Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: Comparison with linear subspace techniques

Kadeethum, Teeratorn; Ballarin, Francesco; Choi, Youngsoo; O'Malley, Daniel; Yoon, Hongkyu; Bouklas, Nikolaos

doi:10.1016/j.advwatres.2021.104098

Title: Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: Comparison with linear subspace techniques

Journal Article · 03 January 2022 · Advances in Water Resources

DOI: https://doi.org/10.1016/j.advwatres.2021.104098 · OSTI ID:1842833

^[1];

^[2]; Choi, Youngsoo ^[3];

^[4]; Yoon, Hongkyu ^[5];

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Cornell Univ., Ithaca, NY (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Catholic University of the Sacred Heart, Brescia (Italy)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Cornell Univ., Ithaca, NY (United States)

Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of CO₂ sequestration). Here, we extend and present a non-intrusive reduced order model of natural convection in porous media employing deep convolutional autoencoders for the compression and reconstruction and either radial basis function (RBF) interpolation or artificial neural networks (ANNs) for mapping parameters of partial differential equations (PDEs) on the corresponding nonlinear manifolds. To benchmark our approach, we also describe linear compression and reconstruction processes relying on proper orthogonal decomposition (POD) and ANNs. Further, we present comprehensive comparisons among different models through three benchmark problems. The reduced order models, linear and nonlinear approaches, are much faster than the finite element model, obtaining a maximum speed-up of 7 × 10⁶ because our framework is not bound by the Courant–Friedrichs–Lewy condition; hence, it could deliver quantities of interest at any given time contrary to the finite element model. Our model’s accuracy still lies within a relative error of 7% in the worst-case scenario. We illustrate that, in specific settings, the nonlinear approach outperforms its linear counterpart and vice versa. We hypothesize that a visual comparison between principal component analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE) could indicate which method will perform better prior to employing any specific compression strategy.

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Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); Horizon 2020 Program; European Research Council (ERC); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: NA0003525; AC52-07NA27344; 89233218CNA000001

OSTI ID:: 1842833

Report Number(s):: SAND--2022-0981J; LLNL-JRNL--824706; LA-UR-21-26841; 703131

Journal Information:: Advances in Water Resources, Journal Name: Advances in Water Resources Vol. 160; ISSN 0309-1708

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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