LLM-driven design of physics-constrained constitutive models: two agents are better than one

2026-05-22

AI Summary

This work addresses the limitations of traditional constitutive modeling, which relies heavily on expert knowledge, and current large language model (LLM)-based approaches that lack systematic verification against physical principles. The authors propose the first dual-agent collaborative framework: a Creator agent generates candidate constitutive models, while an Inspector agent audits them against nine fundamental physical constraints and drives iterative refinement. This approach ensures physically consistent and trustworthy automated model discovery. Notably, the framework is decoupled from specific technical implementations, enabling seamless integration with advancing LLMs. Evaluated on brain tissue and rubber datasets, the method improves physical compliance of models generated by Claude Opus from 91% to 100% and Kimi from 37% to 56%, while preserving high predictive accuracy and strong extrapolation capability to unseen loading paths.

Abstract

Developing constitutive models that capture how materials deform under load traditionally requires years of specialized expertise in continuum mechanics, machine learning, and scientific programming. Large language models (LLMs) have recently been shown to lower this barrier by generating constitutive models on demand, but existing single-agent pipelines lack systematic checks that the resulting models respect fundamental physical laws. To close this gap, we introduce the first multi-agent LLM-driven approach for constitutive model generation: a Creator agent proposes a model tailored to the data, while an Inspector agent critically audits each proposal against nine physical constraints and returns it for refinement whenever a violation is detected. We demonstrate this concept with constitutive artificial neural networks (CANNs) and benchmark it on brain tissue, experimental rubber, and synthetic rubber, using two different LLM backbones (Claude Opus 4.7 and Kimi K2.5). Adding the Inspector raises the share of exported models that truly satisfy all physical constraints from 91% to a perfect 100% for Opus and from 37% to 56% for Kimi, while preserving near-baseline accuracy and remarkable generalization to unseen loading paths. In combination, the generated models are physically valid, highly accurate, and extrapolate reliably beyond the training data - properties that together make them directly usable in practice. Separating generation from inspection thus turns LLM-driven constitutive modeling into a genuinely trustworthy process. The paradigm is deliberately technique-agnostic and scales automatically with advances in LLM capability, opening a promising path toward automated, physics-aware model discovery.

Problem

• constitutive models
• physics constraints
• large language models
• physical validity
• model generation

Innovation

• multi-agent LLM
• physics-constrained modeling
• constitutive models
• model validation
• CANNs