Neural learning of chaotic dynamics: the error propagation algorithm

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 data reduction; the prediction model consists of both a linear model and a multi-layer-perceptron; the effective prediction horizon during training is user-adjustable, due to 'error propagation': prediction errors are partially propagated to the next time step; and to decide when to stop training, a criterion is monitored during training to select the model that has a chaotic attractor most similar to the real system's 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.