Title :
Numerical solution of elliptic partial differential equation by growing radial basis function neural networks
Author :
Li, Jianyu ; Luo, Siwei ; Qi, Yingjian ; Huang, Yaping
Author_Institution :
Dept. of Comput. Sci., Northern Jiaotong Univ., Beijing, China
Abstract :
In this paper a neural network for solving partial differential equations (PDE) is described. The activation functions of the hidden nodes are the radial basis functions (RBF) whose parameters are learnt by a two-stage gradient descent strategy. A new growing radial basis functions-node insertion strategy with different radial basis functions is used in order to improve the net performances. The learning strategy is able to save computational time and memory space because of the selective growing of nodes whose activation functions consist of different radial basis functions. An analysis of the learning capabilities and a comparison of the net performances with other approaches have been performed. It is shown that the resulting network improves the approximation results.
Keywords :
learning (artificial intelligence); partial differential equations; radial basis function networks; elliptical partial differential equation; growing radial basis function neural networks; learning capabilities; two-stage gradient descent strategy; Broadcasting; Computer science; Differential equations; Educational institutions; Finite difference methods; Neural networks; Partial differential equations; Radial basis function networks; Scattering; Stability;
Conference_Titel :
Neural Networks, 2003. Proceedings of the International Joint Conference on
Print_ISBN :
0-7803-7898-9
DOI :
10.1109/IJCNN.2003.1223302