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A prominent bottleneck for advancing our understanding of astrophysicalturbulence is the limited resolution of numerical simulations, which inhibitsfully sampling scales in the inertial range. Machine learning (ML) techniqueshave demonstrated promise in up-scaling resolution in both image analysis andnumerical simulations (i.e., superresolution). Here we employ and furtherdevelop a physics-constrained convolutional neural network (CNN) ML modelcalled "MeshFreeFlowNet'' for superresolution studies of turbulent systems. TheMeshFreeFlowNet CNN is trained both on the simulation images as well as theevaluated PDEs, making it sensitive to the underlying physics of a particularfluid system. In particular, we aim to generate a superresolution framework for2D turbulent Rayleigh-B\'enard convection (RBC) generated with the Dedaluscode. We modify the MeshFreeFlowNet architecture to include the full set ofsimulation PDEs and the boundary conditions. Our training set includes fullydeveloped turbulence sampling Rayleigh numbers (Ra) of Ra=10^6-10^{10}. Weevaluate the success of the learned simulations by comparing the direct Dedalussimulation power spectra to the predicted CNN output power spectra. We compareboth ground truth and predicted power spectral inertial range scalings totheoretical predictions. We find that the network performs well at all Rastudied here in recovering large-scale information, including the inertialrange slopes. We find that our updated architecture performs well on laminarand turbulent flows, but the results towards smaller-scales are significantlybetter as the flow transitions to more turbulent regimes. This is likelybecause more turbulent systems have a rich variety of structures at many lengthscales compared to laminar flows. We also find that the superresolutionprediction is overly dissipative at smaller scales than that of the inertialrange.

Extending a Physics-Informed Machine Learning Network for Superresolution Studies of Rayleigh-B\'enard Convection