  Simulating the dynamics of a nonequilibrium quantum many-body system by
computing the two-time Green's function associated with such a system is
computationally challenging. However, we are often interested in the time
diagonal of such a Green's function or time dependent physical observables that
are functions of one time. In this paper, we discuss the possibility of using
dynamic model decomposition (DMD), a data-driven model order reduction
technique, to characterize one-time observables associated with the
nonequilibrium dynamics using snapshots computed within a small time window.
The DMD method allows us to efficiently predict long time dynamics from a
limited number of trajectory samples. We demonstrate the effectiveness of DMD
on a model two-band system. We show that, in the equilibrium limit, the DMD
analysis yields results that are consistent with those produced from a linear
response analysis. In the nonequilibrium case, the extrapolated dynamics
produced by DMD is more accurate than a special Fourier extrapolation scheme
presented in this paper. We point out a potential pitfall of the standard DMD
method caused by insufficient spatial/momentum resolution of the discretization
scheme. We show how this problem can be overcome by using a variant of the DMD
method known as higher order DMD.
