Statistical learning for fluid flows: Sparse Fourier divergence-free approximations
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2022-09-27
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Stochastic Numerics Research Group
KAUST Grant Number
OSRURF/1/2281-01-01
URF/1/2584-01-01
Date
2021-09-27Preprint Posting Date
2021-07-15Online Publication Date
2021-09-27Print Publication Date
2021-09Embargo End Date
2022-09-27Submitted Date
2021-07-27Permanent link to this record
http://hdl.handle.net/10754/672243
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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 L2 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.Citation
Espath, L., Kabanov, D., Kiessling, J., & Tempone, R. (2021). Statistical learning for fluid flows: Sparse Fourier divergence-free approximations. Physics of Fluids, 33(9), 097108. doi:10.1063/5.0064862Sponsors
This work was partially supported by the KAUST Office of Sponsored Research (OSR) under Award Nos. URF/1/2281-01-01 and URF/1/2584-01-01 in the KAUST Competitive Research Grants Program Round 8, the Alexander von Humboldt Foundation, and Coordination for the Improvement of Higher Education Personnel (CAPES).Publisher
AIP PublishingJournal
Physics of FluidsarXiv
2107.07633Additional Links
https://aip.scitation.org/doi/10.1063/5.0064862ae974a485f413a2113503eed53cd6c53
10.1063/5.0064862