Learning solutions to two dimensional electromagnetic equations using LS-SVM

Abstract In this paper, a new approach based on least squares support vector machines (LS-SVM) is proposed for solving the electromagnetic equations. Firstly, the cubic spline function is employed to smooth the discontinuous boundary. LS-SVM is used to solve the modified problem. Secondly, nonlinear electromagnetic equation is solved by LS-SVM. Finally, multimedia electromagnetic equation is solved by LS-SVM. Same as to the artificial neural networks (ANN), the approximate solutions are composed of two parts. The first part is a known function that satisfies the boundary conditions. The second part is the product of two terms. One term is also a known function which vanished on the boundary. The left part is the combination of kernel functions containing regression parameters. The parameters can be obtained by solving a system of equations. The numerical results show that the proposed method in this paper is feasible.