  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.
