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

TL;DR

This work introduces GenCANNs, an on-demand framework where a large language model designs physics-constrained constitutive neural networks (CANNs) tailored to specific materials and datasets. By combining a two-part LLM prompt with a preprocessing–network–postprocessing pipeline, GenCANNs achieve high fidelity to experimental data and strong generalization to unseen loading paths, often matching or surpassing hand-crafted CANNs and outperforming the prior SGA-based approach. Across brain tissue, rubber, and skin benchmarks, GenCANNs demonstrate robustness, extrapolation capability, and relative data efficiency, signaling a viable path toward end-to-end automation in constitutive modeling. The results point to a practical impact in materials design and biomedical simulations by reducing the expert labor required to develop accurate, physics-consistent constitutive descriptions.

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.

Figures (15)

• Figure 1: Evolution of constitutive modeling in solid mechanics over time. Until the 2010s, scientists manually derived constitutive models to describe experimental observations. Recent data-driven methods, such as constitutive artificial neural networks (CANNs), partially automate model implementation and fully automate model calibration. Our framework leverages LLMs to generate CANNs on demand, pushing towards complete end-to-end automation.
• Figure 2: Process of the LLM-based generation of a constitutive artificial neural network (CANN). Static code translates the material classification into a prompt that includes a task description, continuum mechanics theory, formal requirements, and a rough CANN code skeleton, prompting the LLM to implement a CANN tailored to the specific modeling task. The resulting CANN is then trained and evaluated on experimental data and iteratively refined.
• Figure 3: Predictions of the LLM-generated constitutive artificial neural network (GenCANN) for mechanical stress induced by brain tissue deformation compared against two benchmarks: the LLM-based constitutive scientific generative agent (CSGA) and the human-designed CANN.
• Figure 4: Predictions of the LLM-generated constitutive artificial neural network (GenCANN) for mechanical stress induced by rubber deformation compared against two benchmarks: the LLM-based constitutive scientific generative agent (CSGA) and the human-designed CANN.
• Figure 5: Predictions of the LLM-generated constitutive artificial neural network (GenCANN) for mechanical stress induced by deformation of a fictitious rubber-like material compared against two benchmarks: the LLM-based constitutive scientific generative agent (CSGA) and the human-designed CANN.