Evaluation of Optimization Algorithms and Noise Robustness of Sparsity-Promoting Dynamic Mode Decomposition

In the present study, we organize the existing sparsity-promoting dynamic mode decomposition (DMDsp) in terms of noise robustness, propose faster optimization algorithm for DMDsp, and evaluate its characteristics. Two kinds of DMDsp, namely system-based DMDsp (sDMDsp) and observation-based DMDsp (oD...

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Published in:	IEEE access Vol. 10; pp. 80748 - 80763
Main Authors:	Iwasaki, Yuto, Nonomura, Taku, Nakai, Kumi, Nagata, Takayuki, Saito, Yuji, Asai, Keisuke
Format:	Journal Article
Language:	English
Published:	Piscataway IEEE 2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Data analysis Data mining Decomposition fluid dynamics Greedy algorithms Heuristic algorithms modal analysis Noise measurement Noise robustness Optimization optimization method Robustness system dynamics
ISSN:	2169-3536, 2169-3536
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Abstract	In the present study, we organize the existing sparsity-promoting dynamic mode decomposition (DMDsp) in terms of noise robustness, propose faster optimization algorithm for DMDsp, and evaluate its characteristics. Two kinds of DMDsp, namely system-based DMDsp (sDMDsp) and observation-based DMDsp (oDMDsp), combined with three kinds of optimization algorithm, namely the fast iterative shrinkage thresholding algorithm (FISTA), the alternating direction method of multipliers (ADMM), and a greedy algorithm, are investigated. For both sDMDsp and oDMDsp, FISTA yields the shortest processing time. The processing time for sDMDsp with FISTA is shorter than that for oDMDsp with FISTA. The original data reconstruction errors for sDMDsp and oDMDsp are similar among the three optimization algorithms. The noise robustness for sDMDsp and oDMDsp is evaluated. sDMDsp and oDMDsp have similar robustness to observation noise, except for a system with large system and observation noise, for which oDMDsp outperforms sDMDsp.
AbstractList	In the present study, we organize the existing sparsity-promoting dynamic mode decomposition (DMDsp) in terms of noise robustness, propose faster optimization algorithm for DMDsp, and evaluate its characteristics. Two kinds of DMDsp, namely system-based DMDsp (sDMDsp) and observation-based DMDsp (oDMDsp), combined with three kinds of optimization algorithm, namely the fast iterative shrinkage thresholding algorithm (FISTA), the alternating direction method of multipliers (ADMM), and a greedy algorithm, are investigated. For both sDMDsp and oDMDsp, FISTA yields the shortest processing time. The processing time for sDMDsp with FISTA is shorter than that for oDMDsp with FISTA. The original data reconstruction errors for sDMDsp and oDMDsp are similar among the three optimization algorithms. The noise robustness for sDMDsp and oDMDsp is evaluated. sDMDsp and oDMDsp have similar robustness to observation noise, except for a system with large system and observation noise, for which oDMDsp outperforms sDMDsp.
Author	Iwasaki, Yuto Asai, Keisuke Nakai, Kumi Nonomura, Taku Nagata, Takayuki Saito, Yuji
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SubjectTerms	Data analysis Data mining Decomposition fluid dynamics Greedy algorithms Heuristic algorithms modal analysis Noise measurement Noise robustness Optimization optimization method Robustness system dynamics
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Title	Evaluation of Optimization Algorithms and Noise Robustness of Sparsity-Promoting Dynamic Mode Decomposition
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