Solving Ordinary Differential Equations by means of an Artificial Neural Network

Abstract

This paper describes a method for the numerical solution of ordinary differential equations using an artificial neural network. Unlike other reported methods, the loss function is constructed from the same formalization of the differential equation and is done using Pytorch computational resources for self-differentiation. The proposed method is applied in the resolution of four types of differential equations and the results obtained are shown. The design of the resulting neural network was oriented to its subsequent implementation in reconfigurable logic.