Back-propagation learning of an infinite-dimensional dynamical system

A delay-differential equational model of recurrent neural network, the feedback connections of which are adopted by the backpropagation learning algorithm, is introduced. In contrast with the conventional recursive-ordinary-differential neural networks, which have been reported to be capable of learning complex dynamics only when enough observable dimensions of the target dynamical systems are available, our proposed delay-differential equational model acquires a diversity of time-continuous motions that are observed as an one-dimensional single time series. The system capability is demonstrated through practical experiments.