Solving Partial Differential Equations with Bernstein Neural Networks

  • Sina Razvarz
  • Raheleh JafariEmail author
  • Alexander Gegov
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 840)


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.


Neural network Bernstein polynomial Partial Differential Equations 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Departamento de Control AutomaticoCINVESTAV-IPN (National Polytechnic Institute)Mexico CityMexico
  2. 2.Centre for Artificial Intelligence Research (CAIR)University of AgderGrimstadNorway
  3. 3.School of ComputingUniversity of PortsmouthPortsmouthUK

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