# Automated Constitutive Model Discovery by Pairing Sparse Regression Algorithms with Model Selection Criteria

arXiv: https://arxiv.org/abs/2509.16040 · HTML: https://mlsanity.com/paper/2509.16040/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 79 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 17 of 17)

- [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 unified sparse optimization framework to learn parsimonious physics-informed models from data](https://mlsanity.com/paper/1906.10612/) (2019)
- [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)
- [Automated discovery of generalized standard material models with EUCLID](https://mlsanity.com/paper/2211.04453/) (2022)
- [Discovering plasticity models without stress data](https://mlsanity.com/paper/2202.04916/) (2022)
- [A machine learning based plasticity model using proper orthogonal decomposition](https://mlsanity.com/paper/2001.03438/) (2020)
- [Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties](https://mlsanity.com/paper/2203.07422/) (2022)
- [Extreme sparsification of physics-augmented neural networks for interpretable model discovery in mechanics](https://mlsanity.com/paper/2310.03652/) (2023)
- [On sparse regression, Lp-regularization, and automated model discovery](https://mlsanity.com/paper/2310.06872/) (2023)
- [Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)](https://mlsanity.com/paper/2503.05617/) (2025)
- [Automated discovery of interpretable hyperelastic material models for human brain tissue with EUCLID](https://mlsanity.com/paper/2305.16362/) (2023)
- [Neural networks meet anisotropic hyperelasticity: A framework based on generalized structure tensors and isotropic tensor functions](https://mlsanity.com/paper/2410.03378/) (2024)
- [Polyconvex Physics-Augmented Neural Network Constitutive Models in Principal Stretches](https://mlsanity.com/paper/2503.00575/) (2025)
- [Non-smooth optimization meets automated material model discovery](https://mlsanity.com/paper/2507.10196/) (2025)

## Built on by (most cited first, 3 of 3)

- [Data-efficient Bayesian-guided design selection from large candidate sets: Application to hyperelastic stochastic metamaterials](https://mlsanity.com/paper/2603.15917/) (2026)
- [CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data](https://mlsanity.com/paper/2606.14565/) (2026)
- [Learning the Constitutive Behavior of Materials via Neural Operators and Causal Attention: Case Studies in Plasticity and Damage](https://mlsanity.com/paper/2609.02194/) (2026)

## Abstract (arXiv)

The automated discovery of constitutive models from data has recently emerged as a promising alternative to the traditional model calibration paradigm. In this work, we present a fully automated framework for constitutive model discovery that systematically pairs three sparse regression algorithms Least Absolute Shrinkage and Selection Operator (LASSO), Least Angle Regression (LARS), and Orthogonal Matching Pursuit (OMP)) with three model selection criteria: K-fold cross-validation (CV), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). This pairing yields nine distinct algorithms for model discovery and enables a systematic exploration of the trade-off between sparsity, predictive performance, and computational cost. While LARS serves as an efficient path-based solver for the ℓ1-constrained problem, OMP is introduced as a tractable heuristic for ℓ0-regularized selection. The framework is applied to both isotropic and anisotropic hyperelasticity, utilizing both synthetic and experimental datasets. Results reveal that all nine algorithm-criterion combinations perform consistently well in discovering isotropic and anisotropic materials, yielding highly accurate constitutive models. These findings broaden the range of viable discovery algorithms beyond ℓ1-based approaches such as LASSO.