Modelling Temporal Series Through Synaptic Delay-based Neural Networks

In this paper we address the problem of the dynamic reconstruction of chaotic time series using a new training algorithm for delay-based neural networks, where the delays can be trained. In signal reconstruction terms, trainable delay-based Artificial Neural Networks (ANN) directly implement a form of the embedding theorem, and the training algorithm we have developed for this particular type of networks implicitly and autonomously obtains the embedding dimension and the normalised embedding delay. This structure and training algorithm permit training neural networks for temporal reasoning without resorting to any explicit time windowing process or determining parameters of the signal, such as the best dimension for the state space in which to unambiguously represent its evolution orthe appropriate sampling rate. In this work, the capacity of the neural network and training algorithm in the modeling of time series is tested in the prediction of future values of chaotic time series using iterative multistep prediction. Finally, to provide some indication of the real world operation of these types of systems in the reconstruction of signals, we present some results obtained in the prediction of hot wire anemometer measurements of the velocity of a turbulent flow in a Karman Vortex Street, which is a difficult problem in fluid dynamics.