Symbolic Regression as Feature Engineering Method for Machine and Deep Learning Regression Tasks

Abstract

In the realm of machine and deep learning regression tasks, the role of effective feature engineering (FE) is pivotal in enhancing model performance. Traditional approaches of FE often rely on domain expertise to manually design features for machine learning models. In the context of deep learning models, the FE is embedded in the neural network's architecture, making it hard for interpretation. In this study, we propose to integrate symbolic regression (SR) as an FE process before a machine learning model to improve its performance. We show, through extensive experimentation on synthetic and real-world physics-related datasets, that the incorporation of SR-derived features significantly enhances the predictive capabilities of both machine and deep learning regression models with 34-86% root mean square error (RMSE) improvement in synthetic datasets and 4-11.5% improvement in real-world datasets. In addition, as a realistic use-case, we show the proposed method improves the machine learning performance in predicting superconducting critical temperatures based on Eliashberg theory by more than 20% in terms of RMSE. These results outline the potential of SR as an FE component in data-driven models.