SparsityPromoting Dynamic Mode DecompositionMihailo R. Jovanovic, Peter J. Schmid, and Joseph W. Nichols AbstractDynamic 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 sparsitypromoting variant of the standard DMD algorithm. Sparsity is induced by regularizing the leastsquares deviation between the matrix of snapshots and the linear combination of DMD modes with an additional term that penalizes the 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 wellsuited 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. Reference
