Randomized methods to characterize large-scale vortical flow networks

Zhe Bai, N. Benjamin Erichson, Muralikrishnan Gopalakrishnan Meena, Kunihiko Taira, Steven L. Brunton, Fang-Bao Tian
2019 PLoS ONE  
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
more » ... 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 pmid:31738778 pmcid:PMC6860431 fatcat:gl3oqlypozatna4zolpwq53zoq