Sparsity-promoting dynamic mode decomposition

Mihailo R. Jovanovic; Peter J. Schmid; Joseph W. Nichols

doi:10.1063/1.4863670

journal article Feb 01, 2014

Sparsity-promoting dynamic mode decomposition

Mihailo R. Jovanovic Peter J. Schmid

Joseph W. Nichols

Physics of Fluids Vol. 26 No. 2 · AIP Publishing

View at Publisher Save 10.1063/1.4863670

Abstract

Dynamic mode decomposition (DMD) represents an effective means for capturing the essential features of numerically or experimentally generated flow fields. In order to achieve a desirable tradeoff between the quality of approximation and the number of modes that are used to approximate the given fields, we develop a sparsity-promoting variant of the standard DMD algorithm. Sparsity is induced by regularizing the least-squares deviation between the matrix of snapshots and the linear combination of DMD modes with an additional term that penalizes the ℓ1-norm of the vector of DMD amplitudes. The globally optimal solution of the resulting regularized convex optimization problem is computed using the alternating direction method of multipliers, an algorithm well-suited for large problems. Several examples of flow fields resulting from numerical simulations and physical experiments are used to illustrate the effectiveness of the developed method.

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See supplementary material at http://dx.doi.org/10.1063/1.4863670 for a brief description of MATLAB implementation of the Sparsity-Promoting Dynamic Mode Decomposition (DMDSP) algorithm and for additional information about the examples considered in this paper, including Matlab source codes and problem data.

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Details

Published: Feb 01, 2014
Vol/Issue: 26(2)

Authors

M

Mihailo R. Jovanovic

University of Minnesota 1 Department of Electrical and Computer Engineering, , Minneapolis, Minnesota 55455, USA

P

Peter J. Schmid

Ecole Polytechnique 2 Laboratoire d’Hydrodynamique (LadHyX), , 91128 Palaiseau cedex, France

J

Joseph W. Nichols

University of Minnesota 3 Department of Aerospace Engineering and Mechanics, , Minneapolis, Minnesota 55455, USA

Cite This Article

Mihailo R. Jovanovic, Peter J. Schmid, Joseph W. Nichols (2014). Sparsity-promoting dynamic mode decomposition. Physics of Fluids, 26(2). https://doi.org/10.1063/1.4863670

Sparsity-promoting dynamic mode decomposition

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