Neural Networks: From Black Box towards Transparent Box Application to Evapotranspiration Modeling
Neural networks are well known for their ability to
model non linear functions, but as statistical methods usually does,
they use a no parametric approach thus, a priori knowledge is not
obvious to be taken into account no more than the a posteriori
knowledge. In order to deal with these problematics, an original way
to encode the knowledge inside the architecture is proposed. This
method is applied to the problem of the evapotranspiration inside
karstic aquifer which is a problem of huge utility in order to deal
with water resource.
[1] Y. Oussar, G. Dreyfus. "How to be a Gray Box: Dynamic
Semi-physical Modeling". Neural Networks, invited paper, vol. 14,
2001, pp. 1161-1172.
[2] A. Johannet, A. Mangin, D. D'Hulst. "Subterranean Water Infiltration
Modelling by Neural Networks: Use of Water Source Flow". In Proc. of
ICANN, M. Marinaro and P.G. Morasso eds, Springer, 1994, pp. 1033-
1036.
[3] G. Cybenko. "Approximation by Superposition of a Sigmoidal
Function". Math. Ctrl Signal Syst, 2, 1989, pp. 293-342.
[4] H. Moradkhani, K. Hsu, H. V. Gupta, S. Sorooshian. "Improved
Streamflow Forecasting Using Self-Organizing Radial Basis Function
Artificial Neural Networks". Journal of Hydrology, 295, 2004, pp. 246-
262.
[5] I. N. Daliakopoulos, P. Coulibaly, I. K. Tsanis. "Groundwater Level
Forecasting Using Artificial Neural Networks". Journal of Hydrology
309, 2005, pp. 229-240.
[6] D. I. Jeong, Y. O. Kim. "Rainfall-Runoff models using artificial neural
networks for ensemble streamflow prediction". Hydrological Processes,
19, 2005, pp. 3819-3835.
[7] B. Kurtulus M. Rasac. "Evaluation of the ability of an artificial neural
network model to simulate the input-outpout responses of a large karstic
aquifer : the Larochefoucault aquifer (Charente - France)".
Hydrogeological Journal, 2006.
[8] A. P. Jaquin, A. Y. Shamseldin. "Development of rainfall-runoff models
using Takagi-Sugeno fuzzy inference systems". Journal of Hydrology,
329, 2006, pp. 145-173.
[9] A.-L. Courbis, E. Touraud and B. Vayssade. "Water balance diagnosis
based on a simulation tool". ENVIROSOFT'98, 1998, pp. 199-208.
[10] A. Johannet, P-A. Ayral, B. Vayssade. "Modelling non Measurable
Processes by Neural Networks: Forecasting Underground Flow Case
Study of the Cèze Basin (Gard - France)". CISSE, 2006.
[11] D. Rumelhart, G. Hinton, R. Williams. "Learning Internal
Representation by Error Propagation". PDP, MIT Press, 1988.
[12] E.A. Bender. "Mathematical Method for Artificial Intelligence". IEEE
Computer Society Press, 1996.
[13] A.J. Shepherd. "Second-Order Methods for Neural Networks". Springer,
1997.
[14] D.W. Marquardt. Journal of the Society for Industrial and Applied
Mathematics, vol 11, pp. 431-441.
[15] W.H. Press, S.A.Teukolsky, W.T. Vetterling, B.P. Flannery. "Numerical
recipies in C". Cambridge University Press, 1992.
[16] Narendra K. S., Parthasarathy K. "Gradient Methods for the
Optimization of Dynamical Systems Containning Neural Networks".
IEEE trans. neur. net., vol 2, 1991, n┬░2, pp. 252-262.
[17] Werbos P.J. "Backpropagation Throught Time : What it Does and How
to Do It". Proc. IEEE, 78, N┬░10, 1990, pp. 1550-1560.
[18] Mangin A. (1970). "Le système karstique du Baget (Ariège)". Annales
de Spéléologie, vol 25, fasc. 3.
[19] J.E. Nash, J. V. Sutcliffe. "River Flow Forecasting through Conceptual
Model. Part I - A Discussion of Principles". Journal of Hydrology, 10,
1970, pp. 282-290.
[20] L. Oudin et al. "Which potential evapotranspiration input for a lumped
rainfall-runoff model? Part 2 Towards a simple and efficient potential
evapotranspiration model for rainfall-runoff modelling". Journal of
hydrology, 303, 2005, pp. 290-306.
[21] Geman S. Bienenstock E. & Doursat R. "Neural networks and the
bias/variance dilemma". Neural Computation 4, 1992, pp. 1-58.
[1] Y. Oussar, G. Dreyfus. "How to be a Gray Box: Dynamic
Semi-physical Modeling". Neural Networks, invited paper, vol. 14,
2001, pp. 1161-1172.
[2] A. Johannet, A. Mangin, D. D'Hulst. "Subterranean Water Infiltration
Modelling by Neural Networks: Use of Water Source Flow". In Proc. of
ICANN, M. Marinaro and P.G. Morasso eds, Springer, 1994, pp. 1033-
1036.
[3] G. Cybenko. "Approximation by Superposition of a Sigmoidal
Function". Math. Ctrl Signal Syst, 2, 1989, pp. 293-342.
[4] H. Moradkhani, K. Hsu, H. V. Gupta, S. Sorooshian. "Improved
Streamflow Forecasting Using Self-Organizing Radial Basis Function
Artificial Neural Networks". Journal of Hydrology, 295, 2004, pp. 246-
262.
[5] I. N. Daliakopoulos, P. Coulibaly, I. K. Tsanis. "Groundwater Level
Forecasting Using Artificial Neural Networks". Journal of Hydrology
309, 2005, pp. 229-240.
[6] D. I. Jeong, Y. O. Kim. "Rainfall-Runoff models using artificial neural
networks for ensemble streamflow prediction". Hydrological Processes,
19, 2005, pp. 3819-3835.
[7] B. Kurtulus M. Rasac. "Evaluation of the ability of an artificial neural
network model to simulate the input-outpout responses of a large karstic
aquifer : the Larochefoucault aquifer (Charente - France)".
Hydrogeological Journal, 2006.
[8] A. P. Jaquin, A. Y. Shamseldin. "Development of rainfall-runoff models
using Takagi-Sugeno fuzzy inference systems". Journal of Hydrology,
329, 2006, pp. 145-173.
[9] A.-L. Courbis, E. Touraud and B. Vayssade. "Water balance diagnosis
based on a simulation tool". ENVIROSOFT'98, 1998, pp. 199-208.
[10] A. Johannet, P-A. Ayral, B. Vayssade. "Modelling non Measurable
Processes by Neural Networks: Forecasting Underground Flow Case
Study of the Cèze Basin (Gard - France)". CISSE, 2006.
[11] D. Rumelhart, G. Hinton, R. Williams. "Learning Internal
Representation by Error Propagation". PDP, MIT Press, 1988.
[12] E.A. Bender. "Mathematical Method for Artificial Intelligence". IEEE
Computer Society Press, 1996.
[13] A.J. Shepherd. "Second-Order Methods for Neural Networks". Springer,
1997.
[14] D.W. Marquardt. Journal of the Society for Industrial and Applied
Mathematics, vol 11, pp. 431-441.
[15] W.H. Press, S.A.Teukolsky, W.T. Vetterling, B.P. Flannery. "Numerical
recipies in C". Cambridge University Press, 1992.
[16] Narendra K. S., Parthasarathy K. "Gradient Methods for the
Optimization of Dynamical Systems Containning Neural Networks".
IEEE trans. neur. net., vol 2, 1991, n┬░2, pp. 252-262.
[17] Werbos P.J. "Backpropagation Throught Time : What it Does and How
to Do It". Proc. IEEE, 78, N┬░10, 1990, pp. 1550-1560.
[18] Mangin A. (1970). "Le système karstique du Baget (Ariège)". Annales
de Spéléologie, vol 25, fasc. 3.
[19] J.E. Nash, J. V. Sutcliffe. "River Flow Forecasting through Conceptual
Model. Part I - A Discussion of Principles". Journal of Hydrology, 10,
1970, pp. 282-290.
[20] L. Oudin et al. "Which potential evapotranspiration input for a lumped
rainfall-runoff model? Part 2 Towards a simple and efficient potential
evapotranspiration model for rainfall-runoff modelling". Journal of
hydrology, 303, 2005, pp. 290-306.
[21] Geman S. Bienenstock E. & Doursat R. "Neural networks and the
bias/variance dilemma". Neural Computation 4, 1992, pp. 1-58.
@article{"International Journal of Information, Control and Computer Sciences:64001", author = "A. Johannet and B. Vayssade and D. Bertin", title = "Neural Networks: From Black Box towards Transparent Box Application to Evapotranspiration Modeling", abstract = "Neural networks are well known for their ability to
model non linear functions, but as statistical methods usually does,
they use a no parametric approach thus, a priori knowledge is not
obvious to be taken into account no more than the a posteriori
knowledge. In order to deal with these problematics, an original way
to encode the knowledge inside the architecture is proposed. This
method is applied to the problem of the evapotranspiration inside
karstic aquifer which is a problem of huge utility in order to deal
with water resource.", keywords = "Neural-Networks, Hydrology, Evapotranpiration, Hidden Function Modeling.", volume = "2", number = "6", pages = "2226-8", }