UDC 519.632
DOI: 10.36871/2618-9976.2023.09.010
Authors
Tatyana V. Lazovskaya,
Senior Lecturer, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia. Peter
the Great, St. Petersburg, Russia
Dmitriy M. Pashkovsky,
Student, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia. Peter the Great,
St. Petersburg, Russia
Dmitry A. Tarkhov,
Doctor of Technical Sciences, Professor, Peter the Great St. Petersburg Polytechnic University,
St. Petersburg, Russia
Abstract
An algorithm for neural network approximation of the solution
of a boundary value problem for the twodimensional
Laplace
equation on a square domain is proposed. An approximate solution
of the Laplace equation is a radial basis neural network with
one hidden layer (RBF network). Optimal parameters of the RBF
network are obtained from the minimization problem of the
quadratic functional for the Laplace equation.
In our work we also proposed an algorithm for choosing the
minimum number of neurons on the hidden layer of the RBFnetwork
for a given accuracy of the approximate solution. Two
problems for Laplace equation with different boundary conditions
were considered. In the first problem for the Laplace equation,
we set discontinuous boundary conditions in the corners
of the square, and in the second problem we set regular boundary
conditions with error.
Keywords
Laplace equation, RBF neural network, Solution approximation, Neural net architecture search
