GEPINN: An innovative hybrid method for a symbolic solution to the Lane–Emden type equation based on grammatical evolution and physics-informed neural networks

Abstract

In this paper, we present an innovative and powerful combination of grammatical evolution and a physics-informed neural network approach for symbolically solving the Lane–Emden type equation, which is a nonlinear ordinary differential equation. We employ a grammatical evolution algorithm based on a context-free grammar to construct a mathematical expression comprising some parameters. Subsequently, these parameters are determined using the physics-informed neural networks approach. To achieve this, the computational graph of the mathematical expression generated in each iteration of the grammatical evolution is treated as a network. To assess the proposed method, we consider the Lane–Emden type equation. The proposed method demonstrated that it is a capable method for symbolically solving nonlinear ordinary differential equations accurately.