Inferring the temperature from planar velocity measurements in Rayleigh-Bénard convection by deep learning

Abstract

The simultaneous, spatially- and temporally-resolved direct measurement of velocity and temperature fields in Rayleigh-Bénard experiments is laborious, expensive and sometimes not even feasible. Hence, we assess the capabilities of a deep learning model to support such measurements and reduce the necessary effort. Here, we use a u-net-based model to predict the temperature from the corresponding velocity field obtained from measurements in Rayleigh-Bénard convection at Pr = 7.1 and Ra = 2× 105, 4×105, 7×105. We conduct a hyper-parameter search and ablation study to ensure appropriate training convergence and test different architectural variations for the u-net. We define two application scenarios, one in which the u-net is trained with data of the same experimental run and one in which the u-net is trained on data of different Ra. Our analysis showed that the u-net can predict temperature fields similar to the measurement data and preserves typical spatial structure sizes. Moreover, the analysis of the heat transfer associated with the temperature fields unveiled that the results are physically reasonable and are in good agreement with the ground truth data when the u-net is trained with data of the same experimental run. We conclude that deep learning has the potential to supplement measurements and can partially replace the requirement of additional temperature measurements.