2013/09/17 by Mihailo R. Jovanović, Peter J. Schmid, Joseph W. Nichols · 2 citations
Physics and Astronomy · Mathematics · #physics.flu-dyn #math.DS #math.OC #physics.data-an
paper · pdf · doi:10.1063/1.4863670
published as Phys. Fluids, vol. 26, no. 2, p. 024103 (22 pages), February 2014 · Submitted to Physics of Fluids
arxiv created 2013/09/17 · arxiv updated 2014/12/11
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 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.