# Automating modeling in mechanics: LLMs as designers of physics-constrained neural networks for constitutive modeling of materials arXiv: https://arxiv.org/abs/2512.01735 ยท HTML: https://mlsanity.com/paper/2512.01735/ ## Key facts - Cited by 2 papers in the map (data through 14 Oct 2026). - Placed in Multimodal and embodied agents, one of 16 directions in LLM agents and tool use. - Builds on 28 of its 60 references that are in the map. - First posted on arXiv 1 Dec 2025. ## Placed in - LLM agents and tool use / [Multimodal and embodied agents](https://mlsanity.com/agents/multimodal-and-embodied-agents/) ## Builds on (most cited first, 28 of 28) - [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024) - [A Dynamic LLM-Powered Agent Network for Task-Oriented Agent Collaboration](https://mlsanity.com/paper/2310.02170/) (2023) - [AutoAgents: A Framework for Automatic Agent Generation](https://mlsanity.com/paper/2309.17288/) (2023) - [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024) - [EvoAgent: Towards Automatic Multi-Agent Generation via Evolutionary Algorithms](https://mlsanity.com/paper/2406.14228/) (2024) - [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) - [MechAgents: Large language model multi-agent collaborations can solve mechanics problems, generate new data, and integrate knowledge](https://mlsanity.com/paper/2311.08166/) (2023) - [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) - [Neural networks meet hyperelasticity: A guide to enforcing physics](https://mlsanity.com/paper/2302.02403/) (2023) - [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) - [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) - [Discovering plasticity models without stress data](https://mlsanity.com/paper/2202.04916/) (2022) - [Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties](https://mlsanity.com/paper/2203.07422/) (2022) - [Large Language Models as Surrogate Models in Evolutionary Algorithms: A Preliminary Study](https://mlsanity.com/paper/2406.10675/) (2024) - [PINNsAgent: Automated PDE Surrogation with Large Language Models](https://mlsanity.com/paper/2501.12053/) (2025) - [Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations](https://mlsanity.com/paper/2302.03598/) (2023) - [On sparse regression, Lp-regularization, and automated model discovery](https://mlsanity.com/paper/2310.06872/) (2023) - [Data-driven Modeling of the Mechanical Behavior of Anisotropic Soft Biological Tissue](https://mlsanity.com/paper/2107.05388/) (2021) - [Data-driven fracture mechanics](https://mlsanity.com/paper/2006.03133/) (2020) - [Viscoelastic Constitutive Artificial Neural Networks (vCANNs) - a framework for data-driven anisotropic nonlinear finite viscoelasticity](https://mlsanity.com/paper/2303.12164/) (2023) - [Automatic generation of interpretable hyperelastic material models by symbolic regression](https://mlsanity.com/paper/2206.15099/) (2022) - [GRAIL: Graph Edit Distance and Node Alignment Using LLM-Generated Code](https://mlsanity.com/paper/2505.02124/) (2025) - [FUsion-based ConstitutivE model (FuCe): Towards model-data augmentation in constitutive modelling](https://mlsanity.com/paper/2411.03318/) (2024) ## Built on by (most cited first, 2 of 2) - [LLM-driven design of physics-constrained constitutive models: two agents are better than one](https://mlsanity.com/paper/2605.23754/) (2026) - [LEIA: Learned Environment for Interactive Architected Materials](https://mlsanity.com/paper/2605.28368/) (2026) ## Abstract (arXiv) Large language model (LLM)-based agentic frameworks increasingly adopt the paradigm of dynamically generating task-specific agents. We suggest that not only agents but also specialized software modules for scientific and engineering tasks can be generated on demand. We demonstrate this concept in the field of solid mechanics. There, so-called constitutive models are required to describe the relationship between mechanical stress and body deformation. Constitutive models are essential for both the scientific understanding and industrial application of materials. However, even recent data-driven methods of constitutive modeling, such as constitutive artificial neural networks (CANNs), still require substantial expert knowledge and human labor. We present a framework in which an LLM generates a CANN on demand, tailored to a given material class and dataset provided by the user. The framework covers LLM-based architecture selection, integration of physical constraints, and complete code generation. Evaluation on three benchmark problems demonstrates that LLM-generated CANNs achieve accuracy comparable to or greater than manually engineered counterparts, while also exhibiting reliable generalization to unseen loading scenarios and extrapolation to large deformations. These findings indicate that LLM-based generation of physics-constrained neural networks can substantially reduce the expertise required for constitutive modeling and represent a step toward practical end-to-end automation.