Tensor-based dynamic mode decomposition
Tensor-based dynamic mode decomposition
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DOI：
10.1088/1361-6544/aabc8f
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发表时间：
2018-07-01
期刊：
影响因子：
1.7
通讯作者：
Schuette, Christof
中科院分区：
文献类型：
--
作者：
Klus, Stefan;Gelss, Patrick;Schuette, Christof
动态模态分解（DMD）是近年来发展起来的一种分析复杂动力系统行为的工具。在本文中，我们将提出DMD的扩展，该扩展利用潜在高维数据集的低秩张量分解来计算相应的DMD模式和特征值。我们的目标是降低计算复杂度，以及存储数据所需的内存量，以减轻维数灾难。这些张量为基础的方法的效率将说明与几个不同的流体动力学问题，如冯卡门涡街和两个合并涡的模拟的帮助。
Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially high-dimensional data sets to compute the corresponding DMD modes and eigenvalues. The goal is to reduce the computational complexity and also the amount of memory required to store the data in order to mitigate the curse of dimensionality. The efficiency of these tensor-based methods will be illustrated with the aid of several different fluid dynamics problems such as the von Karman vortex street and the simulation of two merging vortices.