Back-propagation learning of infinite-dimensional dynamical systems

Authors:
Isao Tokuda;Ryuji Tokunaga;Kazuyuki Aihara
Affiliations:
Department of Computer Science and Systems Engineering, Muroran Institute of Technology, Muroran, Hokkaido 050-0071, Japan;Institute of Information Sciences and Electronics, University of Tsukuba, Ibaraki 305-8573, Japan;Department of Mathematical Engineering and Information Pysics, Faculty of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan and CREST, Japan Scince and Technology Corporation ...
Venue:
Neural Networks
Year:
2003

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Abstract

This paper presents numerical studies of applying back-propagation learning to a delayed recurrent neural network (DRNN). The DRNN is a continuous-time recurrent neural network having time delayed feedbacks and the back-propagation learning is to teach spatio-temporal dynamics to the DRNN. Since the time-delays make the dynamics of the DRNN infinite-dimensional, the learning algorithm and the learning capability of the DRNN are different from those of the ordinary recurrent neural network (ORNN) having no time-delays. First, two types of learning algorithms are developed for a class of DRNNs. Then, using chaotic signals generated from the Mackey-Glass equation and the Rössler equations, learning capability of the DRNN is examined. Comparing the learning algorithms, learning capability, and robustness against noise of the DRNN with those of the ORNN and time delay neural network, advantages as well as disadvantages of the DRNN are investigated.