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Prediction of Discretization of GMsFEM Using Deep Learning

Author

Listed:
  • Min Wang

    (Department of Mathematics, Texas A&M University, College Station, TX 77843, USA)

  • Siu Wun Cheung

    (Department of Mathematics, Texas A&M University, College Station, TX 77843, USA)

  • Eric T. Chung

    (Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, China)

  • Yalchin Efendiev

    (Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
    Multiscale Model Reduction Laboratory, North-Eastern Federal University, 677980 Yakutsk, Russia)

  • Wing Tat Leung

    (Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA)

  • Yating Wang

    (Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
    Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA)

Abstract

In this paper, we propose a deep-learning-based approach to a class of multiscale problems. The generalized multiscale finite element method (GMsFEM) has been proven successful as a model reduction technique of flow problems in heterogeneous and high-contrast porous media. The key ingredients of GMsFEM include mutlsicale basis functions and coarse-scale parameters, which are obtained from solving local problems in each coarse neighborhood. Given a fixed medium, these quantities are precomputed by solving local problems in an offline stage, and result in a reduced-order model. However, these quantities have to be re-computed in case of varying media (various permeability fields). The objective of our work is to use deep learning techniques to mimic the nonlinear relation between the permeability field and the GMsFEM discretizations, and use neural networks to perform fast computation of GMsFEM ingredients repeatedly for a class of media. We provide numerical experiments to investigate the predictive power of neural networks and the usefulness of the resultant multiscale model in solving channelized porous media flow problems.

Suggested Citation

  • Min Wang & Siu Wun Cheung & Eric T. Chung & Yalchin Efendiev & Wing Tat Leung & Yating Wang, 2019. "Prediction of Discretization of GMsFEM Using Deep Learning," Mathematics, MDPI, vol. 7(5), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:412-:d:229268
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    Cited by:

    1. Zecheng Zhang & Eric T. Chung & Yalchin Efendiev & Wing Tat Leung, 2020. "Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations," Mathematics, MDPI, vol. 8(5), pages 1-17, May.

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