Obtaining transparent models of chaotic systems with multi-objective simulated annealing algorithms
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- @Article{Sanchez2008952,
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author = "Luciano Sanchez and Jose R. Villar",
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title = "Obtaining transparent models of chaotic systems with
multi-objective simulated annealing algorithms",
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journal = "Information Sciences",
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volume = "178",
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number = "4",
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pages = "952--970",
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year = "2008",
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ISSN = "0020-0255",
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DOI = "doi:10.1016/j.ins.2007.09.029",
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URL = "http://www.sciencedirect.com/science/article/B6V0C-4PW05F5-1/2/7e686808a49819363815d713ef4ddd03",
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keywords = "genetic algorithms, genetic programming,
Multi-objective simulated annealing, Chaotic systems,
Transparent models, MOSA",
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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
Citations