Genetic Programming for Inductive Inference of Chaotic Series

  • I. De Falco
  • A. Della Cioppa
  • A. Passaro
  • E. Tarantino
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3849)


In the context of inductive inference Solomonoff complexity plays a key role in correctly predicting the behavior of a given phenomenon. Unfortunately, Solomonoff complexity is not algorithmically computable. This paper deals with a Genetic Programming approach to inductive inference of chaotic series, with reference to Solomonoff complexity, that consists in evolving a population of mathematical expressions looking for the ‘optimal’ one that generates a given series of chaotic data. Validation is performed on the Logistic, the Henon and the Mackey–Glass series. The results show that the method is effective in obtaining the analytical expression of the first two series, and in achieving a very good approximation and forecasting of the Mackey–Glass series.


Genetic programming Solomonoff complexity chaotic series 


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  1. 1.
    Solomonoff, R.J.: A formal theory of inductive inference. Information and Control 7(1-22), 224–254 (1964)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Kolmogorov, A.N.: Three approaches to the quantitative definition of information. Problems of Information and Transmission 1, 1–7 (1965)Google Scholar
  3. 3.
    Falcioni, M., Loreto, V., Vulpiani, A.: Kolmogorov’s legacy about entropy, chaos and complexity. Lect. Notes Phys. 608, 85–108 (2003)MathSciNetGoogle Scholar
  4. 4.
    Koza, J.R.: Genetic Programming II: Automatic Discovery of Reusable Programs. MIT Press, Cambridge (1994)MATHGoogle Scholar
  5. 5.
    Whigham, P.A.: Grammatical Bias for Evolutionary Learning. PhD thesis, School of Computer Science, University of New South Wales, Australia (1996)Google Scholar
  6. 6.
    Strogatz, S.: Nonlinear Dynamics and Chaos. Perseus Publishing, Cambridge (2000)Google Scholar
  7. 7.
    Hénon, M.: A two–dimensional mapping with a strange attractor. Communications of Mathematical Physics 50, 69–77 (1976)MATHCrossRefGoogle Scholar
  8. 8.
    Mackey, M.C., Glass, L.: Oscillations and chaos in physiological control systems. Science 287 (1977)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • I. De Falco
    • 1
  • A. Della Cioppa
    • 2
  • A. Passaro
    • 3
  • E. Tarantino
    • 1
  1. 1.Institute of High Performance Computing and NetworkingNational Research Council of Italy (ICAR–CNR)NaplesItaly
  2. 2.Natural Computation Lab – DIIIEUniversity of SalernoFisciano (SA)Italy
  3. 3.Department of Computer ScienceUniversity of PisaPisaItaly

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