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arXiv · 1309.4165

Sparsity-promoting dynamic mode decomposition

Mihailo R. Jovanović·Peter J. Schmid·Joseph W. Nichols
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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. In our method, 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 $\ell_1$-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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Mihailo R. Jovanović, Peter J. Schmid, Joseph W. Nichols. 2013-09-17. Sparsity-promoting dynamic mode decomposition. https://doi.org/10.1063/1.4863670

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