Deep multiscale model learning

Wang, Yating; Cheung, Siu Wun; Chung, Eric T.; Efendiev, Yalchin; Wang, Min

doi:10.1016/j.jcp.2019.109071

Deep multiscale model learning

Journal Article · Thu Nov 21 00:00:00 EST 2019 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2019.109071· OSTI ID:1802155

Wang, Yating ^[1]; ^[2]; Chung, Eric T. ^[3]; Efendiev, Yalchin ^[4]; Wang, Min ^[5]

Texas A & M Univ., College Station, TX (United States); Purdue Univ., West Lafayette, IN (United States); OSTI
Texas A & M Univ., College Station, TX (United States)
Chinese University of Hong Kong (Hong Kong)
Texas A & M Univ., College Station, TX (United States); North-Eastern Federal University, Yakutsk (Russia)
Texas A & M Univ., College Station, TX (United States); Duke Univ., Durham, NC (United States)

The objective of this article is to design novel multi-layer neural networks for multiscale simulations of flows taking into account the observed fine data and physical modeling concepts. Our approaches use deep learning techniques combined with local multiscale model reduction methodologies to predict flow dynamics. Using reduced-order model concepts is important for constructing robust deep learning architectures since the reduced-order models provide fewer degrees of freedom. We consider flow dynamics in porous media as multi-layer networks in this work. More precisely, the solution (e.g., pressures and saturation) at the time instant n+1 depends on the solution at the time instant n and input parameters, such as permeability fields, forcing terms, and initial conditions. One can regard the solution as a multi-layer network, where each layer, in general, is a nonlinear forward map and the number of layers relates to the internal time steps. We will rely on rigorous model reduction concepts to define unknowns and connections between layers. It is critical to use reduced-order models for this purpose, which will identify the regions of influence and the appropriate number of variables. Furthermore, due to the lack of available observed fine data, the reduced-order model can provide us sufficient inexpensive data as needed. The designed deep neural network will be trained using both coarse simulation data which is obtained from the reduced-order model and observed fine data. We will present the main ingredients of our approach and numerical examples. Numerical results show that using deep learning with data generated from multiscale models as well as available observed fine data, we can obtain an improved forward map which can better approximate the fine scale model.

View Accepted Manuscript (DOE)

Research Organization:: Texas A & M Univ., College Station, TX (United States)

Sponsoring Organization:: CUHK; National Priorities Research Program; National Science Foundation (NSF); Russian Federation Government; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0010713

OSTI ID:: 1802155

Alternate ID(s):: OSTI ID: 1691935

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 406; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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