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 timeseries. The algorithm has four special features: 1. The state of the system is extracted from the time-series using delays, followed by weighted Principal Component Analysis (PCA) data reduction. 2. The prediction model consists of both a linear model and a Multi-Layer-Perceptron (MLP). 3. The effective prediction horizon during training is user-adjustable, due to ‘error propagation’: prediction errors are partially propagated to the next time step. 4. 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.