A data-driven surrogate modeling approach for time-dependent incompressible Navier-Stokes equations with dynamic mode decomposition and manifold interpolation
This work introduces a novel approach for data-driven model reduction of time-dependent parametric partial differential equations. Using a multi-step procedure consisting of proper orthogonal decomposition, dynamic mode decomposition, and manifold interpolation, the proposed approach allows to accur...
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| Published in | Advances in computational mathematics Vol. 49; no. 2 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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01.04.2023
Springer Nature B.V |
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| Abstract | This work introduces a novel approach for data-driven model reduction of time-dependent parametric partial differential equations. Using a multi-step procedure consisting of proper orthogonal decomposition, dynamic mode decomposition, and manifold interpolation, the proposed approach allows to accurately recover field solutions from a few large-scale simulations. Numerical experiments for the Rayleigh-Bénard cavity problem show the effectiveness of such multi-step procedure in two parametric regimes, i.e., medium and high Grashof number. The latter regime is particularly challenging as it nears the onset of turbulent and chaotic behavior. A major advantage of the proposed method in the context of time-periodic solutions is the ability to recover frequencies that are not present in the sampled data. |
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| AbstractList | This work introduces a novel approach for data-driven model reduction of time-dependent parametric partial differential equations. Using a multi-step procedure consisting of proper orthogonal decomposition, dynamic mode decomposition, and manifold interpolation, the proposed approach allows to accurately recover field solutions from a few large-scale simulations. Numerical experiments for the Rayleigh-Bénard cavity problem show the effectiveness of such multi-step procedure in two parametric regimes, i.e., medium and high Grashof number. The latter regime is particularly challenging as it nears the onset of turbulent and chaotic behavior. A major advantage of the proposed method in the context of time-periodic solutions is the ability to recover frequencies that are not present in the sampled data. |
| ArticleNumber | 22 |
| Author | Quaini, Annalisa Hess, Martin W. Rozza, Gianluigi |
| Author_xml | – sequence: 1 givenname: Martin W. surname: Hess fullname: Hess, Martin W. email: mhess@sissa.it organization: mathLab, SISSA – sequence: 2 givenname: Annalisa surname: Quaini fullname: Quaini, Annalisa email: quaini@math.uh.edu organization: Department of Mathematics, University of Houston – sequence: 3 givenname: Gianluigi orcidid: 0000-0002-0810-8812 surname: Rozza fullname: Rozza, Gianluigi email: gianluigi.rozza@sissa.it organization: mathLab, SISSA |
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De Gruyter. https://doi.org/10.1515/9783110498967-007 (2021) SL Brunton (10016_CR23) 2016; 113 10016_CR3 MW Hess (10016_CR19) 2019; 351 10016_CR2 10016_CR1 R Zimmermann (10016_CR49) 2014; 36 PJ Schmid (10016_CR26) 2010; 656 H Herrero (10016_CR8) 2013; 261-262 10016_CR29 F Pichi (10016_CR15) 2020; 42 10016_CR22 10016_CR25 F Pichi (10016_CR12) 2019; 81 J Degroote (10016_CR45) 2010; 63 10016_CR21 10016_CR20 T Sayadi (10016_CR28) 2015; 27 A Noor (10016_CR4) 1982; 34 SL Brunton (10016_CR16) 2014; 13 G Pitton (10016_CR11) 2017; 344 B Kramer (10016_CR17) 2017; 16 A Noor (10016_CR5) 1994; 5 P Benner (10016_CR44) 2015; 57 10016_CR14 10016_CR13 JL Guermond (10016_CR35) 2003; 41 Z Gao (10016_CR27) 2021; 452 A Noor (10016_CR7) 1983; 16 GE Karniadakis (10016_CR36) 1991; 97 BO Koopman (10016_CR24) 1931; 17 DG Giovanis (10016_CR50) 2020; 370 K Kakimoto (10016_CR34) 1995; 30 10016_CR47 10016_CR46 D Amsallem (10016_CR43) 2011; 33 S Le Clainche (10016_CR41) 2017; 16 F Pla (10016_CR9) 2015; 119 G Pitton (10016_CR10) 2017; 73 H Arbabi (10016_CR42) 2017; 16 MW Hess (10016_CR18) 2022; 56 10016_CR38 10016_CR37 10016_CR39 N Demo (10016_CR40) 2018; 3 10016_CR30 A Noor (10016_CR6) 1983; 19 H Peuscher (10016_CR48) 2010; 58 10016_CR32 10016_CR31 |
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| SubjectTerms | Computational mathematics Computational Mathematics and Numerical Analysis Computational Science and Engineering Grashof number Interpolation Manifolds Mathematical and Computational Biology Mathematical Modeling and Industrial Mathematics Mathematical models Mathematics Mathematics and Statistics Model reduction Navier-Stokes equations Partial differential equations Proper Orthogonal Decomposition Time dependence Visualization |
| Title | A data-driven surrogate modeling approach for time-dependent incompressible Navier-Stokes equations with dynamic mode decomposition and manifold interpolation |
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