AI Extracts Interpretable Constitutive Laws From Solid Mechanics Data

Researchers at the Eastern Institute of Technology in Ningbo have developed an artificial intelligence framework that autonomously extracts interpretable constitutive equations directly from solid-mechanics experimental data. Published in Science Advances, the study introduces GraphED, a graph-based equation discovery system that significantly improves predictive accuracy over conventional empirical models while preserving explicit, physically meaningful mathematical structures. Traditional constitutive modeling in solid mechanics relies on predefined mathematical forms derived from physical intuition, followed by parameter calibration against experimental data. This approach inherently limits descriptive and predictive capabilities, particularly for complex metallic and nonmetallic materials. The GraphED framework shifts this paradigm by treating constitutive equation discovery as a computational optimization problem. Instead of relying on fixed equation architectures, the system encodes mathematical expressions as directed graphs. In this structure, nodes represent physical variables and mathematical operators, while edges define their logical relationships, fixed constants, and tunable material-specific parameters. This graph-based representation enables the simultaneous optimization of equation topology and material parameterization. The framework iteratively generates, evaluates, and refines candidate graph-structured equations, filtering for physically consistent, computationally compact, and human-interpretable laws that maintain high predictive fidelity. Lead author Hao Xu and co-corresponding author Yuntian Chen noted that this approach resolves the critical bottleneck of efficiently encoding equation architectures into machine-searchable formats. The researchers validated GraphED across three distinct material systems exhibiting complex mechanical behaviors. For alloy steels, the model autonomously discovered explicit equations governing strain-rate dependence and strain-hardening, delivering superior predictive accuracy compared to the widely used Johnson-Cook model. In the case of lithium metal, a material critical to next-generation energy devices whose behavior is highly sensitive to temperature and strain rate, GraphED generated concise plastic-flow constitutive equations that closely matched experimental measurements. The framework also successfully captured compact hyperelastic constitutive equations for filled rubbers, maintaining robust accuracy across varying compositions and thermal conditions. Dongxiao Zhang, chair professor and corresponding author, emphasized that traditional empirical models often fail to adequately describe complex material responses. By enabling direct extraction of rigorous mathematical descriptions from observational data, graph-based AI establishes a new research paradigm. Beyond computational mechanics and materials science, the GraphED framework demonstrates broad applicability to any discipline seeking interpretable physical laws directly from experimental datasets. This advancement marks a significant step toward automated, physics-informed model discovery that balances data-driven flexibility with analytical transparency.