# Simulation of hyperelastic materials in real-time using Deep Learning

## TL;DR

This paper introduces U-Mesh, a deep learning approach using U-Net architecture to simulate hyperelastic materials in real-time, significantly reducing computation time while maintaining accuracy compared to traditional methods.

## Contribution

The paper presents a novel data-driven method that leverages deep learning to efficiently approximate FEM solutions for hyperelastic materials, enabling real-time simulations.

## Key findings

- U-Mesh achieves fast simulation speeds across different geometries and mesh resolutions.
- The method maintains very small errors compared to FEM and POD benchmarks.
- U-Mesh outperforms traditional model reduction techniques in computational efficiency.

## Abstract

The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition, parallel computing, adaptive meshing, and model order reduction. In this paper we present U-Mesh: a data-driven method based on a U-Net architecture that approximates the non-linear relation between a contact force and the displacement field computed by a FEM algorithm. We show that deep learning, one of the latest machine learning methods based on artificial neural networks, can enhance computational mechanics through its ability to encode highly non-linear models in a compact form. Our method is applied to two benchmark examples: a cantilever beam and an L-shape subject to moving punctual loads. A comparison between our method and proper orthogonal decomposition (POD) is done through the paper. The results show that U-Mesh can perform very fast simulations on various geometries, mesh resolutions and number of input forces with very small errors.