Neural Learning of Chaotic Dynamics: The Error Propagation Algorithm

Abstract

An algorithm is introduced that trains a neural network to identify chaotic dynamics from a single measured time-series. The algorithm has four special features:

The state of the system is extracted from the time-series using delays, followed by weighted Principal Component Analysis (PCA) data reduction. The prediction model consists of both a linear model and a Multi- Layer-Perceptron (MLP). The effective prediction horizon during training is user-adjustable due to error propagation: prediction errors are partially propagated to the next time step. A criterion is monitored during training to select the model that as a chaotic attractor is most similar to the real system attractor.

The algorithm is applied to laser data from the Santa Fe time-series competition (set A). The resulting model is not only useful for short-term predictions but it also generates time-series with similar chaotic characteristics as the measured data. _Also cross-referenced as UMIACS-TR-97-77)