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Conference Papers Year : 2017

Optimal Low-Rank Dynamic Mode Decomposition


Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This extension is of particular interest for reduced-order modeling in various applicative domains, e.g. for climate prediction, to study molecular dynamics or micro-electromechanical devices. This low-rank extension takes the form of a non-convex optimization problem. To the best of our knowledge, only sub-optimal algorithms have been proposed in the literature to compute the solution of this problem. In this paper, we prove that there exists a closed-form optimal solution to this problem and design an effective algorithm to compute it based on Singular Value Decomposition (SVD). A toy-example illustrates the gain in performance of the proposed algorithm compared to state-of-the-art techniques.

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hal-01429975 , version 1 (09-01-2017)



Patrick Héas, Cédric Herzet. Optimal Low-Rank Dynamic Mode Decomposition. Proceedings of the 2017 IEEE International Conference on Acoustics, Speech and Signal Processing, New Orleans 2017, Mar 2017, New Orleans, United States. ⟨10.1109/ICASSP.2017.7952999⟩. ⟨hal-01429975⟩
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