Sparsity-promoting dynamic mode decomposition

Mihailo R. Jovanovic (1) , Peter J. Schmid (2) , Joseph W. Nichols (3)

1 Department of Electrical and Computer Engineering
2 LadHyX - Laboratoire d'hydrodynamique
3 AEM - Department of Aerospace Engineering and Mechanics [Minneapolis]

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 l(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. (C) 2014 AIP Publishing LLC.

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Mihailo R. Jovanovic, Peter J. Schmid, Joseph W. Nichols. Sparsity-promoting dynamic mode decomposition. Physics of Fluids, 2014, 26 (2), ⟨10.1063/1.4863670⟩. ⟨hal-00995141⟩