Artificial neural network methods for the solution of second order boundary value problems

Cosmin Anitescu, Elena Atroshchenko, Naif Alajlan, Timon Rabczuk

    Research output: Contribution to journalArticlepeer-review

    635 Citations (Scopus)

    Abstract

    We present a method for solving partial differential equations using artificial neural networks and an adaptive collocation strategy. In this procedure, a coarse grid of training points is used at the initial training stages, while more points are added at later stages based on the value of the residual at a larger set of evaluation points. This method increases the robustness of the neural network approximation and can result in significant computational savings, particularly when the solution is non-smooth. Numerical results are presented for benchmark problems for scalar-valued PDEs, namely Poisson and Helmholtz equations, as well as for an inverse acoustics problem.

    Original languageEnglish
    Pages (from-to)345-359
    Number of pages15
    JournalComputers, Materials and Continua
    Volume59
    Issue number1
    DOIs
    Publication statusPublished - 2019

    Bibliographical note

    Funding Information:
    Acknowledgements: N. Alajlan and T. Rabczuk acknowledge the Distinguished Scientist Fellowship Program (DSFP) at King Saud University for supporting this work.

    Publisher Copyright:
    Copyright © 2019 Tech Science Press.

    Keywords

    • Adaptive collocation
    • Artificial neural networks
    • Deep learning
    • Inverse problems

    ASJC Scopus subject areas

    • Biomaterials
    • Modelling and Simulation
    • Mechanics of Materials
    • Computer Science Applications
    • Electrical and Electronic Engineering

    Fingerprint

    Dive into the research topics of 'Artificial neural network methods for the solution of second order boundary value problems'. Together they form a unique fingerprint.

    Cite this