Beyond empirical models: Discovering new constitutive laws in solids with graph-based equation discovery

2025-11-13

AI Summary

Traditional constitutive models rely on pre-specified functional forms, suffering from poor generalizability and limited interpretability. To address this, we propose a graph-structured equation discovery framework: symbolic expressions are modeled as parameter-dependent directed graphs, where nodes represent variables and operators, and edges encode computational relationships and parameter dependencies. Integrating graph neural networks with symbolic regression, our method enables end-to-end joint optimization of constitutive equation structure and parameters. Crucially, it operates without expert-defined priors, supporting discovery of arbitrary physical relations directly from data. Evaluated on strain-rate effects in alloy steel and deformation modeling of lithium metal, the framework automatically discovers novel constitutive models that are structurally more compact and achieve significantly higher prediction accuracy than classical empirical models. These results demonstrate its effectiveness and interpretability for modeling complex material responses.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Constitutive models are fundamental to solid mechanics and materials science, underpinning the quantitative description and prediction of material responses under diverse loading conditions. Traditional phenomenological models, which are derived through empirical fitting, often lack generalizability and rely heavily on expert intuition and predefined functional forms. In this work, we propose a graph-based equation discovery framework for the automated discovery of constitutive laws directly from multisource experimental data. This framework expresses equations as directed graphs, where nodes represent operators and variables, edges denote computational relations, and edge features encode parametric dependencies. This enables the generation and optimization of free-form symbolic expressions with undetermined material-specific parameters. Through the proposed framework, we have discovered new constitutive models for strain-rate effects in alloy steel materials and the deformation behavior of lithium metal. Compared with conventional empirical models, these new models exhibit compact analytical structures and achieve higher accuracy. The proposed graph-based equation discovery framework provides a generalizable and interpretable approach for data-driven scientific modelling, particularly in contexts where traditional empirical formulations are inadequate for representing complex physical phenomena.

Problem

• Automating discovery of constitutive laws from multisource experimental data
• Overcoming limitations of traditional empirical phenomenological material models
• Developing interpretable equations for complex material behaviors using graphs

Innovation

• Graph-based equation discovery for constitutive laws
• Generating free-form symbolic expressions from data
• Automated framework with interpretable graph structures