Neural-network methods for boundary value problems with irregular boundaries

Partial differential equations (PDEs) with boundary conditions (Dirichlet o r Neumann) defined on boundaries with simple geometry hare been successfull y treated using sigmoidal multilayer perceptrons in previous works. This ar ticle deals,vith the case of complex: boundary geometry, where the boundary is determined by a number of points that belong to it and are closely loca ted, 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 exact satisfaction of the boundary conditions, The method has been successfully tested on two-dimensional and three-dimensiona l PDEs and has yielded accurate results.