The HF-GKBA offers an approximate numerical procedure for propagating the
two-time non-equilibrium Green's function(NEGF). Here we compare the HF-GKBA to
exact results for a variety of systems with long and short-range interactions,
different two-body interaction strengths and various non-equilibrium
preparations. We find excellent agreement between the HF-GKBA and exact time
evolution in models when more realistic long-range exponentially decaying
interactions are considered. This agreement persists for long times and for
intermediate to strong interaction strengths. In large systems, HF-GKBA becomes
prohibitively expensive for long-time evolutions. For this reason, look at the
use of dynamical mode decomposition(DMD) to reconstruct long-time NEGF
trajectories from a sample of the initial trajectory. Using no more than 16\%
of the total time evolution we reconstruct the total trajectory with high
fidelity. Our results show the potential for DMD to be used in conjunction with
HF-GKBA to calculate long time trajectories in large-scale systems