A combined convolutional autoencoder–recurrent neural network machine learning model is presented to directly analyze and forecast the dynamics and low-order statistics of the local convective heat flux field in a two-dimensional turbulent Rayleigh–Bénard convection flow at Prandtl number [Formula: see text] and Rayleigh number [Formula: see text]. Two recurrent neural networks are applied for the temporal advancement of turbulent heat transfer data in the reduced latent data space, an echo state network, and a recurrent gated unit. Thereby, our work exploits the modular combination of three different machine learning algorithms to build a fully data-driven and reduced model for the dynamics of the turbulent heat transfer in a complex thermally driven flow. The convolutional autoencoder with 12 hidden layers is able to reduce the dimensionality of the turbulence data to about 0.2% of their original size. Our results indicate a fairly good accuracy in the first- and second-order statistics of the convective heat flux. The algorithm is also able to reproduce the intermittent plume-mixing dynamics at the upper edges of the thermal boundary layers with some deviations. The same holds for the probability density function of the local convective heat flux with differences in the far tails. Furthermore, we demonstrate the noise resilience of the framework. This suggests that the present model might be applicable as a reduced dynamical model that delivers transport fluxes and their variations to coarse grids of larger-scale computational models, such as global circulation models for atmosphere and ocean.

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.