TR on learning chaotic dynamics

[Rembrandt Bakker]

The following manuscript (7 pages) is now available at the WWW sites 
listed below:
www.neci.nj.nec.com/homepages/bakker/UMD-CS-TR-3843.ps.gz
www.neci.nj.nec.com/homepages/giles/papers/UMD-CS-TR-3843.neural.learning.chaotic.dynamics.ps.Z

We apologize in advance for any multiple postings that may occur.

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                Neural Learning of Chaotic Dynamics:
                  The Error Propagation Algorithm

Rembrandt Bakker(1), Jaap C. Schouten(1), C. Lee Giles(2,3), C.M. van den Bleek (1)
(1) Delft University of Technology, Dept. Chemical Process Technology,
    Julianalaan 136, 2628 BL  Delft, The Netherlands.
(2) NEC Research Institute, 4 Independence Way, Princeton, NJ 08540, USA.
(3) Institute for Advanced Computer Studies, University of Maryland, 
    College Park, MD 20742, USA.


                        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 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.


Keywords - time series, neural networks, chaotic dynamics, laser data,
Santa Fe time series competition, Lyapunov exponents, principal component
analysis, error propagation.

--
Rembrandt Bakker
r.bakker at stm.tudelft.nl
http://www.neci.nj.nec.com/homepages/bakker