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
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:66062-66083, 2025.

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 this Paper

BibTeX
@InProceedings{pmlr-v267-wei25e, 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}, pages = {66062--66083}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/wei25e/wei25e.pdf}, url = {https://proceedings.mlr.press/v267/wei25e.html}, 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.} }
Endnote
%0 Conference Paper %T Closed-form Solutions: A New Perspective on Solving Differential Equations %A Shu Wei %A Yanjie Li %A Lina Yu %A Weijun Li %A Min Wu %A Linjun Sun %A Jingyi Liu %A Hong Qin %A Yusong Deng %A Jufeng Han %A Yan Pang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-wei25e %I PMLR %P 66062--66083 %U https://proceedings.mlr.press/v267/wei25e.html %V 267 %X 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.
APA
Wei, S., Li, Y., Yu, L., Li, W., Wu, M., Sun, L., Liu, J., Qin, H., Deng, Y., Han, J. & Pang, Y.. (2025). Closed-form Solutions: A New Perspective on Solving Differential Equations. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:66062-66083 Available from https://proceedings.mlr.press/v267/wei25e.html.

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