  Advancing our understanding of astrophysical turbulence is bottlenecked by
the limited resolution of numerical simulations that may not fully sample
scales in the inertial range. Machine learning (ML) techniques have
demonstrated promise in up-scaling resolution in both image analysis and
numerical simulations (i.e., superresolution). Here we employ and further
develop a physics-constrained convolutional neural network (CNN) ML model
called "MeshFreeFlowNet'' (MFFN) for superresolution studies of turbulent
systems. The model is trained both on the simulation images as well as the
evaluated PDEs, making it sensitive to the underlying physics of a particular
fluid system. We develop a framework for 2D turbulent Rayleigh-B\'enard
convection (RBC) generated with the \textsc{Dedalus} code by modifying the MFFN
architecture to include the full set of simulation PDEs and the boundary
conditions. Our training set includes fully developed turbulence sampling
Rayleigh numbers ($Ra$) of $Ra=10^6-10^{10}$. We evaluate the success of the
learned simulations by comparing the power spectra of the direct
\textsc{Dedalus} simulation to the predicted model output, and compare both
ground truth and predicted power spectral inertial range scalings to
theoretical predictions. We find that the updated network performs well at all
$Ra$ studied here in recovering large-scale information, including the inertial
range slopes. The superresolution prediction is overly dissipative at smaller
scales than that of the inertial range in all cases, but the smaller-scales are
better recovered in more turbulent, than laminar, regimes. This is likely
because more turbulent systems have a rich variety of structures at many length
scales compared to laminar flows.
