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

2025-12-01

AI Summary

Conventional constitutive modeling heavily relies on expert knowledge and suffers from low automation. Method: This paper proposes a large language model (LLM)-driven, end-to-end framework for constitutive modeling. It is the first approach enabling an LLM to autonomously design physics-constrained neural networks (CANNs) tailored for solid mechanics—automatically embedding physical laws, generating network architectures, and producing executable code based solely on input material type and experimental data. The framework tightly integrates domain knowledge with data-driven learning, eliminating manual architecture design and hard-coded physical constraints. Contribution/Results: Evaluated on multiple benchmark problems, the automatically generated models achieve accuracy comparable to or exceeding that of handcrafted models, while demonstrating superior extrapolation capability and generalization across diverse loading conditions.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Cognitive Modeling & Cognitive Systems: (Computational) Cognitive Architectures
• Natural Language Processing: (Large) Language Models

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• Automates constitutive model design for materials using LLMs
• Reduces expert knowledge needed for physics-constrained neural networks
• Generates tailored neural networks for material stress-deformation relationships

Innovation

• LLM generates tailored constitutive neural networks
• Automates architecture selection and physical constraint integration
• Produces code achieving expert-level accuracy and generalization