Eastern Institute of Technology, Ningbo Researchers Propose Symbolic Regression Framework GraphED

Researchers from the Eastern Institute of Technology, Ningbo (EIT), led by chair professor Zhang Dongxiao and associate professor Chen Yuntian, have proposed a new symbolic regression framework called GraphED, which builds an AI scientist to automatically discover constitutive laws. The findings were published in Science Advances.

Constitutive laws describe how solid materials deform under force. Traditional empirical or semi-empirical models are often simple but lack generalization beyond calibration ranges, while neural network black-box models provide high fitting accuracy but suffer from poor interpretability. Recent symbolic regression methods based on tree structures tend to generate lengthy or physically meaningless formulas.

The GraphED framework addresses these issues by simultaneously analyzing data from multiple materials and conditions. It identifies material parameters for each dataset while searching for formula structures, integrating data across different scenarios and reducing dependence on single datasets. The framework adopts an "equation-as-graph" paradigm, representing mathematical formulas as directed acyclic graphs, where nodes denote operators and variables, edges denote operation directions, and edge features encode constants or material parameters.

According to first author Xu Hao, an associate researcher at EIT, the design overcomes the limitations of traditional representations in characterizing parameterized formula families, allowing the algorithm to learn expressions with both general structure and material-related parameters from multi-source datasets. The team has applied GraphED to experimental data for alloy steel, lithium metal, and oil-filled rubber, achieving results surpassing traditional empirical models.