INVERSION OF A SEMI-PHYSICAL ODE MODEL

Laurent Bourgois, Gilles Roussel, Mohammed Benjelloun

2007

Abstract

This study proposes to examine the design methodology and the performances of an inverse dynamic model by fusion of statistical training and deterministic modeling. We carry out an inverse semi-physical model using a recurrent neural network and illustrate it on a didactic example. This technique leads to the realization of a neural network inverse problem solver (NNIPS). In the first step, the network is designed by a discrete reverse-time state form of the direct model. The performances in terms of generalization, regularization and training effort are highlighted in comparison with the number of weights needed to estimate the neural network. Finally, some tests are carried out on a simple second order model, but we suggest the form of a dynamic system characterized by an ordinary differential equation (ODE) of an unspecified r order.

References

  1. Cherkassky, V., Krasnopolsky, V. M., Solomatine, D., and Valdes, J. (2006). Computational intelligence in earth sciences and environmental applications: Issues and challenges. Neural Networks, 19, issue 2:113-121.
  2. Dreyfus, G., Martinez, J. M., Samuelides, M., Gordon, M. B., Badran, F., Thiria, S., and Hérault, L. (2004). Réseaux de Neurones: Méthodologies et Applications. Eyrolles, 2ème édition, Paris.
  3. Groetsch, C. W. (1993). Inverse Problems in the Mathematical Sciences. Vieweg Sohn, Wiesbaden.
  4. Hornik, K., Stinchcombe, M., and White, H. (1989). Multilayer feedforward networks are universal approximators. Neural Networks, 2:359-366.
  5. Idier, J. (2001). Approche Bayesienne pour les Problèmes Inverses. Traité IC2, Série Traitement du Signal et de l'Image, Hermès, Paris.
  6. Krasnopolsky, V. M. and Fox-Rabinovitz, S. F. (2006). Complex hybrid models combining deterministic and machine learning components for numerical climate modeling and weather prediction. Neural Networks, 19:122-134.
  7. Krasnopolsky, V. M. and Schillerb, H. (2003). Some neural network applications in environmental sciences. part i: Forward and inverse problems in geophysical remote measurements. Neural Networks, 16:321-334.
  8. Ljung, L. (1999). System Identification, Theory for the User. Prentice Hall, N. J.
  9. Mohammad-Djafari, A., Giovannelli, J. F., Demoment, G., and Idier, J. (2002). Regularization, maximum entropy and probabilistic methods in mass spectrometry data processing problems. Int. Journal of Mass Spectrometry, 215, issue 1:175-193.
  10. Nguyen, D. and Widrow, B. (1990). Improving the learning speed of 2-layer neural networks by choosing initial values of the adaptive weigths. Proceedings of the International Joint Conference on Neural Networks, 3:21-26.
  11. Oussar, Y. and Dreyfus, G. (2001). How to be a gray box : Dynamic semi-physical modeling. Neurocomputing, 14:1161-1172.
  12. Sontag, E. D. (1996). Recurrent neural networks : Some systems-theoretic aspects. Technical Report NB, Dept of mathematics, Rutgers University, U.S.A.
  13. Thikhonov, A. N. and Arsenin, V. Y. (1977). Solutions of ill Posed Problems. John Wiley, New York.
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Paper Citation


in Harvard Style

Bourgois L., Roussel G. and Benjelloun M. (2007). INVERSION OF A SEMI-PHYSICAL ODE MODEL . In Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-972-8865-82-5, pages 364-371. DOI: 10.5220/0001641803640371


in Bibtex Style

@conference{icinco07,
author={Laurent Bourgois and Gilles Roussel and Mohammed Benjelloun},
title={INVERSION OF A SEMI-PHYSICAL ODE MODEL},
booktitle={Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2007},
pages={364-371},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001641803640371},
isbn={978-972-8865-82-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - INVERSION OF A SEMI-PHYSICAL ODE MODEL
SN - 978-972-8865-82-5
AU - Bourgois L.
AU - Roussel G.
AU - Benjelloun M.
PY - 2007
SP - 364
EP - 371
DO - 10.5220/0001641803640371