表征大尺度旋涡流动网络的随机方法
Randomized methods to characterize large-scale vortical flow network
摘要：
我们证明了有效地使用随机方法线性代数进行网络为基础的分析复杂的涡流。网络理论方法可以揭示一组涡元之间的连通性结构，分析它们的集体动力学行为。这些方法最近已被推广到分析高维湍流，网络计算可能变得过于昂贵。在这项工作中，我们提出了有效的方法来近似网络数量，如领先的特征分解的邻接矩阵，使用随机方法。具体来说，我们使用Nyström方法来近似的领导特征值和特征向量，实现显着的计算节省和减少内存需求。所提出的技术的有效性被证明在两个高维流场：二维流动通过翼型和二维湍流。我们发现，准均匀列采样优于均匀列采样，而两者具有相同的计算复杂性。
英文摘要：
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.
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