Neural networks represent a class of functions for the efficient identification and forecasting of dynamical systems. It has been shown that feedforward networks are able to approximate any (Borel-)measurable function on a compact domain [1,2,3], Recurrent neural networks (RNNs) have been developed for a better understanding and analysis of open dynamical systems. Compared to feed-forward networks they have several advantages which have been discussed extensively in several papers and books, e.g. [4]. Still the question often arises if RNNs are able to map every open dynamical system, which would be desirable for a broad spectrum of applications. In this paper we give a proof for the universal approximation ability of RNNs in state space model form. The proof is based on the work of Hornik, Stinchcombe, and White about feedforward neural networks [1]. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Schäfer, A. M., & Zimmermann, H. G. (2006). Recurrent neural networks are universal approximators. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4131 LNCS-I, pp. 632–640). Springer Verlag. https://doi.org/10.1007/11840817_66
Mendeley helps you to discover research relevant for your work.