  Recent works have explored the potential of machine learning as data-driven
turbulence closures for RANS and LES techniques. Beyond these advances, the
high expressivity and agility of physics-informed neural networks (PINNs) make
them promising candidates for full fluid flow PDE modeling. An important
question is whether this new paradigm, exempt from the traditional notion of
discretization of the underlying operators very much connected to the flow
scales resolution, is capable of sustaining high levels of turbulence
characterized by multi-scale features? We investigate the use of PINNs
surrogate modeling for turbulent Rayleigh-B{\'e}nard (RB) convection flows in
rough and smooth rectangular cavities, mainly relying on DNS temperature data
from the fluid bulk. We carefully quantify the computational requirements under
which the formulation is capable of accurately recovering the flow hidden
quantities. We then propose a new padding technique to distribute some of the
scattered coordinates-at which PDE residuals are minimized-around the region of
labeled data acquisition. We show how it comes to play as a regularization
close to the training boundaries which are zones of poor accuracy for standard
PINNs and results in a noticeable global accuracy improvement at iso-budget.
Finally, we propose for the first time to relax the incompressibility condition
in such a way that it drastically benefits the optimization search and results
in a much improved convergence of the composite loss function. The RB results
obtained at high Rayleigh number Ra = 2 $\bullet$ 10 9 are particularly
impressive: the predictive accuracy of the surrogate over the entire half a
billion DNS coordinates yields errors for all flow variables ranging between
[0.3% -- 4%] in the relative L 2 norm, with a training relying only on 1.6% of
the DNS data points.
