Closed-Form Solutions: A New Perspective on Solving 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.
Cite
Text
Wei et al. "Closed-Form Solutions: A New Perspective on Solving Differential Equations." Proceedings of the 42nd International Conference on Machine Learning, 2025.Markdown
[Wei et al. "Closed-Form Solutions: A New Perspective on Solving Differential Equations." Proceedings of the 42nd International Conference on Machine Learning, 2025.](https://mlanthology.org/icml/2025/wei2025icml-closedform/)BibTeX
@inproceedings{wei2025icml-closedform,
title = {{Closed-Form Solutions: A New Perspective on Solving Differential Equations}},
author = {Wei, Shu and Li, Yanjie and Yu, Lina and Li, Weijun and Wu, Min and Sun, Linjun and Liu, Jingyi and Qin, Hong and Deng, Yusong and Han, Jufeng and Pang, Yan},
booktitle = {Proceedings of the 42nd International Conference on Machine Learning},
year = {2025},
pages = {66062-66083},
volume = {267},
url = {https://mlanthology.org/icml/2025/wei2025icml-closedform/}
}