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

2025-09-19

AI Summary

This work addresses the limitation of conventional constitutive modeling—its reliance on manual parameter calibration—by proposing a data-driven framework for automated constitutive discovery. Methodologically, it systematically integrates three sparse regression algorithms (LASSO, LARS, and Orthogonal Matching Pursuit—OMP) with three model selection criteria (K-fold cross-validation, AIC, and BIC), yielding nine distinct algorithm–criterion combinations. Notably, OMP enables ℓ⁰-norm–based sparse structure identification, overcoming inherent limitations of ℓ¹ regularization. Key contributions include: (i) uncovering systematic trade-offs among sparsity, predictive accuracy, and computational efficiency across algorithms; (ii) successfully identifying high-fidelity, physically interpretable constitutive models on both synthetic data and real experimental data—including isotropic and anisotropic hyperelastic materials; and (iii) demonstrating robust performance across all nine combinations, thereby validating the framework’s generality, reliability, and engineering applicability.

Technology Category

• Machine Learning: Feature Construction/Reformulation
• Search and Optimization: Algorithm Configuration
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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 $ell_1$-constrained problem, OMP is introduced as a tractable heuristic for $ell_0$-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 for the discovery of isotropic and anisotropic materials, yielding highly accurate constitutive models. These findings broaden the range of viable discovery algorithms beyond $ell_1$-based approaches such as LASSO.

Problem

• Automating constitutive model discovery from data
• Systematically pairing sparse regression with selection criteria
• Exploring trade-offs between sparsity and predictive performance

Innovation

• Pairing sparse regression with model selection
• Using LASSO, LARS, OMP algorithms systematically
• Applying framework to isotropic anisotropic hyperelasticity