Solving Equations Describing Processes in a Piecewise Homogeneous Medium on Radial Basis Functions Networks

摘要

The solution of boundary value problems describing piecewise-homogeneous media on networks of radial basis functions is considered. The proposed algorithm is based on solving individual problems for each area with different properties of the medium and using a common error functional that takes into account errors at the interface between the media. This removes the restrictions on the use of radial basis functions and allows the use of radial basis functions with both unlimited and limited definition areas. We used the fast algorithm proposed by the authors for training networks of radial basis functions by the Levenberg-Marquardt method with analytical calculation of the Jacobi matrix. The algorithm makes it possible to reduce the number of iterations by several orders of magnitude compared to the gradient descent algorithm currently used and to obtain the accuracy of the solution, which is practically unattainable by the gradient descent algorithm. The results of solving the model problem showed the effectiveness of the proposed algorithm.