This repository has two purposes:
- Provides an implementation for Hessian-vector products in implicit differentiable programming
- Shows more examples of differentiable finite elements based on JAX-FEM
Differentiable programming breaks the boundary between deep learning and differentiable physics.
This repository is based on JAX-FEM to solve differentiable physics problems, providing second-order derivative information in the form of Hessian-vector products.
Refer to simple.ipynb for a simple illustrative example.
Works with JAX-FEM version 0.0.9.
Goal: Change the source term to match observed data.
Predicted solutions gradually match the reference data.
Goal: Change the boundary traction force to match observed displacement.
Predicted displacements gradually match the reference displacement.
Goal: Change the boundary temperature to achieve desired deformation.
Predicted displacements gradually match the reference displacement.
Goal: Rotate the square-shaped holes for better beam stiffness.
Compliance minimization by changing orientations of the square holes.
Refer to the arXiv version for more details.
@article{xue2025implicit,
title={Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics},
author={Xue, Tianju},
journal={arXiv preprint arXiv:2505.12646},
year={2025}
}