%0 Journal Article
%T Sparsity-promoting dynamic mode decomposition
%A Mihailo R. Jovanovi£¿
%A Peter J. Schmid
%A Joseph W. Nichols
%J Mathematics
%D 2013
%I arXiv
%R 10.1063/1.4863670
%X 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.
%U http://arxiv.org/abs/1309.4165v1