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

arXiv: https://arxiv.org/abs/2605.23754 · HTML: https://mlsanity.com/paper/2605.23754/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Medical and scientific domain agents, one of 16 directions in LLM agents and tool use.
- Builds on 58 of its 140 references that are in the map.
- First posted on arXiv 22 May 2026.

## Placed in

- LLM agents and tool use / [Medical and scientific domain agents](https://mlsanity.com/agents/medical-and-scientific-domain-agents/)

## Builds on (most cited first, 30 of 58)

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- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [A Dynamic LLM-Powered Agent Network for Task-Oriented Agent Collaboration](https://mlsanity.com/paper/2310.02170/) (2023)
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- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discovery](https://mlsanity.com/paper/2405.09783/) (2024)
- [Agentic AI for Scientific Discovery: A Survey of Progress, Challenges, and Future Directions](https://mlsanity.com/paper/2503.08979/) (2025)
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- [ProtAgents: Protein discovery via large language model multi-agent collaborations combining physics and machine learning](https://mlsanity.com/paper/2402.04268/) (2024)
- [MechAgents: Large language model multi-agent collaborations can solve mechanics problems, generate new data, and integrate knowledge](https://mlsanity.com/paper/2311.08166/) (2023)
- [Polyconvex anisotropic hyperelasticity with neural networks](https://mlsanity.com/paper/2106.14623/) (2021)
- [Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systems](https://mlsanity.com/paper/2205.08304/) (2022)
- [AutoAgent: A Fully-Automated and Zero-Code Framework for LLM Agents](https://mlsanity.com/paper/2502.05957/) (2025)
- [Unsupervised discovery of interpretable hyperelastic constitutive laws](https://mlsanity.com/paper/2010.13496/) (2020)
- [TDAG: A Multi-Agent Framework based on Dynamic Task Decomposition and Agent Generation](https://mlsanity.com/paper/2402.10178/) (2024)
- [A new family of Constitutive Artificial Neural Networks towards automated model discovery](https://mlsanity.com/paper/2210.02202/) (2022)
- [Neural networks meet hyperelasticity: A guide to enforcing physics](https://mlsanity.com/paper/2302.02403/) (2023)
- [LLMatDesign: Autonomous Materials Discovery with Large Language Models](https://mlsanity.com/paper/2406.13163/) (2024)
- [CodePDE: An Inference Framework for LLM-driven PDE Solver Generation](https://mlsanity.com/paper/2505.08783/) (2025)
- [A review on data-driven constitutive laws for solids](https://mlsanity.com/paper/2405.03658/) (2024)
- [SR-Scientist: Scientific Equation Discovery With Agentic AI](https://mlsanity.com/paper/2510.11661/) (2025)
- [LLMs for Science: Usage for Code Generation and Data Analysis](https://mlsanity.com/paper/2311.16733/) (2023)
- [NN-EUCLID: deep-learning hyperelasticity without stress data](https://mlsanity.com/paper/2205.06664/) (2022)
- [Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equations](https://mlsanity.com/paper/2110.03774/) (2021)

## Abstract (arXiv)

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...