This repository provides the code and examples for the paper:

Learning elastoplasticity with implicit layers, by Jérémy Bleyer

The project explores a novel machine learning framework that integrates elastoplastic material models with implicit layers using differentiable convex optimization. This approach is particularly suited for learning constitutive laws directly from data with embedded convexity.

The scripts require pytorch as well as cvxpy and cvxpylayers libraries available at:

• https://www.cvxpy.org/

• GitHub - cvxgrp/cvxpylayers: Differentiable convex optimization layers

• implicit_learning.py implements the implicit learning architecture based on differentiable optimization layers.

• convex_sets.py implements different convex set parametrization including Polyhedron, Ellipsoids, ConvexHullEllipsoids and Spectrahedron

• utils.py contains various utility functions

• examples/ contains use-case scripts from the paper, including datasets and code to reproduce experiments.

If you use this code in your work, please cite the following:

@misc{bleyer2025elastoplasticity,
  author       = {Bleyer, Jérémy},
  title        = {Learning elastoplasticity with implicit layers},
  year         = 2025,
  doi          = {10.5281/zenodo.15168994},
  url          = {https://doi.org/10.5281/zenodo.15168994}
}