自动发现材料本构模型，九种组合均表现优异。
Automated Constitutive Model Discovery by Pairing Sparse Regression Algorithms with Model Selection Criteria
- 用三种稀疏回归+三种筛选准则配对，系统探索模型选择
- 在合成与实验数据上准确复现各向同性/异向性超弹性材料
- 突破传统LASSO限制，首次验证OMP等效于ℓ₀正则化
从数据中自动发现本构模型已成为传统模型标定的有前景替代方案。本文提出一个完全自动化的本构模型发现框架，系统地将三种稀疏回归算法（LASSO、LARS、OMP）与三种模型选择准则（K折交叉验证、AIC、BIC）配对，形成九种不同算法，可系统分析稀疏性、预测性能与计算成本之间的权衡。其中LARS作为ℓ₁约束问题的高效路径求解器，而OMP被引入为ℓ₀正则化选择的可行启发式方法。该框架应用于各向同性和各向异性超弹性材料，使用合成与实验数据集。结果表明，所有九种算法-准则组合在发现各向同性及各向异性材料时表现一致良好，能构建高度精确的本构模型。研究拓展了可行发现算法的范围，超越了传统的ℓ₁基方法如LASSO。
原文摘要 · Abstract (English)
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.
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