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

作者：Chen Hong^*; Kong Li; Leng Wen Jun

来源：Applied Soft Computing, 2011, 11(1): 855-860.

DOI：10.1016/j.asoc.2010.01.005

• Radial basis functions
• Approximation
• Partial differential equation
• Collocation

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.

• 出版日期2011-1
• 单位武汉第二船舶设计研究所; 华中科技大学