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Article: Deep multiscale model learning

TitleDeep multiscale model learning
Authors
KeywordsMultiscale
Deep learning
Upscaling
Porous media
Neural network
Issue Date2020
Citation
Journal of Computational Physics, 2020, v. 406, article no. 109071 How to Cite?
AbstractThe objective of this paper 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.
Persistent Identifierhttp://hdl.handle.net/10722/303641
ISSN
2020 Impact Factor: 3.553
2020 SCImago Journal Rankings: 1.882
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorWang, Yating-
dc.contributor.authorCheung, Siu Wun-
dc.contributor.authorChung, Eric T.-
dc.contributor.authorEfendiev, Yalchin-
dc.contributor.authorWang, Min-
dc.date.accessioned2021-09-15T08:25:43Z-
dc.date.available2021-09-15T08:25:43Z-
dc.date.issued2020-
dc.identifier.citationJournal of Computational Physics, 2020, v. 406, article no. 109071-
dc.identifier.issn0021-9991-
dc.identifier.urihttp://hdl.handle.net/10722/303641-
dc.description.abstractThe objective of this paper 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.-
dc.languageeng-
dc.relation.ispartofJournal of Computational Physics-
dc.subjectMultiscale-
dc.subjectDeep learning-
dc.subjectUpscaling-
dc.subjectPorous media-
dc.subjectNeural network-
dc.titleDeep multiscale model learning-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.jcp.2019.109071-
dc.identifier.scopuseid_2-s2.0-85077756823-
dc.identifier.volume406-
dc.identifier.spagearticle no. 109071-
dc.identifier.epagearticle no. 109071-
dc.identifier.eissn1090-2716-
dc.identifier.isiWOS:000514822600017-

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