Abstract
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.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
Langley, P.W., Simon, H.A., Bradshaw, G.L., Zytkow, J.M.: Scientific Discovery; Computational Explorations of the Creative Process. MIT Press, Cambridge (1987)
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)
Falkenhainer, B.C., Michalski, R.S.: Integrating quantitative and qualitative discovery: The abacus system. Machine Learning 1, 367–401 (1986)
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)
Dzeroski, S., Todorovski, L.: Discovering dynamics: from inductive logic programing to machine discovery. Journal of Intelligent Information Systems 4, 89–108 (1995)
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)
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)
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)
Berge, P., Pomeau, Y., Vidal, C.: Order in Chaos - For understanding turbulent flow. Hermann, Paris, France (1984)
Luce, D.R.: On the possible psychological laws. Psychological Review 66, 81–95 (1959)
Luenberger, D.G.: Linear and Nonlinear Programing. Adison-Wesley, Cambridge (1989)
Doucet, A., Godsill, S., Andrieu, C.: On sequential monte carlo sampling methods for bayesian filtering. Statistics and Computing 10, 197–208 (2000)
Haykin, S.S.: Kalman Filtering and Neural Networks. John Wiley & Sons, Inc., Hoboken (2001)
Gawthrop, P.J., Smith, L.S.: Metamodelling: Bond Graphs and Dynamic Systems. Prentice-Hall, Englewood Cliffs (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Washio, T., Adachi, F., Motoda, H. (2005). SCALETRACK: A System to Discover Dynamic Law Equations Containing Hidden States and Chaos. In: Hoffmann, A., Motoda, H., Scheffer, T. (eds) Discovery Science. DS 2005. Lecture Notes in Computer Science(), vol 3735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11563983_22
Download citation
DOI: https://doi.org/10.1007/11563983_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29230-2
Online ISBN: 978-3-540-31698-5
eBook Packages: Computer ScienceComputer Science (R0)