SCALETRACK: A System to Discover Dynamic Law Equations Containing Hidden States and Chaos

  • Takashi Washio
  • Fuminori Adachi
  • Hiroshi Motoda
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3735)


This paper proposes a novel system to discover simultaneous time differential law equations reflecting first principles underlying objective processes. The system has the power to discover equations containing hidden state variables and/or representing chaotic dynamics without using any detailed domain knowledge. These tasks have not been addressed in any mathematical and engineering domains in spite of their essential importance. Its promising performance is demonstrated through applications to both mathematical and engineering examples.


Chaotic Dynamic Ratio Scale Interval Scale State Tracking Golden Ratio 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Langley, P.W., Simon, H.A., Bradshaw, G.L., Zytkow, J.M.: Scientific Discovery; Computational Explorations of the Creative Process. MIT Press, Cambridge (1987)Google Scholar
  2. 2.
    Koehn, B.W., Zytkow, J.M.: Experimeting and theorizing in theory formation. In: Proceedings of the International Symposium on Methodologies for Intelligent Systems, Knoxville, Tennessee, pp. 296–307. ACM SIGART Press, New York (1986)CrossRefGoogle Scholar
  3. 3.
    Falkenhainer, B.C., Michalski, R.S.: Integrating quantitative and qualitative discovery: The abacus system. Machine Learning 1, 367–401 (1986)Google Scholar
  4. 4.
    Washio, T., Motoda, H.: Discovering admissible models of complex systems based on scale-types and identity constraints. In: Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence, Nagoya, Japan, pp. 810–817 (1997)Google Scholar
  5. 5.
    Dzeroski, S., Todorovski, L.: Discovering dynamics: from inductive logic programing to machine discovery. Journal of Intelligent Information Systems 4, 89–108 (1995)CrossRefGoogle Scholar
  6. 6.
    Todorovski, L., Dzeroski, S.: Declarative bias in equation discovery. In: Proceedings of the Fourteenth International Conference on Machine Learning, San Mateo, California, pp. 376–384. Morgan Kaufmann, San Francisco (1997)Google Scholar
  7. 7.
    Langley, P., George, D., Bay, S., Saito, K.: Robust induction of process models from time-series data. In: Proceedings of the Twentieth International Conference on Machine Learning, pp. 432–439. AAAI Press, Menlo Park (2003)Google Scholar
  8. 8.
    Bradley, E.A., O’Gallagher, A.A., Rogers, J.E.: Global solutions for nonlinear systems using qualitative reasoning. Annals of Mathematics and Artificial Intelligence 23, 211–228 (1998)zbMATHCrossRefGoogle Scholar
  9. 9.
    Berge, P., Pomeau, Y., Vidal, C.: Order in Chaos - For understanding turbulent flow. Hermann, Paris, France (1984)Google Scholar
  10. 10.
    Luce, D.R.: On the possible psychological laws. Psychological Review 66, 81–95 (1959)CrossRefGoogle Scholar
  11. 11.
    Luenberger, D.G.: Linear and Nonlinear Programing. Adison-Wesley, Cambridge (1989)Google Scholar
  12. 12.
    Doucet, A., Godsill, S., Andrieu, C.: On sequential monte carlo sampling methods for bayesian filtering. Statistics and Computing 10, 197–208 (2000)CrossRefGoogle Scholar
  13. 13.
    Haykin, S.S.: Kalman Filtering and Neural Networks. John Wiley & Sons, Inc., Hoboken (2001)CrossRefGoogle Scholar
  14. 14.
    Gawthrop, P.J., Smith, L.S.: Metamodelling: Bond Graphs and Dynamic Systems. Prentice-Hall, Englewood Cliffs (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Takashi Washio
    • 1
  • Fuminori Adachi
    • 1
  • Hiroshi Motoda
    • 1
  1. 1.I.S.I.R.Osaka UniversityIbaraki City, OsakaJapan

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