ニューロ・ファジィ有限要素法と誤差解析

抄録

For approximating nonlinear mappings, especially interpolating the datapoints in a high dimensional space, RBF networks with adaptive learning algorithm are attracting a great deal of interest due to their rapid training, generality and simplicity. RBF network is interpreted as three-layered neural networks and/or fuzzy reasoning rules.
In this paper, we propose a neuro-fuzzy method to find a solution of partial differential equations. The elements in Finite Element Method (FEM) are replaced by fuzzy subsets defined by Gaussian membership functions, and the adaptive learning method is employed.
For almost all problems in practical engineering where FEM is applied, the analytical solutions are not obtained. Hence, the approximate solution of FEM needs some tools for error estimation. So a method of error estimation based on the neuro-fuzzy scheme is also proposed.