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Statistical learnin...
Statistical learning for fluid flows : Sparse Fourier divergence-free approximations
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- Espath, Luis (author)
- Rhein Westfal TH Aachen, Dept Math, Gebaude-1953 1-OG,Pontdriesch 14-16, D-52062 Aachen, Germany.
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- Kabanov, Dmitry (author)
- Rhein Westfal TH Aachen, Dept Math, Gebaude-1953 1-OG,Pontdriesch 14-16, D-52062 Aachen, Germany.
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- Kiessling, Jonas (author)
- KTH,Matematik (Inst.),H Ai AB, Box 5216, S-10245 Stockholm, Sweden.
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- Tempone, Raul (author)
- Rhein Westfal TH Aachen, Dept Math, Gebaude-1953 1-OG,Pontdriesch 14-16, D-52062 Aachen, Germany.;Rhein Westfal TH Aachen, Math Uncertainty Quantificat, Aachen, Germany.;King Abdullah Univ Sci & Technol KAUST, Comp Elect & Math Sci & Engn Div CEMSE, Thuwal 239556900, Saudi Arabia.
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Rhein Westfal TH Aachen, Dept Math, Gebaude-1953 1-OG,Pontdriesch 14-16, D-52062 Aachen, Germany Matematik (Inst.) (creator_code:org_t)
- AIP Publishing, 2021
- 2021
- English.
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In: Physics of fluids. - : AIP Publishing. - 1070-6631 .- 1089-7666. ; 33:9
- Related links:
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http://arxiv.org/pdf...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Subject headings
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- We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free approximation based on a discrete L & nbsp;projection. Within this physics-informed type of statistical learning framework, we adaptively build a sparse set of Fourier basis functions with corresponding coefficients by solving a sequence of minimization problems where the set of basis functions is augmented greedily at each optimization problem. We regularize our minimization problems with the seminorm of the fractional Sobolev space in a Tikhonov fashion. In the Fourier setting, the incompressibility (divergence-free) constraint becomes a finite set of linear algebraic equations. We couple our spatial approximation with the truncated singular-value decomposition of the flow measurements for temporal compression. Our computational framework thus combines supervised and unsupervised learning techniques. We assess the capabilities of our method in various numerical examples arising in fluid mechanics.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- MEDICIN OCH HÄLSOVETENSKAP -- Klinisk medicin -- Annan klinisk medicin (hsv//swe)
- MEDICAL AND HEALTH SCIENCES -- Clinical Medicine -- Other Clinical Medicine (hsv//eng)
Publication and Content Type
- ref (subject category)
- art (subject category)
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