Neuro-monte carlo solution of electrostatic problems

Abstract

This paper presents the use of artificial neural networks (ANNs) in solving electrostatic boundary value problems. In forming a solution system, one ANN is combined with one Monte Carlo method (namely, the floating random walk or the Markov chain method). Two separate Neuro-Monte Carlo systems are used to solve Laplace's and Poisson's equations for homogeneous and inhomogeneous problems. Neuro-Monte Carlo solutions reflect higher computation speed without loss of accuracy or significant “down time” with respect to the time needed to train the ANN with the data obtained from the partial solution using a Monte Carlo method.