Add CUDA GPU tests for AD gradient computation

[zazabap]

Summary

Add GPU tests verifying that the AD gradient pipeline (RiemannianProjectionBackend) works correctly with CuArray inputs. 11 tests, all verified passing on RTX 3090.

No code changes to ManifoldDiff.jl itself — the library already works on GPU because it delegates to DifferentiationInterface.jl and ManifoldsBase operations. This PR adds test coverage to verify and document this.

What works on GPU

AD Backend	GPU status	Notes
RiemannianProjectionBackend(AutoZygote())	✅ Works	Zygote reverse-mode AD supports CuArrays natively
RiemannianProjectionBackend(AutoForwardDiff())	❌ Fails	ForwardDiff's seed! uses scalar indexing — fundamental limitation, not version-specific

Operations tested

Operation	Manifold	GPU status
ManifoldDiff.gradient(M, f, p, backend)	Euclidean	✅ Float64 and Float32
ManifoldDiff.gradient(M, f, p, backend)	Sphere	✅ Riemannian gradient in tangent space
CPU-vs-GPU equivalence	Euclidean	✅ isapprox(Array(gpu), cpu; atol=1e-12)

End-to-end GPU solver pipeline

With ManifoldDiff + Manifolds CUDA ext + Manopt _produce_type (#577):

using CUDA, Manifolds, Manopt, ManifoldDiff, Zygote, ADTypes
M = Euclidean(1000)
target = CuArray(randn(1000))
f(M, p) = sum((p .- target).^2) / 2

# AD-computed gradient — entirely on GPU
result = gradient_descent(M, f, p0;
    evaluation=InplaceEvaluation())  # uses ManifoldDiff default backend

This works transparently with CuArrays when Zygote is the AD backend.

Tests: 11/11 verified passing

Test	What's verified
Euclidean gradient Float64	grad isa CuArray{Float64}, matches analytical p
Euclidean gradient Float32	grad isa CuArray{Float32}, correct with atol=1e-4
Sphere Riemannian gradient	Tangent space: dot(grad, p) ≈ 0, matches a - dot(a,p)*p
CPU-vs-GPU equivalence	isapprox(Array(grad_gpu), grad_cpu; atol=1e-12)
Quadratic objective	grad = p - target, verified against analytical solution

All tests use dot(a, p) instead of p[1] to avoid scalar indexing on Sphere.
All tests gracefully skip when CUDA/Zygote is not available.

Changes

• test/test_cuda_ext.jl — new test file (11 tests)
• test/runtests.jl — added include("test_cuda_ext.jl")
• Project.toml — added CUDA to [compat], [extras], and [targets]

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.69%. Comparing base (59ead53) to head (e156e17).

Additional details and impacted files

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  Coverage   95.69%   95.69%           
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  Files          13       13           
  Lines         395      395           
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  Hits          378      378           
  Misses         17       17           

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[kellertuer]

Thanks for that, the two tests missing are

• make sure your code follows the code formatting (on this repository still JulilaFormatter for now)
• any PR has to have a short entry in the changelog, so all changes are properly documented therein.

[gdalle]

I have ideas on how to make ForwardDiff gradients work on GPUs via DI, if you're interested. It was low-priority but it wouldn't take long for me to implement

[kellertuer]

Help on that side would be very welcome.

[gdalle]

If you check out the branch from JuliaDiff/DifferentiationInterface.jl#974 and use DI.AutoForwardFromPrimitive(AutoForwardDiff()), the ForwardDiff gradients should run on the GPU (but there will still be data transfer with the CPU, as explained here). Let me know if it works / speeds things up for you or not