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
Abstract
The pursuit of analytical solutions for differential equations has historically been limited by the need for extensive prior knowledge and mathematical prowess; however, machine learning methods like genetic algorithms have recently been applied to this end, albeit with issues of significant time consumption and complexity. This paper presents a novel machine learning-based solver, SSDE (Symbolic Solver for Differential Equations), which employs reinforcement learning to derive symbolic closed-form solutions for various differential equations. Our evaluations on a range of ordinary and partial differential equations demonstrate that SSDE provides superior performance in achieving analytical solutions compared to other machine learning approaches.
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