Solving partial differential equations with Bernstein neural networks

Sina Razvarz, Raheleh Jafari, Alexander Gegov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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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.
Original languageEnglish
Title of host publicationAdvances in Computational Intelligence Systems
Subtitle of host publicationContributions Presented at the 18th UK Workshop on Computational Intelligence, September 5-7, 2018, Nottingham, UK
EditorsAhmad Lotfi, Hamid Bouchachia, Alexander Gegov, Caroline Langensiepen, Martin McGinnity
PublisherSpringer
Pages57-70
ISBN (Electronic)978-3-319-97982-3
ISBN (Print)978-3-319-97981-6
DOIs
Publication statusPublished - Sep 2018
Event18th UK Workshop on Computational Intelligence - Nottingham, United Kingdom
Duration: 5 Sep 20187 Sep 2018

Publication series

NameAdvances in Intelligent Systems and Computing
PublisherSpringer
Volume840
ISSN (Print)2194-5357
ISSN (Electronic)2194-5365

Workshop

Workshop18th UK Workshop on Computational Intelligence
Country/TerritoryUnited Kingdom
Period5/09/187/09/18

Keywords

  • Neural Network
  • Bernstein Polynomial
  • Partial Differential Equations.

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