PhyGRU - A Physics-Biased Variant for Gated Recurrent Unit

Companion Preprint: Available at https://doi.org/10.5281/zenodo.18911329

Appendix and Variants:

• Residual Latent Injection: https://doi.org/10.5281/zenodo.19632174

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Overwiew

Modeling dynamical systems with partial physical knowledge and limited data is challenging. Purely data-driven recurrent networks can struggle to generalize, while simplified physical models often fail to capture the full system dynamics. PhyGRU addresses this by embedding an explicit physics-informed candidate state within a standard Gated Recurrent Unit architecture.

In PhyGRU, the candidate state is obtained by forward integrating a parametric physical model, optionally complemented by a low-dimensional latent state that captures unmodeled dynamics. The standard GRU update gate is preserved, allowing smooth blending between the previous state and the physics-informed candidate. Unlike conventional GRUs, the reset gate is removed for the physical component to maintain continuity and physical consistency.

This design enables interpretable, physics-guided temporal propagation while maintaining the flexibility of recurrent neural networks. PhyGRU requires only minimal changes to a standard GRU, making it easy to integrate into existing pipelines. The approach is particularly suited to scenarios where partial physical knowledge exists and fully data-driven models alone are insufficient, offering a principled way to combine prior knowledge with learned corrections.

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Installation

Clone the repository and install dependencies using pip:

git clone https://github.com/GirolamoOddo/PhyGRU.git
cd PhyGRU
pip install -r requirements.txt

The file PhyGRU_user_examples.py provides a ready-to-run example demonstrating how to use PhyGRU in a PyTorch environment. It shows how to initialize a minimal PhyGRU model, using the different API setup available. The file presents the results obtained, showing PhyGRU in various usage modes, including: No Prior, No Latent, Linear Latent*, MLP Latent, Latent at Gate Level* and Latent as Residual Compensation.
This is just a starting point for developing more complex models with mixed layers, including PhyGRU in the pipeline.
*(as presented in the preprint)

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