Evolving Equation Learner For Symbolic Regression

Abstract

Symbolic regression, a multifaceted optimization challenge involving the refinement of both structural components and coefficients, has gained significant research interest in recent years. The Equation Learner (EQL), a neural network designed to optimize both equation structure and coefficients through gradient-based optimization algorithms, has emerged as an important topic of concern within this field. Thus far, several variations of EQL have been introduced. Nevertheless, these existing EQL methodologies suffer from a fundamental constraint that they necessitate a predefined network structure. This limitation imposes constraints on the complexity of equations and makes them ill-suited for high-dimensional or high-order problem domains. To tackle the aforementioned shortcomings, we present a novel approach known as the evolving Equation Learner (eEQL). eEQL introduces a unique network structure characterized by automatically defined functions (ADFs). This new architectural design allows for dynamic adaptations of the network structure. Moreover, by engaging in self-learning and self-evolution during the search process, eEQL facilitates the generation of intricate, high-order, and constructive sub-functions. This enhancement can improve the accuracy and efficiency of the algorithm. To evaluate its performance, the proposed eEQL method has been tested across various datasets, including benchmark datasets, physics datasets, and real-world datasets. The results have demonstrated that our approach outperforms several well-known methods.