Learning Radial Basis Functions Networks in Solving Boundary Value Problems

The authors considered the solution of boundary problems, arising from objects modeling with distributed parameters, of radial basis functions networks. The gradient algorithms analysis for learning radial basis functions networks when solving boundary value problems is carried out. The widely used the first order method-the gradient method descent does not provide high learning rate and the solution accuracy. The fastest of the second order method - the method of trust regions is very complicated. Developed implementations of the first order method-the accelerated Nesterov gradient and the second order method-Levenberg Marquardt for learning radial basic functions networks in solving boundary value problems. A comparison is made of the Levenberg Marquardt methods and trust regions for learning radial basis functions networks. The results are presented of solving model problem using the developed methods. The Levenberg-Marquardt method, with a simpler implementation, showed the results compared with the fastest method of the second order - the method of trust regions.