  We investigate the capabilities of Physics-Informed Neural Networks (PINNs)
to reconstruct turbulent Rayleigh-Benard flows using only temperature
information. We perform a quantitative analysis of the quality of the
reconstructions at various amounts of low-passed-filtered information and
turbulent intensities. We compare our results with those obtained via nudging,
a classical equation-informed data assimilation technique. At low Rayleigh
numbers, PINNs are able to reconstruct with high precision, comparable to the
one achieved with nudging. At high Rayleigh numbers, PINNs outperform nudging
and are able to achieve satisfactory reconstruction of the velocity fields only
when data for temperature is provided with high spatial and temporal density.
When data becomes sparse, the PINNs performance worsens, not only in a
point-to-point error sense but also, and contrary to nudging, in a statistical
sense, as can be seen in the probability density functions and energy spectra.
