A Neuro-Symbolic Method for Solving Differential and Functional Equations

• URL: http://arxiv.org/abs/2011.02415v1
• Date: Wed, 4 Nov 2020 17:13:25 GMT
• Title: A Neuro-Symbolic Method for Solving Differential and Functional Equations
• Authors: Maysum Panju, Ali Ghodsi
• Abstract summary: We introduce a method for generating symbolic expressions to solve differential equations. Unlike existing methods, our system does not require learning a language model over symbolic mathematics. We show how the system can be effortlessly generalized to find symbolic solutions to other mathematical tasks.
• Score: 6.899578710832262
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions to solve differential equations while leveraging deep learning training methods. Unlike existing methods, our system does not require learning a language model over symbolic mathematics, making it scalable, compact, and easily adaptable for a variety of tasks and configurations. As part of the method, we propose a novel neural architecture for learning mathematical expressions to optimize a customizable objective. The system is designed to always return a valid symbolic formula, generating a useful approximation when an exact analytic solution to a differential equation is not or cannot be found. We demonstrate through examples how our method can be applied on a number of differential equations, often obtaining symbolic approximations that are useful or insightful. Furthermore, we show how the system can be effortlessly generalized to find symbolic solutions to other mathematical tasks, including integration and functional equations.

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