Comparative testing of algorithms for constructing an approximate neural network and finite-element solutions of the model boundary value problem

Abstract

In this paper we study two methods for solving the boundary value problem for the Laplace equation in the unit square. The first is based on the application of the square of the discrepancy to satisfy the Laplace equation, the second is based on the application of the energy functional. We compare the results obtained using functions characteristic of the finite element method and neural networks. Also, we implement a quality assessment and comparison of the approximate solution methods for different sampling point selection methods.