Neural Network Methods for Boundary Value Problems Defined in Arbitrarily Shaped Domains
Neural and Evolutionary Computing
2007-05-23 v1 Disordered Systems and Neural Networks
Numerical Analysis
Mathematical Physics
math.MP
Numerical Analysis
Computational Physics
Abstract
Partial differential equations (PDEs) with Dirichlet boundary conditions defined on boundaries with simple geometry have been succesfuly treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a reasonable representation. Two networks are employed: a multilayer perceptron and a radial basis function network. The later is used to account for the satisfaction of the boundary conditions. The method has been successfuly tested on two-dimensional and three-dimensional PDEs and has yielded accurate solutions.
Cite
@article{arxiv.cs/9812003,
title = {Neural Network Methods for Boundary Value Problems Defined in Arbitrarily Shaped Domains},
author = {I. E. Lagaris and A. Likas and D. G. Papageorgiou},
journal= {arXiv preprint arXiv:cs/9812003},
year = {2007}
}