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

Machine learning for computational science and engineering, vol. 2, pp. 51

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 and rubber as isotropic materials, and on porcine skin tissue as a transversely isotropic material with a preferred fiber direction, using two different LLM backbones (Claude Opus 4.7 and Kimi K2.5). Whether a generated model satisfies the physical constraints is assessed numerically, by probing each constraint across a broad sample of deformation states, rotations, and perturbation directions. Adding the Inspector raises the share of exported models that pass all these checks from 90% to 95% for Opus and from 47% to 60% for Kimi. In addition, the generated models are on par with or even surpass expert-designed models in accuracy, extrapolate reliably beyond the training data, and generalize remarkably well to unseen loading paths. Separating generation from inspection thus turns LLM-driven constitutive modeling into a substantially more 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.

Authors 7

1. M. Tacke corresponding

   Helmholtz-Zentrum Hereon

   Affiliation as printed

   Helmholtz-Zentrum Hereon, Geesthacht, Germany

2. M. Busch

   Hamburg University of Technology

   Affiliation as printed

   Hamburg University of Technology, Hamburg, Germany

3. Kian P. Abdolazizi

   Hamburg University of Technology

   Affiliation as printed

   Hamburg University of Technology, Hamburg, Germany

4. Jonas Eichinger

   Helmholtz-Zentrum Hereon

   Affiliation as printed

   Helmholtz-Zentrum Hereon, Geesthacht, Germany

5. Kevin Linka Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

6. Roland Can Aydin

   Saarland University · Hamburg University of Technology · German Research Centre for Artificial Intelligence

   Affiliation as printed

   German Center for Artificial Intelligence, Kaiserslautern, Germany

   Hamburg University of Technology, Hamburg, Germany

   Saarland University, Saarbrücken, Germany

7. Christian Johannes Cyron corresponding

   Hamburg University of Technology · Helmholtz-Zentrum Hereon

   Affiliation as printed

   Hamburg University of Technology, Hamburg, Germany

   Helmholtz-Zentrum Hereon, Geesthacht, Germany