Numerical solution of PDEs via integrated radial basis function networks with adaptive training algorithm

Authors:
Hong Chen;Li Kong;Wen-Jun Leng
Affiliations:
Department of Control Science and Engineering, Huazhong University of Science and Technology, Zhong Shan Road #450, Wuhan 430074, China and Wuhan Second Ship Design and Research Institute, Wuhan 4 ...;Department of Control Science and Engineering, Huazhong University of Science and Technology, Zhong Shan Road #450, Wuhan 430074, China;Wuhan Second Ship Design and Research Institute, Wuhan 430064, China
Venue:
Applied Soft Computing
Year:
2011

Citing 6
Cited 3

Universal approximation using radial-basis-function networks

Neural Computation
Numerical solution of differential equations using multiquadric radial basis function networks

Neural Networks
Adaptive residual subsampling methods for radial basis function interpolation and collocation problems

Computers & Mathematics with Applications
Adaptive radial basis function methods for time dependent partial differential equations

Applied Numerical Mathematics
Integrated multiquadric radial basis function approximation methods

Computers & Mathematics with Applications
Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximation

IEEE Transactions on Neural Networks

Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: A survey

Computers & Mathematics with Applications
Intelligent control of a constant turning force system with fixed metal removal rate

Applied Soft Computing
Solving differential equations with Fourier series and Evolution Strategies

Applied Soft Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper develops a mesh-free numerical method for solving PDEs, based on integrated radial basis function networks (IRBFNs) with adaptive residual subsampling training scheme. The multiquadratic function is chosen as the transfer function of the neurons. The nonlinear algebraic equation systems for weights training are solved by Levenberg-Marquardt algorithm. The performance of the proposed method is demonstrated in numerical examples by approximating several functions and solving nonlinear PDEs. The result of numerical experiments shows that the IRBFNs with the adaptive procedure requires less neurons to attain the desired accuracy than conventional radial basis function networks.