Obtaining transparent models of chaotic systems with multi-objective simulated annealing algorithms

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  author =       "Luciano Sanchez and Jose R. Villar",
  title =        "Obtaining transparent models of chaotic systems with
                 multi-objective simulated annealing algorithms",
  journal =      "Information Sciences",
  volume =       "178",
  number =       "4",
  pages =        "952--970",
  year =         "2008",
  ISSN =         "0020-0255",
  DOI =          "doi:10.1016/j.ins.2007.09.029",
  URL =          "http://www.sciencedirect.com/science/article/B6V0C-4PW05F5-1/2/7e686808a49819363815d713ef4ddd03",
  keywords =     "genetic algorithms, genetic programming,
                 Multi-objective simulated annealing, Chaotic systems,
                 Transparent models, MOSA",
  abstract =     "Transparent models search for a balance between
                 interpretability and accuracy. This paper is about the
                 estimation of transparent models of chaotic systems
                 from data, which are accurate and simple enough for
                 their expression to be understandable by a human
                 expert. The models we propose are discrete, built upon
                 common blocks in control engineering (gain, delay, sum,
                 etc.) and optimized both in their complexity and
                 accuracy. The accuracy of a discrete model can be
                 measured by means of the average error between its
                 prediction for the next sampling period and the true
                 output at that time, or [`]one-step error'. A perfect
                 model has zero one-step error, but a small error is not
                 always associated with an approximate model, especially
                 in chaotic systems. In chaos, an arbitrarily low
                 difference between two initial states will produce
                 uncorrelated trajectories, thus a model with a low
                 one-step error may be very different from the desired
                 one. Even though a recursive evaluation (multi-step
                 prediction) improves the fitting, in this work we will
                 show that a learning algorithm may not converge to an
                 appropriate model, unless we include some terms that
                 depend on estimates of certain properties of the model
                 (so called [`]invariants' of the chaotic series). We
                 will show this graphically, by means of the
                 reconstructed attractors of the original system and the
                 model. Therefore, we also propose to follow a
                 multi-objective approach to model chaotic processes and
                 to apply a simulated annealing-based optimization to
                 obtain transparent models.",

Genetic Programming entries for Luciano Sanchez Jose R Villar