Exploring the mathematic equations behind the materials science data using interpretable symbolic regression

Symbolic regression (SR), exploring mathematical expressions from a given data set to construct an interpretable model, emerges as a powerful computational technique with the potential to transform the “black box” machining learning methods into physical and chemistry interpretable expressions in material science research. In this review, the current advancements in SR are investigated, focusing on the underlying theories, fundamental flowcharts, various techniques, implemented codes, and application fields. More predominantly, the challenging issues and future opportunities in SR that should be overcome to unlock the full potential of SR in material design and research, including graphics processing unit acceleration and transfer learning algorithms, the trade-off between expression accuracy and complexity, physical or chemistry interpretable SR with generative large language models, and multimodal SR methods, are discussed.