n", @@ -615,9 +371,8 @@ "This is an ill-posed inverse problem: 900 unknowns (temperature at every grid cell)\n", "from 100 noisy observations, through a nonlinear PDE. We add a small Tikhonov term\n", "that penalizes departure from the ambient prior, which regularizes the problem; the\n", - "optimizer is otherwise the same `jax.value_and_grad` + L-BFGS-B as before — only the\n", - "parameter vector grows from 2 to 900. This is exactly where reverse-mode AD stops\n", - "being a nice-to-have:\n", + "optimizer is a standard `jax.value_and_grad` + L-BFGS-B loop over all 900\n", + "unknowns. This is exactly where reverse-mode AD stops being a nice-to-have:\n", "\n", "| Method | Forward solves per iteration |\n", "|--------|----------------------------:|\n", @@ -633,9 +388,16 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 5, "id": "e337f08f8d05", - "metadata": {}, + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-16T21:45:06.766933Z", + "iopub.status.busy": "2026-06-16T21:45:06.766821Z", + "iopub.status.idle": "2026-06-16T21:45:06.805743Z", + "shell.execute_reply": "2026-06-16T21:45:06.803846Z" + } + }, "outputs": [ { "name": "stdout", @@ -649,7 +411,7 @@ } ], "source": [ - "# --- Part 2 setup ---\n", + "# --- Forensics setup ---\n", "# Shorter simulation: 5 seconds (we want residual structure in the initial field)\n", "n_steps_p2 = 100\n", "dt_p2 = 0.05\n", @@ -718,42 +480,63 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 6, "id": "c6473e7ffb35", - "metadata": {}, + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-16T21:45:06.809478Z", + "iopub.status.busy": "2026-06-16T21:45:06.809317Z", + "iopub.status.idle": "2026-06-16T21:45:09.624319Z", + "shell.execute_reply": "2026-06-16T21:45:09.623958Z" + } + }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Initial loss: 4072.76\n", + "Initial loss: 4085.86\n", "Running L-BFGS-B with 900 parameters...\n", - " iter 10: loss=54.0890, elapsed=0.3s\n", - " iter 20: loss=53.9501, elapsed=0.7s\n", - " iter 30: loss=53.9492, elapsed=1.1s\n", - " iter 40: loss=53.9492, elapsed=1.4s\n", - " iter 50: loss=53.9492, elapsed=1.8s\n", - " iter 60: loss=53.9492, elapsed=2.1s\n", + " iter 10: loss=8.0931, elapsed=0.4s\n", + " iter 20: loss=7.5007, elapsed=0.8s\n", + " iter 30: loss=7.4350, elapsed=1.2s\n", + " iter 40: loss=7.4246, elapsed=1.7s\n", + " iter 50: loss=7.4222, elapsed=2.0s\n", + " iter 60: loss=7.4216, elapsed=2.4s\n", + " iter 70: loss=7.4215, elapsed=2.8s\n", + " iter 80: loss=7.4215, elapsed=3.2s\n", + " iter 90: loss=7.4215, elapsed=3.5s\n", + " iter 100: loss=7.4215, elapsed=3.8s\n", + " iter 110: loss=7.4215, elapsed=4.2s\n", + " iter 120: loss=7.4215, elapsed=4.5s\n", + " iter 130: loss=7.4215, elapsed=4.9s\n", + " iter 140: loss=7.4215, elapsed=5.3s\n", + " iter 150: loss=7.4215, elapsed=5.6s\n", + " iter 160: loss=7.4215, elapsed=6.0s\n", + " iter 170: loss=7.4215, elapsed=6.3s\n", + " iter 180: loss=7.4215, elapsed=6.7s\n", "\n", - "Optimization finished: 65 iterations, 2.6s\n", - "Loss: 4072.76 → 53.9492\n", - "T_init correlation: 0.9799\n", + "Optimization finished: 187 iterations, 8.4s\n", + "Loss: 4085.86 → 7.4215\n", + "T_init correlation: 0.9804\n", "\n", "Cost comparison per iteration:\n", - " Finite differences: 901 forward solves = ~28.2s\n", - " Reverse-mode AD: 2 solves (fwd+rev) = ~0.06s\n" + " Finite differences: 901 forward solves = ~30.5s\n", + " Reverse-mode AD: 2 solves (fwd+rev) = ~0.07s\n" ] } ], "source": [ "import time\n", "\n", + "from scipy.optimize import minimize\n", + "\n", "T_obs_p2_jax = jnp.asarray(T_obs_p2)\n", "sensor_grid_jax = jnp.asarray(sensor_grid)\n", "\n", "# Tikhonov regularization weight: penalizes departure from the ambient prior,\n", "# which stabilizes this ill-posed problem (900 unknowns, 100 observations).\n", - "alpha_reg = 0.001\n", + "alpha_reg = 1e-4\n", "\n", "\n", "def loss_fn_p2(T_init_vec):\n", @@ -829,21 +612,20 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 7, "id": "44fd35ce4a54", - "metadata": {}, + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-16T21:45:09.625722Z", + "iopub.status.busy": "2026-06-16T21:45:09.625621Z", + "iopub.status.idle": "2026-06-16T21:45:10.529208Z", + "shell.execute_reply": "2026-06-16T21:45:10.528815Z" + } + }, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/fk/g5ssrkz179z1mjmvqn1j3q1m0000gn/T/ipykernel_73719/182219165.py:92: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n", - " plt.tight_layout()\n" - ] - }, { "data": { - "image/png": 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", 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" ] @@ -853,7 +635,7 @@ } ], "source": [ - "fig, axes = plt.subplots(2, 3, figsize=(16, 9))\n", + "fig, axes = plt.subplots(2, 3, figsize=(16, 9), layout=\"constrained\")\n", "\n", "extent = [0, Lx * 1e3, 0, Ly * 1e3]\n", "\n", @@ -939,12 +721,11 @@ "axes[1, 2].grid(True, alpha=0.3)\n", "\n", "plt.suptitle(\n", - " \"Part 2: Recovering a 900-element initial temperature field from 100 sensors\",\n", + " \"Recovering a 900-element initial temperature field from 100 sensors\",\n", " fontsize=13,\n", " fontweight=\"bold\",\n", - " y=1.01,\n", ")\n", - "plt.tight_layout()\n", + "fig.savefig(FIGURE_DIR / \"thermal_forensics.png\", dpi=180, bbox_inches=\"tight\")\n", "plt.show()" ] }, @@ -967,26 +748,15 @@ "| Solver | Fortran 90 | `thermal_2d_solve` |\n", "\n", "The Fortran solver was never modified. Enzyme differentiated it from the compiled\n", - "LLVM IR, and Tesseract made it callable — and differentiable — from JAX. The\n", - "optimization code is identical for 2 parameters and for 900; only the size of the\n", - "parameter vector changed." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "babc4d54e5a1", - "metadata": {}, - "outputs": [], - "source": [ - "# Tear down the Tesseract to free resources.\n", - "enzyme_tess.teardown()" + "LLVM IR, and Tesseract made it callable — and differentiable — from JAX. The same\n", + "`jax.value_and_grad` call returns all 900 gradient components from a single reverse\n", + "sweep, with no adjoint code written by hand." ] } ], "metadata": { "kernelspec": { - "display_name": "tesseract-core-2 (3.10.16)", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -1000,7 +770,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.10.16" + "version": "3.12.7" } }, "nbformat": 4, diff --git a/demo/enzyme_thermal_2d/figures/fd_convergence.png b/demo/enzyme_thermal_2d/figures/fd_convergence.png deleted file mode 100644 index b51ab3b4e68f0ef5b116b7ceec4c4a7ae83dbe2d..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 106228 zcmdpegF!aI6N_z>A|W84G6Y7q zYz)4e=ka;J<9Pps_dX8wknOtf`?}6P&)<)ihWZ-RR~WCHJ9my+OH&nk?i^Y3xpNmm zm&t*jykKlX0{_VRt6BIP`?~lCI>4RJ={fj6^z!xha({65u`}Gy-PcE4NK`}!0>10! z@Bh$GR#@2kf4(8)3wIUfR{shE?n3!c6XtjB98<&DpYyhiDa_~2pF5|es%#RJw>C== 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zNC_TSK5TDPkYeK=d2rNWr=OC3MiAU~MYR3tgN4Ix2^R7Gi4X-E0tqS3Lp^r6b7$1p zg8V{Ecl%GkQ>sy2|6w=3p8oUH_)8g+E!6&ImV}aUsEdo*R zllIFZ!dCulz(;Q=C2j!7c=8KJH)?pW+1>0l0n=+C2(6+8>ZFxF;`{dd7&*{%9k8@yq*rnAN0I#a) zPDZH6XjNTU$mEcu1e?keK^SG){(Un=cnM5>O^Q1#+2Q6~I}Xmv%?vTqBQcy{5`S31 z;P8aBTT#c}7I zHkZIN&H&~^ivG~D#O3Z@RtPsRfhi&!@oPjzsm6cN*R8A%;9Fl5Y9EH SWd2p5dc)ZATG`cm&;AcZZ}7zc diff --git a/demo/enzyme_thermal_2d/generate_blog_figures.py b/demo/enzyme_thermal_2d/generate_blog_figures.py deleted file mode 100644 index 37bbc21d..00000000 --- a/demo/enzyme_thermal_2d/generate_blog_figures.py +++ /dev/null @@ -1,565 +0,0 @@ -#!/usr/bin/env python3 -# Copyright 2025 Pasteur Labs. All Rights Reserved. -# SPDX-License-Identifier: Apache-2.0 -"""Generate figures for the Enzyme AD blog post. - -Usage: - tesseract build demo/enzyme_thermal_2d/ - python demo/enzyme_thermal_2d/generate_blog_figures.py - -Outputs PNG files to demo/enzyme_thermal_2d/figures/. -""" - -import time -from pathlib import Path - -import matplotlib.pyplot as plt -import numpy as np -from scipy.optimize import minimize - -from tesseract_core import Tesseract - -FIGURE_DIR = Path(__file__).parent / "figures" -FIGURE_DIR.mkdir(exist_ok=True) - -# ── Shared parameters ──────────────────────────────────────────────────────── - -nx, ny = 30, 30 -n = nx * ny -n_steps = 500 -dt = 0.05 -Lx, Ly = 0.1, 0.05 -rho = 7850.0 -cp = 460.0 -h_conv = 25.0 -T_inf = 293.15 -T_hot = 373.15 -Q = np.zeros(n) -T_init_uniform = np.full(n, T_inf) - -k0_true = 45.0 -k1_true = -0.02 - -rng = np.random.default_rng(42) - -plt.rcParams.update( - { - "figure.dpi": 180, - "savefig.dpi": 180, - "font.size": 11, - "axes.titlesize": 12, - "savefig.bbox": "tight", - "savefig.pad_inches": 0.15, - } -) - - -def make_inputs(k0, k1, T_init=None, n_steps_=None, dt_=None): - return { - "T_init": (T_init if T_init is not None else T_init_uniform), - "Q": Q, - "nx": nx, - "ny": ny, - "n_steps": n_steps_ or n_steps, - "k0": float(k0), - "k1": float(k1), - "rho": rho, - "cp": cp, - "h_conv": h_conv, - "T_inf": T_inf, - "T_hot": T_hot, - "Lx": Lx, - "Ly": Ly, - "dt": dt_ or dt, - } - - -# ── Figure 1: FD vs Enzyme convergence ─────────────────────────────────────── - - -def generate_fd_convergence(t): - print("Generating FD vs Enzyme convergence plot...") - - inputs = make_inputs(k0_true, k1_true) - - cotangent = np.ones(n, dtype=np.float64) - vjp = t.vector_jacobian_product( - inputs=inputs, - vjp_inputs=["k0", "k1", "h_conv"], - vjp_outputs=["T_final"], - cotangent_vector={"T_final": cotangent}, - ) - enzyme_dk0 = vjp["k0"] - enzyme_dk1 = vjp["k1"] - enzyme_dh = vjp["h_conv"] - - print(f" Enzyme (VJP) dk0 = {enzyme_dk0:.10e}") - print(f" Enzyme (VJP) dk1 = {enzyme_dk1:.10e}") - print(f" Enzyme (VJP) dh = {enzyme_dh:.10e}") - - epsilons = np.logspace(-1, -12, 24) - fd_errors_k0 = [] - fd_errors_k1 = [] - fd_errors_h = [] - - for i, eps in enumerate(epsilons): - if (i + 1) % 6 == 0: - print(f" FD step {i + 1}/{len(epsilons)}...") - - T_plus = np.array( - t.apply(inputs=make_inputs(k0_true + eps, k1_true))["T_final"] - ) - T_minus = np.array( - t.apply(inputs=make_inputs(k0_true - eps, k1_true))["T_final"] - ) - fd_dk0 = np.sum(T_plus - T_minus) / (2 * eps) - fd_errors_k0.append(abs(fd_dk0 - enzyme_dk0) / (abs(enzyme_dk0) + 1e-30)) - - T_plus = np.array( - t.apply(inputs=make_inputs(k0_true, k1_true + eps))["T_final"] - ) - T_minus = np.array( - t.apply(inputs=make_inputs(k0_true, k1_true - eps))["T_final"] - ) - fd_dk1 = np.sum(T_plus - T_minus) / (2 * eps) - fd_errors_k1.append(abs(fd_dk1 - enzyme_dk1) / (abs(enzyme_dk1) + 1e-30)) - - inp_p = make_inputs(k0_true, k1_true) - inp_m = make_inputs(k0_true, k1_true) - inp_p["h_conv"] = h_conv + eps - inp_m["h_conv"] = h_conv - eps - T_plus = np.array(t.apply(inputs=inp_p)["T_final"]) - T_minus = np.array(t.apply(inputs=inp_m)["T_final"]) - fd_dh = np.sum(T_plus - T_minus) / (2 * eps) - fd_errors_h.append(abs(fd_dh - enzyme_dh) / (abs(enzyme_dh) + 1e-30)) - - fig, ax = plt.subplots(1, 1, figsize=(7, 4.5)) - ax.loglog( - epsilons, - fd_errors_k0, - "o-", - ms=4, - label="$\\partial / \\partial k_0$", - color="#1971c2", - ) - ax.loglog( - epsilons, - fd_errors_k1, - "s-", - ms=4, - label="$\\partial / \\partial k_1$", - color="#e8590c", - ) - ax.loglog( - epsilons, - fd_errors_h, - "^-", - ms=4, - label="$\\partial / \\partial h_{\\mathrm{conv}}$", - color="#2f9e44", - ) - ax.axhline(1e-15, color="gray", ls=":", alpha=0.5, label="Machine precision") - - ax.set_xlabel("Finite difference step size $\\epsilon$") - ax.set_ylabel("Relative error vs. Enzyme gradient") - ax.set_title( - "Enzyme provides exact gradients; finite differences have a sweet spot" - ) - ax.legend(framealpha=0.9) - ax.grid(True, alpha=0.2) - ax.set_ylim(1e-17, 1e1) - - fig.savefig(FIGURE_DIR / "fd_convergence.png") - plt.close(fig) - print(f" Saved {FIGURE_DIR / 'fd_convergence.png'}") - - -# ── Figure 2: Part 1 convergence (3-panel + 4-panel) ───────────────────────── - - -def generate_part1_convergence(t): - print("Generating Part 1 convergence plots...") - - result_true = t.apply(inputs=make_inputs(k0_true, k1_true)) - T_true = np.array(result_true["T_final"]).reshape(ny, nx) - - sensor_ix = [7, 15, 22] - sensor_jy = [7, 15, 22] - sensor_indices = np.array([jy * nx + ix for jy in sensor_jy for ix in sensor_ix]) - sensor_coords = [(ix, jy) for jy in sensor_jy for ix in sensor_ix] - - noise_std = 0.5 - T_obs = T_true.flatten()[sensor_indices] + rng.normal( - 0, noise_std, len(sensor_indices) - ) - - k0_init, k1_init = 60.0, 0.01 - history = {"k0": [k0_init], "k1": [k1_init], "loss": []} - - def obj_grad(params): - k0, k1 = float(params[0]), float(params[1]) - inputs = make_inputs(k0, k1) - result = t.apply(inputs=inputs) - T_pred = np.array(result["T_final"]) - residuals = T_pred[sensor_indices] - T_obs - loss = 0.5 * np.sum(residuals**2) - - cotangent = np.zeros(n, dtype=np.float64) - cotangent[sensor_indices] = residuals - vjp = t.vector_jacobian_product( - inputs=inputs, - vjp_inputs=["k0", "k1"], - vjp_outputs=["T_final"], - cotangent_vector={"T_final": cotangent}, - ) - return loss, np.array([vjp["k0"], vjp["k1"]]) - - loss0, _ = obj_grad([k0_init, k1_init]) - history["loss"].append(loss0) - print(f" Initial loss: {loss0:.4f}") - - def callback(params): - k0, k1 = float(params[0]), float(params[1]) - loss, _ = obj_grad(params) - history["k0"].append(k0) - history["k1"].append(k1) - history["loss"].append(loss) - print(f" k0={k0:.4f}, k1={k1:.6f}, loss={loss:.6f}") - - result_opt = minimize( - fun=obj_grad, - x0=[k0_init, k1_init], - method="L-BFGS-B", - jac=True, - bounds=[(5.0, 80.0), (-0.08, 0.08)], - callback=callback, - options={"maxiter": 50, "ftol": 1e-12, "gtol": 1e-8}, - ) - k0_opt, k1_opt = float(result_opt.x[0]), float(result_opt.x[1]) - - # ── 3-panel convergence ── - fig, axes = plt.subplots(1, 3, figsize=(14, 4)) - - axes[0].semilogy(history["loss"], "k.-", linewidth=1.5) - axes[0].set_xlabel("Iteration") - axes[0].set_ylabel("Loss (sum of squared residuals)") - axes[0].set_title("Convergence") - axes[0].grid(True, alpha=0.3) - - axes[1].plot(history["k0"], "b.-", linewidth=1.5, label="$k_0$ estimate") - axes[1].axhline( - k0_true, color="b", ls="--", alpha=0.5, label=f"$k_0$ true = {k0_true}" - ) - axes[1].set_xlabel("Iteration") - axes[1].set_ylabel("$k_0$ [W/(m K)]") - axes[1].set_title("Base conductivity") - axes[1].legend() - axes[1].grid(True, alpha=0.3) - - axes[2].plot(history["k1"], "r.-", linewidth=1.5, label="$k_1$ estimate") - axes[2].axhline( - k1_true, color="r", ls="--", alpha=0.5, label=f"$k_1$ true = {k1_true}" - ) - axes[2].set_xlabel("Iteration") - axes[2].set_ylabel("$k_1$ [W/(m K$^2$)]") - axes[2].set_title("Temperature coefficient") - axes[2].legend() - axes[2].grid(True, alpha=0.3) - - fig.savefig(FIGURE_DIR / "part1_convergence.png") - plt.close(fig) - print(f" Saved {FIGURE_DIR / 'part1_convergence.png'}") - - # ── 4-panel temperature fields ── - T_opt_field = np.array( - t.apply(inputs=make_inputs(k0_opt, k1_opt))["T_final"] - ).reshape(ny, nx) - T_init_field = np.array( - t.apply(inputs=make_inputs(k0_init, k1_init))["T_final"] - ).reshape(ny, nx) - - vmin = min(T_true.min(), T_opt_field.min(), T_init_field.min()) - vmax = max(T_true.max(), T_opt_field.max(), T_init_field.max()) - extent = [0, Lx * 1e3, 0, Ly * 1e3] - - fig, axes = plt.subplots(1, 4, figsize=(18, 4)) - titles = [ - f"Initial guess\n$k_0$={k0_init}, $k_1$={k1_init}", - f"Recovered\n$k_0$={k0_opt:.2f}, $k_1$={k1_opt:.4f}", - f"Ground truth\n$k_0$={k0_true}, $k_1$={k1_true}", - None, - ] - fields = [T_init_field, T_opt_field, T_true, np.abs(T_opt_field - T_true)] - cmaps = ["hot", "hot", "hot", "Blues"] - - for i, (ax, field, cmap) in enumerate(zip(axes, fields, cmaps, strict=True)): - if i < 3: - im = ax.imshow( - field, - origin="lower", - cmap=cmap, - extent=extent, - aspect="auto", - vmin=vmin, - vmax=vmax, - ) - else: - im = ax.imshow( - field, origin="lower", cmap=cmap, extent=extent, aspect="auto" - ) - ax.set_title(f"|Recovered - Truth|\nmax error: {field.max():.3f} K") - if titles[i]: - ax.set_title(titles[i]) - ax.set_xlabel("x [mm]") - ax.set_ylabel("y [mm]") - for ix, jy in sensor_coords: - x_mm = ix / (nx - 1) * Lx * 1e3 - y_mm = jy / (ny - 1) * Ly * 1e3 - ax.plot(x_mm, y_mm, "ws", ms=5, markeredgecolor="blue", markeredgewidth=1) - - plt.colorbar(im, ax=axes[:3].tolist(), label="Temperature [K]", shrink=0.9) - plt.colorbar(axes[3].images[0], ax=axes[3], label="Error [K]", shrink=0.9) - fig.savefig(FIGURE_DIR / "part1_temperature_fields.png") - plt.close(fig) - print(f" Saved {FIGURE_DIR / 'part1_temperature_fields.png'}") - print( - f" Recovered: k0={k0_opt:.4f}, k1={k1_opt:.6f} in {result_opt.nit} iterations" - ) - - -# ── Figure 3: Part 2 forensics (6-panel) ───────────────────────────────────── - - -def generate_part2_forensics(t): - print("Generating Part 2 forensics plots...") - - n_steps_p2 = 100 - dt_p2 = 0.05 - k0_p2 = 45.0 - k1_p2 = -0.01 - - x_coord = np.linspace(0, Lx, nx) - y_coord = np.linspace(0, Ly, ny) - X, Y = np.meshgrid(x_coord, y_coord) - X_flat, Y_flat = X.flatten(), Y.flatten() - - T_init_true = ( - T_inf - + 40.0 * np.exp(-((X_flat - 0.04) ** 2 + (Y_flat - 0.025) ** 2) / 0.015**2) - + 25.0 * np.exp(-((X_flat - 0.08) ** 2 + (Y_flat - 0.035) ** 2) / 0.01**2) - ) - - def make_inputs_p2(T_init_field): - return { - "T_init": T_init_field.astype(np.float64), - "Q": Q, - "nx": nx, - "ny": ny, - "n_steps": n_steps_p2, - "k0": k0_p2, - "k1": k1_p2, - "rho": rho, - "cp": cp, - "h_conv": h_conv, - "T_inf": T_inf, - "T_hot": T_hot, - "Lx": Lx, - "Ly": Ly, - "dt": dt_p2, - } - - result_true_p2 = t.apply(inputs=make_inputs_p2(T_init_true)) - T_final_true_p2 = np.array(result_true_p2["T_final"]) - - sensor_ix_p2 = np.linspace(3, nx - 4, 10, dtype=int) - sensor_jy_p2 = np.linspace(3, ny - 4, 10, dtype=int) - sensor_grid = np.array([jy * nx + ix for jy in sensor_jy_p2 for ix in sensor_ix_p2]) - - noise_std_p2 = 0.3 - T_obs_p2 = T_final_true_p2[sensor_grid] + rng.normal( - 0, noise_std_p2, len(sensor_grid) - ) - - T_init_guess = np.full(n, T_inf) - loss_history = [] - - # Tikhonov regularization: penalize deviation from prior (uniform T_inf) - # This stabilizes the ill-posed inverse problem (900 unknowns, 100 observations) - alpha_reg = 0.001 - - def obj_grad_p2(T_init_vec): - inputs = make_inputs_p2(T_init_vec) - result = t.apply(inputs=inputs) - T_pred = np.array(result["T_final"]) - residuals = T_pred[sensor_grid] - T_obs_p2 - data_loss = 0.5 * np.sum(residuals**2) - reg_loss = 0.5 * alpha_reg * np.sum((T_init_vec - T_inf) ** 2) - loss = data_loss + reg_loss - - cotangent = np.zeros(n, dtype=np.float64) - cotangent[sensor_grid] = residuals - vjp = t.vector_jacobian_product( - inputs=inputs, - vjp_inputs=["T_init"], - vjp_outputs=["T_final"], - cotangent_vector={"T_final": cotangent}, - ) - grad = np.array(vjp["T_init"]) + alpha_reg * (T_init_vec - T_inf) - return loss, grad - - loss0, _ = obj_grad_p2(T_init_guess) - loss_history.append(loss0) - print(f" Initial loss: {loss0:.2f}") - - iter_count = [0] - t_start = time.time() - - def callback_p2(x): - iter_count[0] += 1 - if iter_count[0] % 10 == 0: - loss, _ = obj_grad_p2(x) - loss_history.append(loss) - elapsed = time.time() - t_start - print( - f" iter {iter_count[0]:3d}: loss={loss:.4f}, elapsed={elapsed:.1f}s" - ) - - result_p2 = minimize( - fun=obj_grad_p2, - x0=T_init_guess, - method="L-BFGS-B", - jac=True, - bounds=[(250.0, 450.0)] * n, - callback=callback_p2, - options={"maxiter": 200, "ftol": 1e-15, "gtol": 1e-10}, - ) - elapsed_total = time.time() - t_start - loss_final, _ = obj_grad_p2(result_p2.x) - loss_history.append(loss_final) - T_init_recovered = result_p2.x - - corr = np.corrcoef(T_init_true, T_init_recovered)[0, 1] - print(f" Optimization: {result_p2.nit} iterations, {elapsed_total:.1f}s") - print(f" Loss: {loss0:.2f} -> {loss_final:.4f}") - print(f" Correlation: {corr:.4f}") - - # Cost comparison - n_fev = result_p2.nfev - print("\n Cost comparison:") - print( - f" FD: {n + 1} forward solves/iter = ~{(n + 1) * elapsed_total / n_fev:.1f}s/iter" - ) - print(f" VJP: 2 solves/iter (fwd+rev) = ~{2 * elapsed_total / n_fev:.2f}s/iter") - print(f" Speedup: ~{(n + 1) / 2:.0f}x") - - # ── 6-panel figure ── - extent = [0, Lx * 1e3, 0, Ly * 1e3] - vmin_init = min(T_init_true.min(), T_init_recovered.min(), T_inf) - vmax_init = max(T_init_true.max(), T_init_recovered.max()) - - fig, axes = plt.subplots(2, 3, figsize=(16, 9)) - - axes[0, 0].imshow( - T_init_guess.reshape(ny, nx), - origin="lower", - cmap="hot", - extent=extent, - aspect="auto", - vmin=vmin_init, - vmax=vmax_init, - ) - axes[0, 0].set_title("Starting guess\n(uniform ambient)") - - axes[0, 1].imshow( - T_init_recovered.reshape(ny, nx), - origin="lower", - cmap="hot", - extent=extent, - aspect="auto", - vmin=vmin_init, - vmax=vmax_init, - ) - axes[0, 1].set_title(f"Recovered $T_0$\n(corr={corr:.3f})") - - im_true = axes[0, 2].imshow( - T_init_true.reshape(ny, nx), - origin="lower", - cmap="hot", - extent=extent, - aspect="auto", - vmin=vmin_init, - vmax=vmax_init, - ) - axes[0, 2].set_title("True $T_0$\n(two Gaussian hot spots)") - - plt.colorbar(im_true, ax=axes[0, :].tolist(), label="Temperature [K]", shrink=0.85) - - for ax in axes[0, :]: - for jy_idx in sensor_jy_p2: - for ix_idx in sensor_ix_p2: - x_mm = ix_idx / (nx - 1) * Lx * 1e3 - y_mm = jy_idx / (ny - 1) * Ly * 1e3 - ax.plot(x_mm, y_mm, ".", color="cyan", ms=2, alpha=0.5) - ax.set_xlabel("x [mm]") - ax.set_ylabel("y [mm]") - - error_p2 = np.abs(T_init_recovered - T_init_true).reshape(ny, nx) - im_err = axes[1, 0].imshow( - error_p2, origin="lower", cmap="Blues", extent=extent, aspect="auto" - ) - axes[1, 0].set_title( - f"|Recovered - True|\nmax={error_p2.max():.1f} K, mean={error_p2.mean():.1f} K" - ) - axes[1, 0].set_xlabel("x [mm]") - axes[1, 0].set_ylabel("y [mm]") - plt.colorbar(im_err, ax=axes[1, 0], label="Error [K]", shrink=0.85) - - axes[1, 1].scatter(T_init_true, T_init_recovered, s=3, alpha=0.5, c="steelblue") - lims = [vmin_init - 5, vmax_init + 5] - axes[1, 1].plot(lims, lims, "k--", alpha=0.5, label="perfect recovery") - axes[1, 1].set_xlim(lims) - axes[1, 1].set_ylim(lims) - axes[1, 1].set_xlabel("True $T_0$ [K]") - axes[1, 1].set_ylabel("Recovered $T_0$ [K]") - axes[1, 1].set_title("True vs. recovered (per grid cell)") - axes[1, 1].legend() - axes[1, 1].set_aspect("equal") - axes[1, 1].grid(True, alpha=0.3) - - axes[1, 2].semilogy(loss_history, "k.-", linewidth=1.5) - axes[1, 2].set_xlabel("Checkpoint") - axes[1, 2].set_ylabel("Loss") - axes[1, 2].set_title(f"Convergence ({result_p2.nit} L-BFGS iterations)") - axes[1, 2].grid(True, alpha=0.3) - - fig.suptitle( - "Recovering a 900-element initial temperature field from 100 sensors", - fontsize=13, - fontweight="bold", - y=1.01, - ) - fig.savefig(FIGURE_DIR / "part2_forensics.png") - plt.close(fig) - print(f" Saved {FIGURE_DIR / 'part2_forensics.png'}") - - -# ── Main ───────────────────────────────────────────────────────────────────── - - -def main(): - print(f"Output directory: {FIGURE_DIR}") - print() - - with Tesseract.from_image("enzyme-thermal-2d:latest") as t: - generate_fd_convergence(t) - print() - generate_part1_convergence(t) - print() - generate_part2_forensics(t) - - print() - print("All figures generated.") - - -if __name__ == "__main__": - main() diff --git a/demo/enzyme_thermal_2d/generate_pipeline_diagram.py b/demo/enzyme_thermal_2d/generate_pipeline_diagram.py index bd6e76b2..ffa11685 100644 --- a/demo/enzyme_thermal_2d/generate_pipeline_diagram.py +++ b/demo/enzyme_thermal_2d/generate_pipeline_diagram.py @@ -1,23 +1,29 @@ #!/usr/bin/env python3 # Copyright 2025 Pasteur Labs. All Rights Reserved. # SPDX-License-Identifier: Apache-2.0 -"""Generate the compilation pipeline diagram for the Enzyme AD blog post.""" +"""Generate the compilation pipeline diagram for the Enzyme AD blog post. + +Vertical recipe: six numbered steps flow top to bottom, each a single stage of +the Fortran -> Enzyme AD -> shared library pipeline. Artifact boxes are +color-coded by what produced them; the command for each step sits on the arrow +that produces the next artifact. +""" from pathlib import Path import matplotlib.patheffects as pe import matplotlib.pyplot as plt -from matplotlib.patches import FancyArrowPatch, FancyBboxPatch +from matplotlib.patches import Circle, FancyArrowPatch, FancyBboxPatch FIGURE_DIR = Path(__file__).parent / "figures" FIGURE_DIR.mkdir(exist_ok=True) -# Colors -C_FORT_BG, C_FORT = "#dbeafe", "#2563eb" -C_IR_BG, C_IR = "#fef9c4", "#ca8a04" -C_ENZ_BG, C_ENZ = "#ede9fe", "#7c3aed" -C_SO_BG, C_SO = "#ffedd5", "#ea580c" -C_WRAP_BG, C_WRAP = "#dcfce7", "#16a34a" +# Colors keyed to the tool that produces each artifact. +C_FORT_BG, C_FORT = "#dbeafe", "#2563eb" # Fortran source +C_WRAP_BG, C_WRAP = "#dcfce7", "#16a34a" # C wrapper source +C_IR_BG, C_IR = "#fef9c4", "#ca8a04" # LLVM IR (LFortran / LLVM) +C_ENZ_BG, C_ENZ = "#ede9fe", "#7c3aed" # Enzyme-differentiated IR +C_SO_BG, C_SO = "#ffedd5", "#ea580c" # final shared library # Arrows carry the mechanism (the flow of compilation), so they lead: dark and # solid. Box borders recede to a thin, muted line — the fill already encodes the # stage, so a heavy border would be redundant data-ink. @@ -25,7 +31,7 @@ C_TEXT = "#374151" -def draw_box(ax, cx, cy, w, h, line1, line2, bg, edge, fs=10): +def draw_box(ax, cx, cy, w, h, line1, line2, bg, edge, fs=11): p = FancyBboxPatch( (cx - w / 2, cy - h / 2), w, @@ -40,10 +46,10 @@ def draw_box(ax, cx, cy, w, h, line1, line2, bg, edge, fs=10): kw = dict(ha="center", va="center", zorder=3, parse_math=False) if line2: ax.text( - cx, cy + 0.13, line1, fontsize=fs, fontweight="bold", color="#1f2937", **kw + cx, cy + 0.16, line1, fontsize=fs, fontweight="bold", color="#1f2937", **kw ) ax.text( - cx, cy - 0.15, line2, fontsize=fs - 2, color="#6b7280", style="italic", **kw + cx, cy - 0.18, line2, fontsize=fs - 3, color="#4a4f5a", style="italic", **kw ) else: ax.text(cx, cy, line1, fontsize=fs, fontweight="bold", color="#1f2937", **kw) @@ -65,146 +71,195 @@ def draw_arrow(ax, x0, y0, x1, y1, rad=0.0): ax.add_patch(a) -def label(ax, x, y, text): - # No box: the chip border was non-data-ink. Plain monospace text reads as a - # command annotation on the arrow it sits beside. +def cmd_label(ax, x, y, text, ha="left"): + # Monospace command annotation sitting beside the arrow it drives. A white + # halo keeps it legible where it crosses an arrow; no enclosing chip (that + # border was non-data-ink). ax.text( x, y, text, - ha="center", + ha=ha, va="center", - fontsize=8, + fontsize=9, color=C_TEXT, fontfamily="monospace", zorder=4, + linespacing=1.3, path_effects=[pe.withStroke(linewidth=3, foreground="white")], ) -def main(): - fig, ax = plt.subplots(figsize=(16, 6)) - - # Y lanes - Y_TOP = 4.6 - Y_BOT = 2.4 - Y_MID = 3.5 - - # X centers — each column gets >= box width + gap of clearance. - # Box width is W; column pitch is 3.4 so there is always a ~1.2 gap. - X = { - "f90": 0.0, - "ll": 3.4, - "opt": 6.8, - "combined": 10.2, - "ad": 13.6, - "so": 17.4, - } - - W, H = 2.2, 0.85 - - ax.set_xlim(X["f90"] - W / 2 - 0.6, X["so"] + (W + 0.6) / 2 + 0.6) - ax.set_ylim(0.4, 6.0) - ax.axis("off") - - # ── TOP TRACK: Fortran source path ── - draw_box( - ax, X["f90"], Y_TOP, W, H, "thermal_2d.f90", "Fortran source", C_FORT_BG, C_FORT +def step_badge(ax, x, y, n, color): + ax.add_patch( + Circle( + (x, y), 0.16, facecolor="white", edgecolor=color, linewidth=1.6, zorder=4 + ) ) - draw_box(ax, X["ll"], Y_TOP, W, H, "thermal_2d.ll", "raw LLVM IR", C_IR_BG, C_IR) - draw_box( - ax, X["opt"], Y_TOP, W, H, "thermal_2d_opt.ll", "optimized IR", C_IR_BG, C_IR + ax.text( + x, + y, + str(n), + ha="center", + va="center", + fontsize=9.5, + fontweight="bold", + color=color, + zorder=5, ) - draw_arrow(ax, X["f90"] + W / 2, Y_TOP, X["ll"] - W / 2, Y_TOP) - label(ax, (X["f90"] + X["ll"]) / 2, Y_TOP - 0.62, "lfortran\n--show-llvm") - - draw_arrow(ax, X["ll"] + W / 2, Y_TOP, X["opt"] - W / 2, Y_TOP) - label(ax, (X["ll"] + X["opt"]) / 2, Y_TOP + 0.62, "opt -O3") - # ── BOTTOM TRACK: C wrapper path ── - draw_box( - ax, X["f90"], Y_BOT, W, H, "wrapper.c", "Enzyme annotations", C_WRAP_BG, C_WRAP - ) - draw_box(ax, X["ll"], Y_BOT, W, H, "wrapper.ll", "wrapper IR", C_IR_BG, C_IR) +def main(): + fig, ax = plt.subplots(figsize=(9, 11)) + + # One row per artifact, descending. Boxes are centered on the main column; + # the C-wrapper source sits in a parallel column and merges at the link step. + X_MAIN = 0.0 + X_SIDE = 3.0 + W, H = 2.6, 0.9 + + # Row y-coordinates (top -> bottom). + Y = { + "f90": 10.0, + "ll": 8.3, + "opt": 6.6, + "combined": 4.9, + "ad": 3.2, + "so": 1.5, + } + # The C wrapper lives beside the main column on the rows it spans, then + # feeds the link step. + Y_WRAPC = 8.3 + Y_WRAPLL = 6.6 - draw_arrow(ax, X["f90"] + W / 2, Y_BOT, X["ll"] - W / 2, Y_BOT) - label(ax, (X["f90"] + X["ll"]) / 2, Y_BOT + 0.62, "clang\n-emit-llvm") + ax.set_xlim(X_MAIN - W / 2 - 2.2, X_SIDE + W / 2 + 3.4) + ax.set_ylim(0.5, 11.4) + ax.axis("off") - # ── MERGE into combined.ll ── - draw_box(ax, X["combined"], Y_MID, W, H, "combined.ll", "linked IR", C_IR_BG, C_IR) + # Command labels sit in the empty left margin, right-aligned toward the + # main column so each reads as an annotation on the arrow beside it. + LX = X_MAIN - W / 2 - 0.3 - # both tracks feed llvm-link; arrows enter the left face of combined.ll - draw_arrow( - ax, X["opt"] + W / 2, Y_TOP, X["combined"] - W / 2, Y_MID + 0.18, rad=-0.18 + # ── Main vertical track ── + draw_box( + ax, + X_MAIN, + Y["f90"], + W, + H, + "thermal_2d.f90", + "Fortran source", + C_FORT_BG, + C_FORT, ) - draw_arrow( - ax, X["ll"] + W / 2, Y_BOT, X["combined"] - W / 2, Y_MID - 0.18, rad=0.18 + draw_box(ax, X_MAIN, Y["ll"], W, H, "thermal_2d.ll", "raw LLVM IR", C_IR_BG, C_IR) + draw_box( + ax, X_MAIN, Y["opt"], W, H, "thermal_2d_opt.ll", "optimized IR", C_IR_BG, C_IR ) - # place the merge label in the open wedge to the left of combined.ll - label(ax, X["combined"] - W / 2 - 1.4, Y_MID, "llvm-link") - - # ── LINEAR: combined -> ad -> .so ── - draw_box(ax, X["ad"], Y_MID, W, H, "ad.ll", "differentiated IR", C_ENZ_BG, C_ENZ) - - W_SO = W + 0.6 + draw_box(ax, X_MAIN, Y["combined"], W, H, "combined.ll", "linked IR", C_IR_BG, C_IR) + draw_box(ax, X_MAIN, Y["ad"], W, H, "ad.ll", "differentiated IR", C_ENZ_BG, C_ENZ) draw_box( ax, - X["so"], - Y_MID, - W_SO, - H + 0.15, + X_MAIN, + Y["so"], + W + 0.5, + H + 0.1, "libthermal_2d_ad.so", "forward / JVP / VJP", C_SO_BG, C_SO, ) - draw_arrow(ax, X["combined"] + W / 2, Y_MID, X["ad"] - W / 2, Y_MID) - label(ax, (X["combined"] + X["ad"]) / 2, Y_MID + 0.72, "opt\n-passes=enzyme") - - draw_arrow(ax, X["ad"] + W / 2, Y_MID, X["so"] - W_SO / 2, Y_MID) - label(ax, (X["ad"] + X["so"]) / 2, Y_MID + 0.72, "opt +\nclang -shared") + # ── C-wrapper side track ── + draw_box( + ax, X_SIDE, Y_WRAPC, W, H, "wrapper.c", "Enzyme annotations", C_WRAP_BG, C_WRAP + ) + draw_box(ax, X_SIDE, Y_WRAPLL, W, H, "wrapper.ll", "wrapper IR", C_IR_BG, C_IR) + + # ── Vertical arrows + step badges + command labels ── + # Main-track commands sit in the left margin, right-aligned to the column. + # Step 1: f90 -> ll + draw_arrow(ax, X_MAIN, Y["f90"] - H / 2, X_MAIN, Y["ll"] + H / 2) + step_badge(ax, X_MAIN, (Y["f90"] + Y["ll"]) / 2, 1, C_FORT) + cmd_label(ax, LX, (Y["f90"] + Y["ll"]) / 2, "lfortran\n--show-llvm", ha="right") + + # Step 2: ll -> opt (mild -O1 BEFORE Enzyme — the whole point of the post) + draw_arrow(ax, X_MAIN, Y["ll"] - H / 2, X_MAIN, Y["opt"] + H / 2) + step_badge(ax, X_MAIN, (Y["ll"] + Y["opt"]) / 2, 2, C_IR) + cmd_label(ax, LX, (Y["ll"] + Y["opt"]) / 2, "opt -O1", ha="right") + + # Step 3: wrapper.c -> wrapper.ll (side track) — label to the right of it. + draw_arrow(ax, X_SIDE, Y_WRAPC - H / 2, X_SIDE, Y_WRAPLL + H / 2) + step_badge(ax, X_SIDE, (Y_WRAPC + Y_WRAPLL) / 2, 3, C_WRAP) + cmd_label( + ax, X_SIDE + W / 2, (Y_WRAPC + Y_WRAPLL) / 2, "clang\n-emit-llvm -O1", ha="left" + ) - # ── Tool labels at bottom, centered under the columns they cover ── - # No chip box (non-data-ink). A short tick links each label to its track so - # the eye reads the grouping without a heavy enclosure. - by = 1.0 - for x0, x1, txt, color in [ - (X["f90"], X["f90"], "LFortran 0.61", C_FORT), - (X["ll"], X["opt"], "LLVM 19", C_IR), - (X["ad"], X["so"], "Enzyme (LLVM pass)", C_ENZ), + # Step 4: opt.ll + wrapper.ll -> combined.ll + draw_arrow(ax, X_MAIN, Y["opt"] - H / 2, X_MAIN, Y["combined"] + H / 2) + # wrapper.ll merges in from the side + draw_arrow( + ax, X_SIDE - W / 2, Y_WRAPLL, X_MAIN + W / 2, Y["combined"] + 0.05, rad=-0.2 + ) + step_badge(ax, X_MAIN, (Y["opt"] + Y["combined"]) / 2, 4, C_IR) + cmd_label(ax, LX, (Y["opt"] + Y["combined"]) / 2, "llvm-link", ha="right") + + # Step 5: combined.ll -> ad.ll (Enzyme) + draw_arrow(ax, X_MAIN, Y["combined"] - H / 2, X_MAIN, Y["ad"] + H / 2) + step_badge(ax, X_MAIN, (Y["combined"] + Y["ad"]) / 2, 5, C_ENZ) + cmd_label(ax, LX, (Y["combined"] + Y["ad"]) / 2, "opt\n-passes=enzyme", ha="right") + + # Step 6: ad.ll -> .so (post-Enzyme -O3 is where -O3 belongs) + draw_arrow(ax, X_MAIN, Y["ad"] - H / 2, X_MAIN, Y["so"] + (H + 0.1) / 2) + step_badge(ax, X_MAIN, (Y["ad"] + Y["so"]) / 2, 6, C_SO) + cmd_label(ax, LX, (Y["ad"] + Y["so"]) / 2, "opt -O3\nclang -shared", ha="right") + + # ── Tool brackets down the right margin, spanning the rows each tool owns ── + # The box fills already encode the tool; the brackets add version context and + # group the stages without a heavy enclosure. + band_x = X_SIDE + W / 2 + 1.9 + tick = 0.18 + for y_hi, y_lo, txt, color in [ + (Y["f90"], Y["f90"], "LFortran 0.61", C_FORT), + (Y["ll"], Y["combined"], "LLVM 19", C_IR), + (Y["ad"], Y["ad"], "Enzyme\n(LLVM pass)", C_ENZ), + (Y["so"], Y["so"], "LLVM 19 +\nclang", C_SO), ]: - cx = (x0 + x1) / 2 + top, bot = y_hi + H / 2, y_lo - H / 2 ax.plot( - [x0 - W / 2, x1 + W / 2], - [by + 0.45, by + 0.45], + [band_x, band_x], + [bot, top], color=color, - lw=1.2, + lw=1.4, zorder=1, solid_capstyle="round", ) + # short inward ticks close the bracket at top and bottom + ax.plot([band_x - tick, band_x], [top, top], color=color, lw=1.4, zorder=1) + ax.plot([band_x - tick, band_x], [bot, bot], color=color, lw=1.4, zorder=1) ax.text( - cx, - by, + band_x + 0.15, + (y_hi + y_lo) / 2, txt, - ha="center", + ha="left", va="center", - fontsize=9, + fontsize=9.5, color=color, fontweight="bold", + linespacing=1.3, ) # Title ax.text( - (X["f90"] + X["so"]) / 2, - 5.7, - "Compilation pipeline: Fortran → Enzyme AD → shared library", + (X_MAIN + X_SIDE) / 2, + 11.1, + "Compilation pipeline:\nFortran → Enzyme AD → shared library", ha="center", va="center", - fontsize=16, + fontsize=15, fontweight="bold", color="#111827", + linespacing=1.3, ) fig.savefig( diff --git a/demo/enzyme_thermal_2d/tesseract_config.yaml b/demo/enzyme_thermal_2d/tesseract_config.yaml index 3af9cf06..e3d78611 100644 --- a/demo/enzyme_thermal_2d/tesseract_config.yaml +++ b/demo/enzyme_thermal_2d/tesseract_config.yaml @@ -55,8 +55,7 @@ build_config: ln -sf $(find /opt/conda -name lfortran -type f | head -1) /usr/local/bin/lfortran && \ echo /opt/conda/lib > /etc/ld.so.conf.d/conda.conf && ldconfig - # Build Enzyme from a pinned release (nightly builds are not reproducible - # and have caused reverse-mode NaN regressions in the past) + # Build Enzyme from a pinned release - | RUN git clone --depth 1 --branch v0.0.258 https://github.com/EnzymeAD/Enzyme.git /tmp/enzyme-src && \ cmake -S /tmp/enzyme-src/enzyme -B /tmp/enzyme-build \ diff --git a/docs/blog/2025-03-10-tesseract-core-announcement.md b/docs/blog/2025-03-10-tesseract-core-announcement.md index f6d32760..f948574f 100644 --- a/docs/blog/2025-03-10-tesseract-core-announcement.md +++ b/docs/blog/2025-03-10-tesseract-core-announcement.md @@ -24,12 +24,13 @@ Tesseracts provide native support for endpoints that interface with automatic di Tesseract Core is a command line app and Python SDK for building end-to-end differentiable pipelines consisting of wildly different components like physical simulators, geometric operators, differentiable meshers and renderers, scientific data transforms, neural networks, and more. -

-Rosenbrock optimization -
Gradient-based optimization of the Rosenbrock function using a Tesseract.
-
+```{figure} ../static/blog/rosenbrock_optimization.gif +:alt: Rosenbrock optimization + +Gradient-based optimization of the Rosenbrock function using a Tesseract. +``` --- -_Tesseract is a free, open-source framework for differentiable scientific computing. `pip install tesseract-core`. -[Docs](https://tesseract.pasteurlabs.ai) · [Demos](https://tesseract.pasteurlabs.ai/content/demo/demo.html) · [GitHub](https://github.com/pasteurlabs/tesseract-core) · [Forum](https://si-tesseract.discourse.group/)_ +_Tesseract is a free, open-source framework for differentiable scientific computing._ +_[Docs](https://tesseract.pasteurlabs.ai) · [Demos](https://tesseract.pasteurlabs.ai/content/demo/demo.html) · [GitHub](https://github.com/pasteurlabs/tesseract-core) · [Forum](https://si-tesseract.discourse.group/)_ diff --git a/docs/blog/2025-06-30-pipeline-autodiff.md b/docs/blog/2025-06-30-pipeline-autodiff.md index f123282f..9b1fb69b 100644 --- a/docs/blog/2025-06-30-pipeline-autodiff.md +++ b/docs/blog/2025-06-30-pipeline-autodiff.md @@ -30,19 +30,21 @@ Autodiff works really well for situations where all calculations can be expresse Our demo is built using JAX-FEM and inspired by the 2D Topology Optimization with the SIMP Method. We've reformulated the problem and solved it as an optimization of a parameterized shape. -
-Data flow through a Tesseract-based pipeline for parametric shape optimization -
Data flow through a Tesseract-based pipeline for parametric shape optimization, involving two separate Tesseracts: one for computing a signed distance field from a parametric geometry, and another for computing the compliance of a structure given a density field via finite element analysis.
-
+```{figure} ../static/blog/pipeline-data-flow.png +:alt: Data flow through a Tesseract-based pipeline for parametric shape optimization + +Data flow through a Tesseract-based pipeline for parametric shape optimization, involving two separate Tesseracts: one for computing a signed distance field from a parametric geometry, and another for computing the compliance of a structure given a density field via finite element analysis. +``` We've implemented this demo using multiple Tesseracts that communicate with each other, forming a multi-step computation pipeline. We then apply end-to-end automatic differentiation to carry out the optimization. The demo clearly shows the feasibility --- and efficacy --- of pipeline-level automatic differentiation with Tesseracts. In particular, Tesseracts simplify heterogeneous gradient computation, as well as managing dependencies, computing resources, and components. -
-Shape optimization demo -
Shape optimization results showing the initial and optimized geometries.
-
+```{figure} ../static/blog/pipeline-demo.png +:alt: Shape optimization demo + +Shape optimization results showing the initial and optimized geometries. +``` --- -_Tesseract is a free, open-source framework for differentiable scientific computing. `pip install tesseract-core`. -[Docs](https://tesseract.pasteurlabs.ai) · [Demos](https://tesseract.pasteurlabs.ai/content/demo/demo.html) · [GitHub](https://github.com/pasteurlabs/tesseract-core) · [Forum](https://si-tesseract.discourse.group/)_ +_Tesseract is a free, open-source framework for differentiable scientific computing._ +_[Docs](https://tesseract.pasteurlabs.ai) · [Demos](https://tesseract.pasteurlabs.ai/content/demo/demo.html) · [GitHub](https://github.com/pasteurlabs/tesseract-core) · [Forum](https://si-tesseract.discourse.group/)_ diff --git a/docs/blog/2025-08-03-beginners-guide.md b/docs/blog/2025-08-03-beginners-guide.md index 93e3dc21..2bf421cc 100644 --- a/docs/blog/2025-08-03-beginners-guide.md +++ b/docs/blog/2025-08-03-beginners-guide.md @@ -26,26 +26,29 @@ To see how this works, let's start with a simple physics example: projectile mot ### Newton's challenge -
-Newton at a low angle -
Newton throws a ball at a low angle.
-
+```{figure} ../static/blog/beginners-newton-low.png +:alt: Newton at a low angle + +Newton throws a ball at a low angle. +``` Imagine you're playing catch with Isaac Newton. He throws a ball from a fixed distance away, and it arrives after a certain flight time. Newton points out that given a fixed distance and flight time, "only one path" exists --- a unique combination of speed and angle. -
-Newton at a high angle -
The same distance can be reached at a high angle with a different speed.
-
+```{figure} ../static/blog/beginners-newton-high.png +:alt: Newton at a high angle + +The same distance can be reached at a high angle with a different speed. +``` ### The equations Under constant gravitational acceleration, we can describe the projectile's motion with two key equations. -
-Projectile trajectory -
Projectile trajectory under constant gravitational acceleration.
-
+```{figure} ../static/blog/beginners-projectile.svg +:alt: Projectile trajectory + +Projectile trajectory under constant gravitational acceleration. +``` **Time of flight:** @@ -57,10 +60,11 @@ $$s_x = \frac{u^2 \sin 2\theta}{g}$$ Where $u$ is the initial velocity, $\theta$ is the launch angle, and $g = 9.81 \, \text{m/s}^2$ is the gravitational acceleration. -
-Velocity vector resolution -
Resolving the velocity vector into horizontal and vertical components.
-
+```{figure} ../static/blog/beginners-resolve-velocity.svg +:alt: Velocity vector resolution + +Resolving the velocity vector into horizontal and vertical components. +``` These equations establish a one-to-one correspondence between input coordinates $(u, \theta)$ and output coordinates $(s_x, t)$. @@ -199,12 +203,13 @@ Verify the Jacobian computation at $u = 10$, $\theta = 0.75$ rad --- the numeric By wrapping even a simple physics model in a Tesseract, we get a containerized, self-documenting component with a standard JSON interface and built-in derivative support. Now you're ready to explore gradient-based optimization[ via Tesseract-JAX](https://github.com/pasteurlabs/tesseract-jax) and interactive visualization [via Tesseract-Streamlit](https://github.com/pasteurlabs/tesseract-streamlit) for these differentiable components. -
-Isaac Newton discovers gravity, 1936 -
"Isaac Newton discovers gravity", 1936.
-
+```{figure} ../static/blog/beginners-newton-gravity.jpg +:alt: Isaac Newton discovers gravity, 1936 + +"Isaac Newton discovers gravity", 1936. +``` --- -_Tesseract is a free, open-source framework for differentiable scientific computing. `pip install tesseract-core`. -[Docs](https://tesseract.pasteurlabs.ai) · [Demos](https://tesseract.pasteurlabs.ai/content/demo/demo.html) · [GitHub](https://github.com/pasteurlabs/tesseract-core) · [Forum](https://si-tesseract.discourse.group/)_ +_Tesseract is a free, open-source framework for differentiable scientific computing._ +_[Docs](https://tesseract.pasteurlabs.ai) · [Demos](https://tesseract.pasteurlabs.ai/content/demo/demo.html) · [GitHub](https://github.com/pasteurlabs/tesseract-core) · [Forum](https://si-tesseract.discourse.group/)_ diff --git a/docs/blog/2025-11-28-rocket-fin-optimization.md b/docs/blog/2025-11-28-rocket-fin-optimization.md index 27f667cc..186c474c 100644 --- a/docs/blog/2025-11-28-rocket-fin-optimization.md +++ b/docs/blog/2025-11-28-rocket-fin-optimization.md @@ -18,19 +18,22 @@ If you work in simulation-driven design, you've probably hit this wall: you have We built a pipeline that does exactly this: optimizing rocket grid fin geometry using Ansys SpaceClaim for CAD, a custom mesh converter, and PyMAPDL for structural analysis. The optimizer sees a single differentiable function, even though the underlying gradient strategies (analytical adjoint, finite differences, and JAX automatic differentiation) are completely different at every stage. -
-Titanium grid fins on a Falcon 9 booster -
Second-generation titanium grid fins on a Falcon 9 booster. SpaceX, Public Domain.
-
+```{figure} ../static/blog/rocket-fins-grid-fins.jpg +:alt: Titanium grid fins on a Falcon 9 booster + +Second-generation titanium grid fins on a Falcon 9 booster. [SpaceX, Public Domain](). +``` ## The pipeline Each grid fin has 8 bars defined by start and end angular positions, giving us 16 design parameters. SpaceClaim generates the geometry, which gets converted to a signed distance field on a regular grid. PyMAPDL then solves the linear elasticity problem and returns compliance, a measure of how much the structure deforms under load. Lower compliance means a stiffer fin. -
-Optimization workflow -
End-to-end optimization workflow connecting Ansys SpaceClaim, SDF conversion, and PyMAPDL via Tesseract.
-
+```{figure} ../static/blog/rocket-fins-workflow.png +:alt: Optimization workflow +:class: blog-img-full + +End-to-end optimization workflow connecting Ansys SpaceClaim, SDF conversion, and PyMAPDL via Tesseract. +``` These tools don't naturally fit together. SpaceClaim runs on Windows with a commercial license. PyMAPDL has its own dependency tree. The optimization logic and glue code run in JAX on Linux. We wrapped each step as a Tesseract: the SDF converter and PyMAPDL run as containerized images on Linux, while SpaceClaim runs directly on the Windows host via `tesseract-runtime serve` (since it needs the local Ansys installation). All three expose the same API regardless of deployment mode, and [Tesseract-JAX](https://github.com/pasteurlabs/tesseract-jax) composes them into a single callable pipeline. @@ -92,5 +95,5 @@ If you want to dig into the details, the [full technical writeup](https://si-tes --- -_Tesseract is a free, open-source framework for differentiable scientific computing. `pip install tesseract-core`. -[Docs](https://tesseract.pasteurlabs.ai) · [Demos](https://tesseract.pasteurlabs.ai/content/demo/demo.html) · [GitHub](https://github.com/pasteurlabs/tesseract-core) · [Forum](https://si-tesseract.discourse.group/)_ +_Tesseract is a free, open-source framework for differentiable scientific computing._ +_[Docs](https://tesseract.pasteurlabs.ai) · [Demos](https://tesseract.pasteurlabs.ai/content/demo/demo.html) · [GitHub](https://github.com/pasteurlabs/tesseract-core) · [Forum](https://si-tesseract.discourse.group/)_ diff --git a/docs/blog/2026-01-20-hackathon-winners.md b/docs/blog/2026-01-20-hackathon-winners.md index caf39f59..9238942f 100644 --- a/docs/blog/2026-01-20-hackathon-winners.md +++ b/docs/blog/2026-01-20-hackathon-winners.md @@ -24,10 +24,11 @@ The inaugural virtual Tesseract Hackathon has concluded, and we're thrilled to a This project explores how agents in flow fields can coordinate without direct communication. The team employed a differentiable PDE solver wrapped as a Tesseract, enabling agents to learn action policies via gradient descent. Notably, policies trained on a set of 20 agents are still useful when actually deploying 60 agents. -
-Multi-Agent DPC architecture -
Multi-Agent Differentiable Predictive Control architecture for zero-shot PDE scalability.
-
+```{figure} ../static/blog/hackathon-multi-agent-dpc.png +:alt: Multi-Agent DPC architecture + +Multi-Agent Differentiable Predictive Control architecture for zero-shot PDE scalability. +```

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