Sparsity-promoting dynamic mode decomposition

TLDR

Dynamic mode decomposition efficiently captures essential features of numerically or experimentally generated flow fields. The study develops a sparsity‑promoting variant of DMD to balance approximation quality with the number of modes used. The method imposes an ℓ1 penalty on DMD amplitudes in a least‑squares fit and solves the resulting convex problem with the alternating direction method of multipliers. Numerical simulations and physical experiments demonstrate the effectiveness of the sparsity‑promoting DMD.

Abstract

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.