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Sparsity-promoting dynamic mode decomposition
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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. [Supplementary Material]
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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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