Closed-form Solutions: A New Perspective on Solving Differential Equations

TL;DR

This paper presents SSDE, a reinforcement learning-based method that efficiently derives symbolic closed-form solutions for differential equations, outperforming existing machine learning approaches in accuracy and speed.

Contribution

Introduction of SSDE, a novel reinforcement learning approach for solving differential equations analytically, improving upon prior machine learning methods.

Findings

SSDE achieves higher accuracy than previous methods.

SSDE reduces computational time significantly.

SSDE successfully solves a diverse set of differential equations.

Abstract

The quest for analytical solutions to differential equations has traditionally been constrained by the need for extensive mathematical expertise. Machine learning methods like genetic algorithms have shown promise in this domain, but are hindered by significant computational time and the complexity of their derived solutions. This paper introduces SSDE (Symbolic Solver for Differential Equations), a novel reinforcement learning-based approach that derives symbolic closed-form solutions for various differential equations. Evaluations across a diverse set of ordinary and partial differential equations demonstrate that SSDE outperforms existing machine learning methods, delivering superior accuracy and efficiency in obtaining analytical solutions.