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)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

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

Original language	English
Title of host publication	Artificial Neural Networks - ICANN 2009 - 19th International Conference, Proceedings
Pages	552-562
Number of pages	11
Edition	PART 2
DOIs	https://doi.org/10.1007/978-3-642-04277-5_56
State	Published - 2009
Event	19th International Conference on Artificial Neural Networks, ICANN 2009 - Limassol, Cyprus Duration: 14 Sep 2009 → 17 Sep 2009

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number	PART 2
Volume	5769 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	19th International Conference on Artificial Neural Networks, ICANN 2009
Country/Territory	Cyprus
City	Limassol
Period	14/09/09 → 17/09/09

Keywords

Adaptive identification
Distributed Parameter Systems
Neural Networks
Partial Differential Equations and Practical Stability

Access to Document

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

Cite this

Fuentes, R., Poznyak, A., Chairez, I., & Poznyak, T. (2009). Partial differential equations numerical modeling using dynamic neural networks. In 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, No. 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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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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Fuentes, R, Poznyak, A, Chairez, I & Poznyak, T 2009, Partial differential equations numerical modeling using dynamic neural networks. in Artificial Neural Networks - ICANN 2009 - 19th International Conference, Proceedings. PART 2 edn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 2, vol. 5769 LNCS, pp. 552-562, 19th International Conference on Artificial Neural Networks, ICANN 2009, Limassol, Cyprus, 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, No. PART 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Partial differential equations numerical modeling using dynamic neural networks

AU - Fuentes, Rita

AU - Poznyak, Alexander

AU - Chairez, Isaac

AU - Poznyak, Tatyana

PY - 2009

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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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KW - Distributed Parameter Systems

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Artificial Neural Networks - ICANN 2009 - 19th International Conference, Proceedings

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Fuentes R, Poznyak A, Chairez I , Poznyak T. Partial differential equations numerical modeling using dynamic neural networks. In 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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