Dynamic mode decomposition for aero-optic wavefront characterization

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...

Dynamic mode decomposition for compressive system identification

Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this work, we integrate and unify two recent innovations that extend DMD to systems with actuation [56] and systems with heavily subsampled measurements [17]. When ...

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