Wavelet‐based dynamic mode decomposition

Randomized Dynamic Mode Decomposition

This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations. They are able to ease the computational challenges arising in the area of ‘big data’. The idea is to derive from the high-dimensional input matrix a smaller matrix, which is then used to effi...

Bayesian Dynamic Mode Decomposition

Dynamic mode decomposition (DMD) is a datadriven method for calculating a modal representation of a nonlinear dynamical system, and it has been utilized in various fields of science and engineering. In this paper, we propose Bayesian DMD, which provides a principled way to transfer the advantages of the Bayesian formulation into DMD. To this end, we first develop a probabilistic model correspon...

Sparsity-promoting dynamic mode decomposition

Sparsity-promoting dynamic mode decomposition Mihailo R. Jovanović,1,a) Peter J. Schmid,2,b) and Joseph W. Nichols3,c) 1Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA 2Laboratoire d’Hydrodynamique (LadHyX), Ecole Polytechnique, 91128 Palaiseau cedex, France 3Department of Aerospace Engineering and Mechanics, University of Minnesota,...

Higher Order Dynamic Mode Decomposition

Low-rank Approximation and 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 low-rank extension takes the form of a nonconvex optimisation problem. To the best of our knowledge, only sub-optimal algorithms have been proposed in the literatu...