Modeling Geomagnetospheric Disturbances with Sequential Bayesian Recurrent Neural Networks

  • Lahcen Ouarbya
  • Derrick T. Mirikitani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5863)


Sequential Bayesian trained recurrent neural networks (RNNs) have not yet been considered for modeling the dynamics of magnetospheric plasma. We provide a discussion of the state-space modeling framework and an overview of sequential Bayesian estimation. Three nonlinear filters are then proposed for online RNN parameter estimation, which include the extended Kalman filter, the unscented Kalman filter, and the ensemble Kalman filter. The exogenous inputs to the RNNs consist of three parameters, \(b_z , b^2\), and \(b^2_y\) , where b, b z , and b y represent the magnitude, the southward and azimuthal components of the interplanetary magnetic field (IMF) respectively. The three models are compared to a model used in operational forecasts on a severe double storm that has so far been difficult to forecast. It is shown that some of the proposed models significantly outperform the current state of the art.


Geomagnetic Storms Recurrent Neural Networks Filtering 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Axford, W.I., Hines, C.O.: A unifying theory of high-latitude geophysical phenomena and geomagnetic storms. Can. J. Phys. 39, 1433–1464 (1961)MathSciNetGoogle Scholar
  2. 2.
    de Menezes, L., Nikolaev, N.: Forecasting with Genetically Programmed Polynomial Neural Networks. International Journal of Forecasting 22(2), 249–265 (2005)CrossRefGoogle Scholar
  3. 3.
    Dungey, J.W.: Interplanetary magnetic field and the auroral zones. Phys. Rev. Lett. 26, 47–48 (2000)Google Scholar
  4. 4.
    Elman, J.L.: Finding Structure in Time. Cognitive Science 14, 179–211 (1990)CrossRefGoogle Scholar
  5. 5.
    Evensen, G.: The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dynamics 53, 343–367 (2003)CrossRefGoogle Scholar
  6. 6.
    Farrugia, C.J., Freeman, M.P., Burlaga, L.F., Lepping, R.P., Takahashi, K.: The earth’s magnetosphere under continued forcing - Substorm activity during the passage of an interplanetary magnetic cloud. J. Geophys. Res. 98, 7657–7671 (1993)CrossRefGoogle Scholar
  7. 7.
    Gleisner, H., Lundstedt, H., Wintoft, P.: Predicting Geomagnetic Storms From Solar-Wind Data Using Time-Delay Neural Networks. Ann. Geophys. 14, 679–686 (1996)CrossRefGoogle Scholar
  8. 8.
    Gonzales, W.D., Joselyn, J.A., Kamide, Y., Kroehl, H.W., Rostoker, G., Tsurutani, B.T., Vasyliunas, V.M.: What is a geomagnetic storm? J. Geophys. Res. 99, 5771–5792 (1994)CrossRefGoogle Scholar
  9. 9.
    Gosling, J.T., McComas, D.J., Phillips, J.L., Bame, S.J.: Geomagnetic activity associated with earth passage of interplanetary shock disturbances and coronal mass ejections. J. Geophys. Res. 96, 7831–7839 (1991)CrossRefGoogle Scholar
  10. 10.
    Haykin, S.: Kalman Filtering and Neural Networks. John Wiley & son, New York (2001)CrossRefGoogle Scholar
  11. 11.
    Julier, S., Uhlmann, J.: A New Extension of the Kalman Filter to Nonlinear Systems. In: Signal Processing, Sensor Fusion, and Target Recognition VI, vol. 3068, pp. 182–193 (1997)Google Scholar
  12. 12.
    Lundstedt, H.: Neural Networks and prediction of solar-terrestrial effects. Planet. Space Sci. 40, 457–464 (1992)CrossRefGoogle Scholar
  13. 13.
    Lundstedt, H., Wintoft, P.: Prediction of geomagnetic storms from solar wind data with the use of a neural network. Ann Geophys. 12, 19–24 (1994)CrossRefGoogle Scholar
  14. 14.
    Lundstedt, H., Gleisner, H., Wintoft, P.: Operational forecasts of the geomagnetic Dst index. Geophys. Res. Lett. 29, 34–1–34–4 (2002)Google Scholar
  15. 15.
    Lund Space Weather Center,
  16. 16.
    Mirikitani, D.T., Nikolaev, N.: Dynamic Modeling with Ensemble Kalman Filter Trained Recurrent Neural Networks. In: ICMLA 2008, pp. 843–848 (2008)Google Scholar
  17. 17.
    Nikolaev, N., de Menezes, L.: Sequential Bayesian Kernel Modelling with Non-Gaussian Noise. Neural Networks 21(1), 36–47 (2008)Google Scholar
  18. 18.
    Nikolaev, N., Iba, H.: Polynomial Harmonic GMDH Learning Networks for Time Series Modeling. Neural Networks 16(10), 1527–1540 (2003)CrossRefGoogle Scholar
  19. 19.
    Pallocchia, G., Amata, E., Consolini, G., Marcucci, M.F., Bertello, I.: Geomagnetic Dst index forecast based on IMF data only. Ann Geophys. 24, 989–999 (2006)CrossRefGoogle Scholar
  20. 20.
    Puskorius, G.V., Feldkamp, L.A.: Neurocontrol of nonlinear dynamical systems with Kalman filter trained recurrent networks. IEEE T Neural Networks 5, 279–297 (1994)CrossRefGoogle Scholar
  21. 21.
    Ruck, D.W., Rogers, S.K., Kabrisky, M., Maybeck, P., Oxle, M.E.: Comparative Analysis of Backpropgation and the Extended Kalman Filter for Training Multilayer Perceptrons. IEEE Trans. Patt. Anal.& Mach. Intell. 14(6), 686–691 (1992)CrossRefGoogle Scholar
  22. 22.
    Schottky, B., Saad, D.: Statistical mechanics of EKF learning in neural networks. J. Phys. A: Math Gen. 32, 1605–1621 (1999)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Lahcen Ouarbya
    • 1
  • Derrick T. Mirikitani
    • 1
  1. 1.Department of Computing, Goldsmiths CollegeUniversity of LondonLondon

Personalised recommendations