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    Statistical learning for fluid flows: Sparse Fourier divergence-free approximations

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    Name:
    Statistical_5.0064862.pdf
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    15.41Mb
    Format:
    PDF
    Description:
    Publisher's version
    Embargo End Date:
    2022-09-27
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    Type
    Article
    Authors
    Espath, Luis cc
    Kabanov, Dmitry cc
    Kiessling, Jonas cc
    Tempone, Raul cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Stochastic Numerics Research Group
    KAUST Grant Number
    OSR
    URF/1/2281-01-01
    URF/1/2584-01-01
    Date
    2021-09-27
    Preprint Posting Date
    2021-07-15
    Online Publication Date
    2021-09-27
    Print Publication Date
    2021-09
    Embargo End Date
    2022-09-27
    Submitted Date
    2021-07-27
    Permanent link to this record
    http://hdl.handle.net/10754/672243
    
    Metadata
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    Abstract
    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:10.1063/5.0064862
    Sponsors
    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 Publishing
    Journal
    Physics of Fluids
    DOI
    10.1063/5.0064862
    arXiv
    2107.07633
    Additional Links
    https://aip.scitation.org/doi/10.1063/5.0064862
    ae974a485f413a2113503eed53cd6c53
    10.1063/5.0064862
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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