Genetic Programming Based Symbolic Regression for Analytical Solutions to Differential Equations

TL;DR

This paper introduces a genetic programming-based symbolic regression method to discover true analytic solutions to differential equations, emphasizing interpretability and accuracy over traditional numerical approximations.

Contribution

It presents a novel, interpretable machine learning approach for analytically solving differential equations, outperforming conventional data-driven methods in recovering true solutions.

Findings

Successfully recovers known analytic solutions

Demonstrates reliability in evolving true or equivalent solutions

Outperforms conventional symbolic regression methods

Abstract

In this paper, we present a machine learning method for the discovery of analytic solutions to differential equations. The method utilizes an inherently interpretable algorithm, genetic programming based symbolic regression. Unlike conventional accuracy measures in machine learning we demonstrate the ability to recover true analytic solutions, as opposed to a numerical approximation. The method is verified by assessing its ability to recover known analytic solutions for two separate differential equations. The developed method is compared to a conventional, purely data-driven genetic programming based symbolic regression algorithm. The reliability of successful evolution of the true solution, or an algebraic equivalent, is demonstrated.