Symbolic Neural Architecture Search for Differential Equations

Abstract

In this paper, we introduce the first use of symbolic integration that leverages the machine learning infrastructure, such as automatic differentiation, to find analytical approximations of ordinary and partial differential equations. Analytical solutions to differential equations are at the core of fundamental mathematical models, which often cannot be determined analytically because of model complexity or non-linearity. Traditionally, the methods for solving these problems have used hand-designed strategies, numerical methods, or iterative methods. We propose a method that is an application of differentiable architecture search to find solutions to differential equations. We demonstrate our proposed method on a set of equations while simultaneously comparing it with numerical solutions to corresponding problems. We demonstrate that the proposed framework allows for solutions to various problems.

Keywords

• Symbolic integration
• machine learning
• PDE
• neural architecture search