# Benchmarking data-driven material models on the classic Treloar dataset

arXiv: https://arxiv.org/abs/2608.14063 · HTML: https://mlsanity.com/paper/2608.14063/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 38 references that are in the map.
- First posted on arXiv 14 Aug 2026.

## Builds on (most cited first, 19 of 19)

- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Polyconvex anisotropic hyperelasticity with neural networks](https://mlsanity.com/paper/2106.14623/) (2021)
- [Unsupervised discovery of interpretable hyperelastic constitutive laws](https://mlsanity.com/paper/2010.13496/) (2020)
- [A new family of Constitutive Artificial Neural Networks towards automated model discovery](https://mlsanity.com/paper/2210.02202/) (2022)
- [Neural networks meet hyperelasticity: A guide to enforcing physics](https://mlsanity.com/paper/2302.02403/) (2023)
- [A review on data-driven constitutive laws for solids](https://mlsanity.com/paper/2405.03658/) (2024)
- [Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equations](https://mlsanity.com/paper/2110.03774/) (2021)
- [Local approximate Gaussian process regression for data-driven constitutive laws: Development and comparison with neural networks](https://mlsanity.com/paper/2105.04554/) (2021)
- [On sparse regression, Lp-regularization, and automated model discovery](https://mlsanity.com/paper/2310.06872/) (2023)
- [Automatic generation of interpretable hyperelastic material models by symbolic regression](https://mlsanity.com/paper/2206.15099/) (2022)
- [Theory and implementation of inelastic Constitutive Artificial Neural Networks](https://mlsanity.com/paper/2311.06380/) (2023)
- [Tensor Basis Gaussian Process Models of Hyperelastic Materials](https://mlsanity.com/paper/1912.10872/) (2019)
- [Automated discovery of interpretable hyperelastic material models for human brain tissue with EUCLID](https://mlsanity.com/paper/2305.16362/) (2023)
- [A generalized dual potential for inelastic Constitutive Artificial Neural Networks: A JAX implementation at finite strains](https://mlsanity.com/paper/2502.17490/) (2025)
- [A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains](https://mlsanity.com/paper/2510.04187/) (2025)
- [Non-smooth optimization meets automated material model discovery](https://mlsanity.com/paper/2507.10196/) (2025)
- [Generalized invariants meet constitutive neural networks: A novel framework for hyperelastic materials](https://mlsanity.com/paper/2508.12063/) (2025)
- [Unsupervised Material Fingerprinting: Ultra-fast hyperelastic model discovery from full-field experimental measurements](https://mlsanity.com/paper/2601.14965/) (2026)
- [Adaptive Material Fingerprinting for the fast discovery of polyconvex feature combinations in isotropic and anisotropic hyperelasticity](https://mlsanity.com/paper/2604.05698/) (2026)

## Abstract (arXiv)

Machine learning is rapidly reshaping constitutive modeling, offers new ways to learn material behavior directly from experimental data, and challenges long-established modeling paradigms. But with a growing number of machine-learning-based approaches available, how do they compare in practice? In this paper, we use the classic experimental data of Treloar to benchmark popular frameworks for hyperelasticity: (Generalized-Invariant) Constitutive Artificial Neural Networks, Physics-Augmented Neural Networks, (Adaptive) Material Fingerprinting, and Efficient Unsupervised Constitutive Law Identification & Discovery. We compare their fitting performance, computational cost, hyperparameter sensitivity, and ease of implementation. Furthermore, we discuss the trade-offs between predictive accuracy and model complexity. The latter is assessed by quantifying both the number of material parameters in the discovered models and the computational time required to evaluate the constitutive model and its derivatives. The results show that all methods can reproduce the benchmark data remarkably well. Rather than identifying a single winner, we highlight the strengths and limitations of each approach and provide practical guidance for their use. The source code for all six methods, including the training and comparison scripts, as well as all results and data used in this study, is publicly available via https://doi.org/10.5281/zenodo.21915635.