# What machine learning can do for computational solid mechanics

arXiv: https://arxiv.org/abs/2109.08419 · HTML: https://mlsanity.com/paper/2109.08419/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2021.

## Built on by (most cited first, 12 of 12)

- [A review on data-driven constitutive laws for solids](https://mlsanity.com/paper/2405.03658/) (2024)
- [NN-EUCLID: deep-learning hyperelasticity without stress data](https://mlsanity.com/paper/2205.06664/) (2022)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [A review of graph neural network applications in mechanics-related domains](https://mlsanity.com/paper/2407.11060/) (2024)
- [Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)](https://mlsanity.com/paper/2503.05617/) (2025)
- [Three-dimensional microstructure generation using generative adversarial neural networks in the context of continuum micromechanics](https://mlsanity.com/paper/2206.01693/) (2022)
- [Spiking neural networks for nonlinear regression](https://mlsanity.com/paper/2210.03515/) (2022)
- [A physics-encoded Fourier neural operator approach for surrogate modeling of divergence-free stress fields in solids](https://mlsanity.com/paper/2408.15408/) (2024)
- [Input convex neural networks: universal approximation theorem and implementation for isotropic polyconvex hyperelastic energies](https://mlsanity.com/paper/2502.08534/) (2025)
- [ML-based identification of the interface regions for coupling local and nonlocal models](https://mlsanity.com/paper/2404.15388/) (2024)
- [Graph Neural Network Surrogates for Contacting Deformable Bodies with Necessary and Sufficient Contact Detection](https://mlsanity.com/paper/2507.13459/) (2025)

## Abstract (arXiv)

Machine learning has found its way into almost every area of science and engineering, and we are only at the beginning of its exploration across fields. Being a popular, versatile and powerful framework, machine learning has proven most useful where classical techniques are computationally inefficient, which applies particularly to computational solid mechanics. Here, we dare to give a non-exhaustive overview of potential avenues for machine learning in the numerical modeling of solids and structures and offer our (subjective) perspective on what is yet to come.