Symbolically Solving Partial Differential Equations using Deep Learning
This addresses the problem of obtaining interpretable solutions for differential equations in natural sciences, though it appears incremental as an extension of existing neural expression methods to PDEs.
The authors developed a neural-based method that generates exact or approximate symbolic solutions to partial differential equations, which can be directly interpreted as mathematical expressions and applied to complex boundary and initial value conditions.
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.