  In this work, we extend our recently developed super-resolution (SR) model
for cosmological simulations to produce fully time consistent evolving
representations of the particle phase-space distribution. We employ a
style-based constrained generative adversarial network (Style-GAN) where the
changing cosmic time is an input style parameter to the network. The matter
power spectrum and halo mass function agree well with results from
high-resolution N-body simulations over the full trained redshift range ($10
\le z \le 0$). Furthermore, we assess the temporal consistency of our SR model
by constructing halo merger trees. We examine progenitors, descendants and mass
growth along the tree branches. All statistical indicators demonstrate the
ability of our SR model to generate satisfactory high-resolution simulations
based on low-resolution inputs.
