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

TL;DR

This paper introduces a graph-based equation discovery method to automatically derive new constitutive laws from experimental data, improving model accuracy and interpretability in solid mechanics.

Contribution

It presents a novel graph-based framework for discovering symbolic constitutive models directly from data, surpassing traditional empirical approaches.

Findings

Discovered new models for strain-rate effects in alloy steel.

Achieved higher accuracy with compact analytical models.

Demonstrated generalizability in complex physical phenomena.

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.