Застосування нейронних мереж для розв’язання крайових задач для звичайних диференціальних рівнянь

Abstract

This paper considers application of feed-forward neural networks to solving boundary value problems for ordinary differential equations. As universal function approximators, neural networks can help dealing with the problems on which classical methods fail, including those with non-linearity, high dimentionality, and complex domain boundary. Particularly, we show how to construct an objective function to fit the feed-forward neural network approximating a solution to an ordinary differential equation with mixed boundary conditions.