Automated Constitutive Model Discovery by Pairing Sparse Regression Algorithms with Model Selection Criteria
This work provides an automated framework for materials science researchers to discover constitutive models, broadening options beyond existing methods, though it appears incremental as it combines known algorithms and criteria.
The paper tackled the problem of automating constitutive model discovery from data by pairing three sparse regression algorithms (LASSO, LARS, OMP) with three model selection criteria (CV, AIC, BIC), resulting in nine algorithms that consistently discovered highly accurate models for isotropic and anisotropic hyperelastic materials.
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 in discovering 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.