Symbolically Solving Partial Differential Equations using Deep Learning

• URL: http://arxiv.org/abs/2011.06673v1
• Date: Thu, 12 Nov 2020 22:16:03 GMT
• Title: Symbolically Solving Partial Differential Equations using Deep Learning
• Authors: Maysum Panju, Kourosh Parand, Ali Ghodsi
• Abstract summary: We describe a neural-based method for generating exact or approximate solutions to differential equations. Unlike other neural methods, our system returns symbolic expressions that can be interpreted directly.
• Score: 5.1964883240501605
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted directly. Our method uses a neural architecture for learning mathematical expressions to optimize a customizable objective, and is scalable, compact, and easily adaptable for a variety of tasks and configurations. The system has been shown to effectively find exact or approximate symbolic solutions to various differential equations with applications in natural sciences. In this work, we highlight how our method applies to partial differential equations over multiple variables and more complex boundary and initial value conditions.

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