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Title: Randomized methods to characterize large-scale vortical flow networks

Abstract

We demonstrate the effective use of randomized methods for linear algebra to perform network-based analysis of complex vortical flows. Network theoretic approaches can reveal the connectivity structures among a set of vortical elements and analyze their collective dynamics. These approaches have recently been generalized to analyze high-dimensional turbulent flows, for which network computations can become prohibitively expensive. In this work, we propose efficient methods to approximate network quantities, such as the leading eigendecomposition of the adjacency matrix, using randomized methods. Specifically, we use the Nyström method to approximate the leading eigenvalues and eigenvectors, achieving significant computational savings and reduced memory requirements. The effectiveness of the proposed technique is demonstrated on two high-dimensional flow fields: two-dimensional flow past an airfoil and two-dimensional turbulence. We find that quasi-uniform column sampling outperforms uniform column sampling, while both feature the same computational complexity.

Authors:
ORCiD logo [1];  [2];  [3];  [3];  [2]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  2. Univ. of Washington, Seattle, WA (United States)
  3. Univ. of California, Los Angeles, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1580871
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
PLoS ONE
Additional Journal Information:
Journal Volume: 14; Journal Issue: 11; Journal ID: ISSN 1932-6203
Publisher:
Public Library of Science
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; network analysis; fluid dynamics; randomized methods; sparse sampling; low-range approximation

Citation Formats

Bai, Zhe, Erichson, N. Benjamin, Gopalakrishnan Meena, Muralikrishnan, Taira, Kunihiko, and Brunton, Steven L. Randomized methods to characterize large-scale vortical flow networks. United States: N. p., 2019. Web. doi:10.1371/journal.pone.0225265.
Bai, Zhe, Erichson, N. Benjamin, Gopalakrishnan Meena, Muralikrishnan, Taira, Kunihiko, & Brunton, Steven L. Randomized methods to characterize large-scale vortical flow networks. United States. doi:10.1371/journal.pone.0225265.
Bai, Zhe, Erichson, N. Benjamin, Gopalakrishnan Meena, Muralikrishnan, Taira, Kunihiko, and Brunton, Steven L. Mon . "Randomized methods to characterize large-scale vortical flow networks". United States. doi:10.1371/journal.pone.0225265. https://www.osti.gov/servlets/purl/1580871.
@article{osti_1580871,
title = {Randomized methods to characterize large-scale vortical flow networks},
author = {Bai, Zhe and Erichson, N. Benjamin and Gopalakrishnan Meena, Muralikrishnan and Taira, Kunihiko and Brunton, Steven L.},
abstractNote = {We demonstrate the effective use of randomized methods for linear algebra to perform network-based analysis of complex vortical flows. Network theoretic approaches can reveal the connectivity structures among a set of vortical elements and analyze their collective dynamics. These approaches have recently been generalized to analyze high-dimensional turbulent flows, for which network computations can become prohibitively expensive. In this work, we propose efficient methods to approximate network quantities, such as the leading eigendecomposition of the adjacency matrix, using randomized methods. Specifically, we use the Nyström method to approximate the leading eigenvalues and eigenvectors, achieving significant computational savings and reduced memory requirements. The effectiveness of the proposed technique is demonstrated on two high-dimensional flow fields: two-dimensional flow past an airfoil and two-dimensional turbulence. We find that quasi-uniform column sampling outperforms uniform column sampling, while both feature the same computational complexity.},
doi = {10.1371/journal.pone.0225265},
journal = {PLoS ONE},
number = 11,
volume = 14,
place = {United States},
year = {2019},
month = {11}
}

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