Engineering-Oriented Symbolic Regression: LLMs as Physics Agents for Discovery of Simulation-Ready Constitutive Laws

TL;DR

This paper introduces EO-SR, a framework using LLMs as physics-informed agents to discover stable, physically consistent constitutive laws for complex materials, validated through hyperelastic modeling of rubber-like substances.

Contribution

It presents a novel symbolic regression approach leveraging LLMs to incorporate physical constraints, enabling discovery of stable, physically consistent constitutive models.

Findings

Discovered a hybrid Mooney-Rivlin model with rational locking term

Model achieves high accuracy and guarantees convexity

Ensures robust finite element convergence under severe deformation

Abstract

The discovery of constitutive laws for complex materials has historically faced a dichotomy between high-fidelity data-driven approaches, which demand prohibitive full-field experimental data, and traditional engineering fitting, which often yields numerically unstable models outside calibration regimes. In this work, we propose an Engineering-Oriented Symbolic Regression (EO-SR) framework that bridges this gap by leveraging Large Language Models (LLMs) as "Physics-Informed Agents." Unlike unconstrained symbolic regression, our framework utilizes an LLM Agent to zero-shot synthesize executable physical constraints -- specifically thermodynamic consistency and frame indifference -- transforming the search process from mathematical curve-fitting into a physics-governed discovery engine. We validate this approach on the hyperelastic modeling of rubber-like materials using standard Treloar datasets. The framework autonomously identifies a novel hybrid constitutive law that combines a Mooney-Rivlin linear base with a rational locking term. This discovered model not only achieves high predictive accuracy across multi-axial deformation modes (including zero-shot prediction of pure shear) but also guarantees unconditional convexity. Finite element validation demonstrates that while industry-standard models (e.g., Ogden N=3) fail due to numerical singularities under severe transverse compression, the EO-SR-discovered model maintains robust convergence. This study establishes a generalized, low-barrier pathway for discovering simulation-ready constitutive closures that satisfy both data accuracy and rigorous physical laws.