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Simulating the dynamics of a nonequilibrium quantum many-body system bycomputing the two-time Green's function associated with such a system iscomputationally challenging. However, we are often interested in the timediagonal of such a Green's function or time dependent physical observables thatare functions of one time. In this paper, we discuss the possibility of usingdynamic model decomposition (DMD), a data-driven model order reductiontechnique, to characterize one-time observables associated with thenonequilibrium dynamics using snapshots computed within a small time window.The DMD method allows us to efficiently predict long time dynamics from alimited number of trajectory samples. We demonstrate the effectiveness of DMDon a model two-band system. We show that, in the equilibrium limit, the DMDanalysis yields results that are consistent with those produced from a linearresponse analysis. In the nonequilibrium case, the extrapolated dynamicsproduced by DMD is more accurate than a special Fourier extrapolation schemepresented in this paper. We point out a potential pitfall of the standard DMDmethod caused by insufficient spatial/momentum resolution of the discretizationscheme. We show how this problem can be overcome by using a variant of the DMDmethod known as higher order DMD.

Analyzing and predicting non-equilibrium many-body dynamics via dynamic mode decomposition