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Computing the numerical solution of the Kadanoff-Baym equations, a set ofnonlinear integral differential equations satisfied by two-time Green'sfunctions derived from many-body perturbation theory for a quantum many-bodysystem away from equilibrium, is a challenging task. Recently, we havesuccessfully applied dynamic mode decomposition (DMD) to construct a datadriven reduced order model that can be used to extrapolate the time-diagonal ofa two-time Green's function from numerical solution of the KBE within a smalltime window. In this paper, we extend the previous work and use DMD to predictoff-diagonal elements of the two-time Green's function. We partition thetwo-time Green's function into a number of one-time functions along thediagonal and subdiagonls of the two-time window as well as in horizontal andvertical directions. We use DMD to construct separate reduced order models topredict the dynamics of these one-time functions in a two-step procedure. Weextrapolate along diagonal and several subdiagonals within a subdiagonal bandof a two-time window in the first step. In the second step, we use DMD toextrapolate the Green's function outside of the sub-diagonal band. Wedemonstrate the efficiency and accuracy of this approach by applying it to atwo-band Hubbard model problem.

Using dynamic mode decomposition to predict the dynamics of a two-time non-equilibrium Green's function