Sparse and randomized sampling methods for scalable turbulent flow networks

This work demonstrates the effective use of scalable algorithms in randomized and sketched linear algebra to perform network-based analysis of complex fluid flows. Network theoretic approaches can help reveal the connectivity structure among a set of fluid 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 leading network quantities, such as the leading eigendecomposition of the adjacency matrix, using sparse and randomized techniques from linear algebra. First, we explore importance sampling to identify key locations to sample in the turbulent vorticity field that are most correlated with network quantities of interest. Importance sampling is then combined with the Nystr\"om method to approximate the leading eigendecomposition, resulting in significant computational savings. The effectiveness of the proposed technique is demonstrated on two and three-dimensional isotropic turbulence.