A neural method for symbolically solving partial differential equations

Anonymous

Keywords: Symbolic mathematics, neuro-symbolic computation, differential equations, deep learning

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.

One-sentence Summary: We describe and demonstrate a neural-based method for obtaining exact or approximate symbolic solutions to partial differential equations over multiple variables..

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