New Neural Network Technique to the Numerical Solution of Mathematical Physics Problems. II: Complicated and Nonstandard Problems

摘要

Neural networks are considered to be the new universal approach to the construction of mathematical models of systems with distributed parameters. These networks allow us to effectively find the approximate solutions of initial and boundary problems for partial differential equations and to take nonlinear effects and coefficient perturbations into account. Neural networks of known and new architecture are applied to the solution of Laplace, Helmholtz, and Schrodinger; heat conduction equations in domains with the fixed, free and controlled boundaries; and original training algorithms of these networks are given. This paper is composed of two parts. Part 2 deals with more complicated and nonstandard problems.