Reconstructing Rayleigh-Bénard flows out of temperature-only measurements using Physics-Informed Neural Networks

We investigate the capabilities of Physics-Informed Neural Networks (PINNs) to reconstruct turbulent Rayleigh-Bénard 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. Visualizations of temperature (top) and vertical velocity (bottom) for the flow with [Formula: see text]. The left column shows the reference data, the other three columns show the reconstructions obtained with [Formula: see text], 14 and 31. The locations of the measuring probes (corresponding to the case with [Formula: see text]) are marked with white dots on top of [Formula: see text]. All visualizations share the same colorbar.