Supermodeling Dynamics and Learning Mechanisms

  • Wim WiegerinckEmail author
  • Miroslav Mirchev
  • Willem Burgers
  • Frank Selten
Part of the Understanding Complex Systems book series (UCS)


At a dozen or so institutes around the world, comprehensive climate models are being developed and improved. Each model provides reasonable simulations of the observed climate, each with its own strengths and weaknesses. In the current multi-model ensemble approach model simulations are combined a posteriori. Recently, it has been proposed to dynamically combine the models and so construct one supermodel. The supermodel parameters are learned from historical observations. Supermodeling has been successfully developed and tested on small chaotic dynamical systems, like the Lorenz 63 system. In this chapter we review and discuss several supermodeling dynamics and learning mechanisms. Methods are illustrated by applications to low-dimensional chaotic systems: the three-dimensional Lorenz 63 and Lorenz 84 models, as well as a 30-dimensional two-layer atmospheric model.


Cost Function Ground Truth Zonal Wind Quadratic Programming Individual Model 
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.



This work has been supported by FP7 FET Open Grant # 266722 (SUMO project).


  1. 1.
    Bakker, R., Schouten, J., Giles, C., Takens, F., Bleek, C.: Learning chaotic attractors by neural networks. Neural Comput. 12(10), 2355–2383 (2000)Google Scholar
  2. 2.
    van den Berge, L.A., Selten, F.M., Wiegerinck, W., Duane, G.S.: A multi-model ensemble method that combines imperfect models through learning. Earth Syst. Dyn. 2(1), 161–177 (2011)Google Scholar
  3. 3.
    Bishop, C.: Pattern Recognition and Machine Learning. Springer, Berlin (2006)Google Scholar
  4. 4.
    Duane, G.: Synchronicity from synchronized chaos (2011). SubmittedGoogle Scholar
  5. 5.
    Duane, G., Tribbia, J., Kirtman, B.: Consensus on long-range prediction by adaptive synchronization of models. In: Arabelos, D.N., Tscherning, C.C. (eds.) EGU General Assembly Conference Abstracts. EGU General Assembly Conference Abstracts, vol. 11, p. 13324 (2009)Google Scholar
  6. 6.
    Duane, G., Yu, D., Kocarev, L.: Identical synchronization, with translation invariance, implies parameter estimation. Phys. Lett. A 371(5–6), 416–420 (2007)Google Scholar
  7. 7.
    Eckmann, J.P., Ruelle, D.: Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57, 617–656 (1985)Google Scholar
  8. 8.
    Frøyland, J., Alfsen, K.H.: Lyapunov-exponent spectra for the lorenz model. Phys. Rev. A 29, 2928–2931 (1984)Google Scholar
  9. 9.
    Houtekamer, P.: Variation of the predictability in a low-order spectral model of the atmospheric circulation. Tellus A 43(3), 177–190 (1991)Google Scholar
  10. 10.
    Kirtman, B., Min, D., Schopf, P., Schneider, E.: A new approach for coupled gcm sensitivity studies. Tech. Rep. 154, COLA (2003)Google Scholar
  11. 11.
    Kocarev, L., Shang, A., Chua, L.: Transition in dynamical regimes by driving: A unified method of control and synchronization of chaos. Int. J. Bifurcation Chaos 3(3), 479–483 (1993)Google Scholar
  12. 12.
    Krogh, A., Vedelsby, J.: Neural network ensembles, cross validation, and active learning. In: Advances in Neural Information Processing Systems, pp. 231–238 (1995)Google Scholar
  13. 13.
    Lapedes, A., Farber, R.: Nonlinear signal processing using neural networks: Prediction and system modelling. In: IEEE International Conference on Neural Networks (1987)Google Scholar
  14. 14.
    Lorenz, E.: Deterministic nonperiodic flow. Atmos. J. Sci. 20, 130–141 (1963)Google Scholar
  15. 15.
    Lorenz, E.: Irregularity: A fundamental property of the atmosphere. Tellus A 36(2), 98–110 (1984)Google Scholar
  16. 16.
    Mirchev, M., Duane, G.S., Tang, W.K., Kocarev, L.: Improved modeling by coupling imperfect models. Commun. Nonlinear Sci. Numer. Simul. 17(7), 2741–2751 (2012)Google Scholar
  17. 17.
    Monteleoni, C., Schmidt, G.A., Saroha, S., Asplund, E.: Tracking climate models. Stat. Anal. Data Mining 4(4), 372–392 (2011)Google Scholar
  18. 18.
    Olfati-Saber, R., Fax, J., Murray, R.: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007)Google Scholar
  19. 19.
    Pecora, L., Carroll, T.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821–824 (1990)Google Scholar
  20. 20.
    Perrone, M., Cooper, L.: When networks disagree: Ensemble methods for hybrid neural networks. In: Mammone, R. (ed.) Artificial Neural Networks for Speech and Vision, p. 126. Chapman & Hall, London (1994)Google Scholar
  21. 21.
    Principe, J., Kuo, J.: Dynamic modelling of chaotic time series with neural networks. In: Advances in Neural Information Processing Systems, 7. Citeseer (1995)Google Scholar
  22. 22.
    Principe, J., Rathie, A., Kuo, J.: Prediction of chaotic time series with neural networks. In: Jansen, B. (ed.) Nonlinear Dynamic of the Brain, pp. 250–258 (1993)Google Scholar
  23. 23.
    Selten, F.: Toward an optimal description of atmospheric flow. J. Atmos. Sci. 50(6), 861–877 (1993)Google Scholar
  24. 24.
    Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K., Tignor, M., Miller, H.: Ipcc, 2007: Climate Change 2007: The Physical Science Basis. Contribution of Working Group to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (2007)Google Scholar
  25. 25.
    Sun, J., Bollt, E., Nishikawa, T.: Master stability functions for coupled nearly identical dynamical systems. Europhys. Lett. 85, 60,011 (2009)Google Scholar
  26. 26.
    Tebaldi, C., Knutti, R.: The use of the multi-model ensemble in probabilistic climate projections. Phil. Trans. Roy. Soc. A: Math. Phys. Eng. Scie. 365(1857), 2053 (2007)Google Scholar
  27. 27.
    Wiegerinck, W., Selten, F.: Supermodeling: Combining imperfect models through learning. In: NIPS Workshop on Machine Learning for Sustainability (MLSUST) (2011). URL
  28. 28.
    Yang, S., Baker, D., Li, H., Cordes, K., Huff, M., Nagpal, G., Okereke, E., Villafañe, J., Kalnay, E., Duane, G.: Data assimilation as synchronization of truth and model: Experiments with the three-variable lorenz system. J. Atmos. Sci. 63(9), 2340–2354 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Wim Wiegerinck
    • 1
    Email author
  • Miroslav Mirchev
    • 2
    • 3
  • Willem Burgers
    • 1
  • Frank Selten
    • 4
  1. 1.Donders Institute for Brain, Cognition and BehaviourRadboud University NijmegenNijmegenThe Netherlands
  2. 2.Macedonian Academy of Sciences and ArtsSkopjeMacedonia
  3. 3.Department of ElectronicsPolitecnico di TorinoTurinItaly
  4. 4.Royal Netherlands Meteorological InstituteDe BiltThe Netherlands

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