  We propose a new method for computing Dynamic Mode Decomposition (DMD)
evolution matrices, which we use to analyze dynamical systems. Unlike the
majority of existing methods, our approach is based on a variational
formulation consisting of data alignment penalty terms and constitutive
orthogonality constraints. Our method does not make any assumptions on the
structure of the data or their size, and thus it is applicable to a wide range
of problems including non-linear scenarios or extremely small observation sets.
In addition, our technique is robust to noise that is independent of the
dynamics and it does not require input data to be sequential. Our key idea is
to introduce a regularization term for the forward and backward dynamics. The
obtained minimization problem is solved efficiently using the Alternating
Method of Multipliers (ADMM) which requires two Sylvester equation solves per
iteration. Our numerical scheme converges empirically and is similar to a
provably convergent ADMM scheme. We compare our approach to various
state-of-the-art methods on several benchmark dynamical systems.
