title: Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems.
abstract: The purpose of this paper is to investigate neural network capability systematically. The main results are: 1) every Tauber-Wiener function is qualified as an activation function in the hidden layer of a three-layered neural network; 2) for a continuous function in S'(R(1 )) to be a Tauber-Wiener function, the necessary and sufficient condition is that it is not a polynomial; 3) the capability of approximating nonlinear functionals defined on some compact set of a Banach space and nonlinear operators has been shown; and 4) the possibility by neural computation to approximate the output as a whole (not at a fixed point) of a dynamical system, thus identifying the system.
authors.affiliation: Dept. of Math., Fudan Univ., Shanghai.
authors.forename: T
authors.initials: T
authors.lastname: Chen
authors.forename: H
authors.initials: H
authors.lastname: Chen