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

Shu Wei, Yanjie Li, Lina Yu, Weijun Li, Min Wu, Linjun Sun, Jingyi Liu, Hong Qin, Yusong Deng, Jufeng Han, Yan Pang

TL;DR: A novel solver for differential equations based on reinforcement learning

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.

Lay Summary:

Solving differential equations—mathematical formulas used to describe how things change over time and space—is a fundamental task in science and engineering. Traditionally, finding exact solutions to these equations requires advanced math skills and often involves tedious manual work. While machine learning has offered some help, existing methods are often slow and produce results that are hard to understand.

In this work, we present SSDE, a new AI-based tool that uses reinforcement learning to automatically discover clean, human-readable solutions to different types of differential equations. Unlike previous methods, SSDE is both faster and more accurate. This makes it a promising step toward making powerful mathematical tools more accessible and automating complex tasks in physics, biology, and beyond.

Link To Code: https://github.com/Hintonein/SSDE

Primary Area: Applications->Chemistry, Physics, and Earth Sciences

Keywords: Reinforcement learning, Closed-form solution, Differential equations, Policy gradient.

Submission Number: 10005