Prediction of Discretization of GMsFEM Using Deep Learning

Min Wang, Siu Wun Cheung, Eric T. Chung, Yalchin Efendiev, Wing Tat Leung and Yating Wang
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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
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

Mathematics, 2019, vol. 7, issue 5, 1-16

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.

Keywords: generalized multiscale finite element method; multiscale model reduction; deep learning (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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