Neural Learning of Chaotic Dynamics: The Error Propagation Algorithm
Neural Learning of Chaotic Dynamics: The Error Propagation Algorithm
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Date
1998-10-15
Authors
Bakker, Rembrandt
Schouten, Jaap C.
Bleek, Cor M. van den
Giles, C. Lee
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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:
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)