Reconstructing Rayleigh-Benard 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-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.

Automated summary

We study the use of Physics-Informed Neural Networks (PINNs) for reconstructing turbulent Rayleigh-Benard flows using temperature information only. We perform a quantitative analysis of the reconstruction quality at different levels of low-pass filtered information and turbulent intensities. Our results show that PINNs achieve high precision reconstruction comparable to nudging at low Rayleigh numbers. At high Rayleigh numbers, PINNs outperform nudging and achieve satisfactory reconstruction of velocity fields with high spatial and temporal density of temperature data. However, the performance of PINNs deteriorates when data becomes sparse, both in terms of point-to-point errors and in a statistical sense, as observed in probability density functions and energy spectra.