Tensor-based dynamic mode decomposition

S. Klus, P. Gelß, S. Peitz, C. Schütte, Nonlinearity 31 (2018) 3359–3380.

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Journal Article | Published | English
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Abstract
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 Kármán vortex street and the simulation of two merging vortices.
Publishing Year
Journal Title
Nonlinearity
Volume
31
Issue
7
Page
3359-3380
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Klus S, Gelß P, Peitz S, Schütte C. Tensor-based dynamic mode decomposition. Nonlinearity. 2018;31(7):3359-3380. doi:10.1088/1361-6544/aabc8f
Klus, S., Gelß, P., Peitz, S., & Schütte, C. (2018). Tensor-based dynamic mode decomposition. Nonlinearity, 31(7), 3359–3380. https://doi.org/10.1088/1361-6544/aabc8f
@article{Klus_Gelß_Peitz_Schütte_2018, title={Tensor-based dynamic mode decomposition}, volume={31}, DOI={10.1088/1361-6544/aabc8f}, number={7}, journal={Nonlinearity}, author={Klus, Stefan and Gelß, Patrick and Peitz, Sebastian and Schütte, Christof}, year={2018}, pages={3359–3380} }
Klus, Stefan, Patrick Gelß, Sebastian Peitz, and Christof Schütte. “Tensor-Based Dynamic Mode Decomposition.” Nonlinearity 31, no. 7 (2018): 3359–80. https://doi.org/10.1088/1361-6544/aabc8f.
S. Klus, P. Gelß, S. Peitz, and C. Schütte, “Tensor-based dynamic mode decomposition,” Nonlinearity, vol. 31, no. 7, pp. 3359–3380, 2018.
Klus, Stefan, et al. “Tensor-Based Dynamic Mode Decomposition.” Nonlinearity, vol. 31, no. 7, 2018, pp. 3359–80, doi:10.1088/1361-6544/aabc8f.

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