Automating modeling in mechanics: LLMs as designers of physics-constrained neural networks for constitutive modeling of materials

TL;DR

This paper presents a framework where large language models automatically generate physics-constrained neural networks for constitutive modeling in mechanics, reducing expert effort and achieving high accuracy and generalization.

Contribution

It introduces a novel LLM-based method for on-demand generation of specialized neural networks for material modeling, integrating physical constraints and code synthesis.

Findings

LLM-generated CANNs match or outperform manual models in accuracy

The approach generalizes well to unseen loading and large deformations

Reduces the need for expert knowledge in constitutive modeling

Abstract

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.