  Models for finite-rate-chemistry in underresolved flows still pose one of the
main challenges for predictive simulations of complex configurations. The
problem gets even more challenging if turbulence is involved. This work
advances the recently developed PIESRGAN modeling approach to turbulent
premixed combustion. For that, the physical information processed by the
network and considered in the loss function are adjusted, the training process
is smoothed, and especially effects from density changes are considered. The
resulting model provides good results for a priori and a posteriori tests on
direct numerical simulation data of a fully turbulent premixed flame kernel.
The limits of the modeling approach are discussed. Finally, the model is
employed to compute further realizations of the premixed flame kernel, which
are analyzed with a scale-sensitive framework regarding their cycle-to-cycle
variations. The work shows that the data-driven PIESRGAN subfilter model can
very accurately reproduce direct numerical simulation data on much coarser
meshes, which is hardly possible with classical subfilter models, and enables
studying statistical processes more efficiently due to the smaller computing
cost.
