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Solving Partial Differential Equations with Bernstein Neural Networks

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 840))

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Abstract

In this paper, a neural network-based procedure is suggested to produce estimated solutions (controllers) for the second-order nonlinear partial differential equations (PDEs). This concept is laid down so as to produce a prevalent approximation on the basis of the learning method which is at par with quasi-Newton rule. The proposed neural network contains the regularizing parameters (weights and biases), that can be utilized for making the error function least. Besides, an advanced technique is presented for resolving PDEs based on the usage of Bernstein polynomial. Numerical experiments alongside comparisons show the fantastic capacity of the proposed techniques.

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Author information

Authors and Affiliations

  1. Departamento de Control Automatico, CINVESTAV-IPN (National Polytechnic Institute), Mexico City, Mexico

    Sina Razvarz

  2. Centre for Artificial Intelligence Research (CAIR), University of Agder, Grimstad, Norway

    Raheleh Jafari

  3. School of Computing, University of Portsmouth, Buckingham Building, Portsmouth, PO13HE, UK

    Alexander Gegov

Authors
  1. Sina Razvarz
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  2. Raheleh Jafari
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  3. Alexander Gegov
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Corresponding author

Correspondence to Raheleh Jafari .

Editor information

Editors and Affiliations

  1. School of Science and Technology, Nottingham Trent University, Nottingham, United Kingdom

    Ahmad Lotfi

  2. Faculty of Science and Technology, Bournemouth University, Poole, Dorset, United Kingdom

    Hamid Bouchachia

  3. School of Computing, University of Portsmouth, Portsmouth, Hampshire, United Kingdom

    Alexander Gegov

  4. School of Science and Technology, Nottingham Trent University, Nottingham, United Kingdom

    Caroline Langensiepen

  5. College of Science and Technology, Nottingham Trent University, Nottingham, United Kingdom

    Martin McGinnity

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Razvarz, S., Jafari, R., Gegov, A. (2019). Solving Partial Differential Equations with Bernstein Neural Networks. In: Lotfi, A., Bouchachia, H., Gegov, A., Langensiepen, C., McGinnity, M. (eds) Advances in Computational Intelligence Systems. UKCI 2018. Advances in Intelligent Systems and Computing, vol 840. Springer, Cham. https://doi.org/10.1007/978-3-319-97982-3_5

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