Neural Learning of Chaotic Dynamics: The Error Propagation Algorithm

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1998-10-15

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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:

  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 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)

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