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
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.
BibTeX
@inproceedings{
wei2025closedform,
title={Closed-form Solutions: A New Perspective on Solving Differential Equations},
author={Shu Wei and Yanjie Li and Lina Yu and Weijun Li and Min Wu and Linjun Sun and Jingyi Liu and Hong Qin and Yusong Deng and Jufeng Han and Yan Pang},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=AIx21InAn2}
}