Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
- 1 July 1995
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Neural Networks
- Vol. 6 (4), 911-917
- https://doi.org/10.1109/72.392253
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.Keywords
This publication has 12 references indexed in Scilit:
- Approximations of continuous functionals by neural networks with application to dynamic systemsIEEE Transactions on Neural Networks, 1993
- Approximation by superposition of sigmoidal and radial basis functionsAdvances in Applied Mathematics, 1992
- Approximations for nonlinear functionsIEEE Transactions on Circuits and Systems I: Regular Papers, 1992
- Approximation theorems for discrete-time systemsIEEE Transactions on Circuits and Systems, 1991
- Gradient methods for the optimization of dynamical systems containing neural networksIEEE Transactions on Neural Networks, 1991
- Identification and control of dynamical systems using neural networksIEEE Transactions on Neural Networks, 1990
- On the approximate realization of continuous mappings by neural networksNeural Networks, 1989
- Multilayer feedforward networks are universal approximatorsNeural Networks, 1989
- Approximation by superpositions of a sigmoidal functionMathematics of Control, Signals, and Systems, 1989
- Construction of neural nets using the radon transformPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1989