Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
作者： Tianping Chen , Hong Chen
DOI: 10.1109/72.392253
关键词: Fixed point 、 Dynamical systems theory 、 Artificial neural network 、 Mathematical analysis 、 Function approximation 、 Dynamical system (definition) 、 Topology 、 Activation function 、 Mathematics 、 Continuous function 、 Nonlinear system
摘要: The purpose of this paper is to investigate neural network capability systematically. main results are: 1) every Tauber-Wiener function qualified as an activation in the hidden layer a three-layered network; 2) for continuous S'(R/sup 1/) be function, necessary and sufficient condition that it not polynomial; 3) approximating nonlinear functionals defined on some compact set Banach space operators has been shown; 4) possibility by computation approximate output whole (not at fixed point) dynamical system, thus identifying system. >
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