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

• URL: http://arxiv.org/abs/2405.14620v2
• Date: Mon, 10 Feb 2025 15:01:34 GMT
• Title: Closed-form Solutions: A New Perspective on Solving Differential Equations
• Authors: Shu Wei, Yanjie Li, Lina Yu, Weijun Li, Min Wu, Linjun Sun, Jufeng Han, Yan Pang,
• Abstract summary: This paper presents a novel machine learning-based solver, SSDE, 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.
• Score: 12.048106653998044
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• 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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