Partial Differential Equations Numerical Modeling Using Dynamic Neural Networks

Authors:
Rita Fuentes;Alexander Poznyak;Isaac Chairez;Tatyana Poznyak
Affiliations:
Automatic Control Department, CINVESTAV-IPN, México;Automatic Control Department, CINVESTAV-IPN, México;Bioelectronics Department, UPIBI-IPN, México;Postgraduete Division, ESIQIE-IPN, México
Venue:
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part II
Year:
2009

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Abstract

In this paper a strategy based on differential neural networks (DNN) for the identification of the parameters in a mathematical model described by partial differential equations is proposed. The identification problem is reduced to finding an exact expression for the weights dynamics using the DNNs properties. The adaptive laws for weights ensure the convergence of the DNN trajectories to the PDE states. To investigate the qualitative behavior of the suggested methodology, here the non parametric modeling problem for a distributed parameter plant is analyzed: the anaerobic digestion system