Extraction of physicochemical laws by symbolic regression using a Bayesian information criterion

Abstract

In the search for new high-performance materials in materials science, especially in polynomial science, it is important to use physicochemical laws linking materials structure and physical properties, and predict the physical properties required for the design. Recently, machine learning (ML) has enabled us to extract patterns from large datasets and construct the data-driven model to predict physical properties. However, ML approach faces challenges such as interpretability and systematic errors of the data-driven model with limited data. Here, we propose a method for extracting an interpretable law from limited data, by combining a symbolic regression method and Bayesian information criterion. We focus on extracting a physicochemical law for the refractive index of polymer materials. The goal is to correct systematic errors and capture physicochemical laws more accurately. Combining explanatory variables from experiments, property calculations, and neural potential approximations, our method involves arithmetic operations on explanatory variables and selection through Bayesian information criterion. The results show that the proposed method is able to correct the results of the neural potential approximation and obtain interpretable and concise expressions for the physicochemical laws linking material structure and physical properties.

Keywords

• Symbolic regression
• Bayesian information criterion
• refractive index
• polymer materials
• neural potential approximation