Partial differential equations numerical modeling using dynamic neural networks

Rita Fuentes; Alexander Poznyak; Isaac Chairez; Tatyana Poznyak

doi:10.1007/978-3-642-04277-5_56

Partial differential equations numerical modeling using dynamic neural networks

Rita Fuentes, Alexander Poznyak, Isaac Chairez, Tatyana Poznyak

Unidad Profesional Interdisciplinaria de Biotecnología (UPIBI)

Producción científica: Capítulo del libro/informe/acta de congreso › Contribución a la conferencia › revisión exhaustiva

2 Citas (Scopus)

Resumen

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

Idioma original	Inglés
Título de la publicación alojada	Artificial Neural Networks - ICANN 2009 - 19th International Conference, Proceedings
Páginas	552-562
Número de páginas	11
Edición	PART 2
DOI	https://doi.org/10.1007/978-3-642-04277-5_56
Estado	Publicada - 2009
Evento	19th International Conference on Artificial Neural Networks, ICANN 2009 - Limassol, Chipre Duración: 14 sep. 2009 → 17 sep. 2009

Serie de la publicación

Nombre	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Número	PART 2
Volumen	5769 LNCS
ISSN (versión impresa)	0302-9743
ISSN (versión digital)	1611-3349

Conferencia

Conferencia	19th International Conference on Artificial Neural Networks, ICANN 2009
País/Territorio	Chipre
Ciudad	Limassol
Período	14/09/09 → 17/09/09

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10.1007/978-3-642-04277-5_56

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Fuentes, R., Poznyak, A., Chairez, I., & Poznyak, T. (2009). Partial differential equations numerical modeling using dynamic neural networks. En Artificial Neural Networks - ICANN 2009 - 19th International Conference, Proceedings (PART 2 ed., pp. 552-562). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5769 LNCS, N.º PART 2). https://doi.org/10.1007/978-3-642-04277-5_56

Fuentes, Rita ; Poznyak, Alexander ; Chairez, Isaac et al. / Partial differential equations numerical modeling using dynamic neural networks. Artificial Neural Networks - ICANN 2009 - 19th International Conference, Proceedings. PART 2. ed. 2009. pp. 552-562 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2).

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title = "Partial differential equations numerical modeling using dynamic neural networks",

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",

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author = "Rita Fuentes and Alexander Poznyak and Isaac Chairez and Tatyana Poznyak",

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Fuentes, R, Poznyak, A, Chairez, I & Poznyak, T 2009, Partial differential equations numerical modeling using dynamic neural networks. En Artificial Neural Networks - ICANN 2009 - 19th International Conference, Proceedings. PART 2 ed., Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), n.º PART 2, vol. 5769 LNCS, pp. 552-562, 19th International Conference on Artificial Neural Networks, ICANN 2009, Limassol, Chipre, 14/09/09. https://doi.org/10.1007/978-3-642-04277-5_56

Partial differential equations numerical modeling using dynamic neural networks. / Fuentes, Rita; Poznyak, Alexander; Chairez, Isaac et al.
Artificial Neural Networks - ICANN 2009 - 19th International Conference, Proceedings. PART 2. ed. 2009. p. 552-562 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5769 LNCS, N.º PART 2).

Producción científica: Capítulo del libro/informe/acta de congreso › Contribución a la conferencia › revisión exhaustiva

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N2 - 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

AB - 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

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Fuentes R, Poznyak A, Chairez I , Poznyak T. Partial differential equations numerical modeling using dynamic neural networks. En Artificial Neural Networks - ICANN 2009 - 19th International Conference, Proceedings. PART 2 ed. 2009. p. 552-562. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2). doi: 10.1007/978-3-642-04277-5_56

Partial differential equations numerical modeling using dynamic neural networks

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