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

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 autoen...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Advances in water resources Ročník 160; s. 104098
Hlavní autoři: Kadeethum, T., Ballarin, F., Choi, Y., O’Malley, D., Yoon, H., Bouklas, N.
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States Elsevier Ltd 01.02.2022
Elsevier
Témata:
carbon dioxide
convection
Data-driven
Deep convolutional autoencoder
Deep convolutional autoencoder Finite element Nonlinear problem
Finite element
finite element analysis
MATHEMATICS AND COMPUTING
Non-intrusive
Nonlinear problem
principal component analysis
Reduced order modeling
water
Non-intrusive
Data-driven
Reduced order modeling
Nonlinear problem
Deep convolutional autoencoder
Finite element
ISSN:0309-1708, 1872-9657
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí: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. 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. •A data-driven framework with deep convolutional autoencoders to approximate natural convection in porous media is developed.•The framework can handle data with adaptive time-stepping and deliver the solution at any time between the training snapshots.•Visualization of latent space can be used to select an appropriate method between linear and nonlinear approaches.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
NA0003525; AC52-07NA27344; 20200575ECR; 89233218CNA000001
European Research Council (ERC)
Horizon 2020 Program
USDOE Laboratory Directed Research and Development (LDRD) Program
USDOE National Nuclear Security Administration (NNSA)
SAND-2022-0981J; LLNL-JRNL-824706; LA-UR-21-26841
ISSN:0309-1708
1872-9657
DOI:10.1016/j.advwatres.2021.104098