Unified approach to constructing the neural network models of real objects. Part 1

Abstract

This article is a two‐part composition. It describes the basics of the methodology developed by the authors to construct approximate neural network solutions of ordinary and partial differential equations. The methodology is illustrated with the sample tasks, ie, for compound domains (with a different type of equations in the subdomains) in the first part, for a variable boundary (caused by phase transition), for a selected boundary, with some heterogeneous information, which includes differential equations, initial and boundary conditions, and experimental and other data in the second part. We show that these different tasks are solved uniformly with the application of general principles.