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:

Bai, Zhe  ^[1];

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Erichson, N. Benjamin ^[2]; Gopalakrishnan Meena, Muralikrishnan ^[3]; Taira, Kunihiko ^[3]; Brunton, Steven L. ^[2]

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+ Show Author Affiliations

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:

2019-11-18

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