  A combined convolutional autoencoder-recurrent neural network machine
learning model is presented to analyse and forecast the dynamics and low-order
statistics of the local convective heat flux field in a two-dimensional
turbulent Rayleigh-B\'{e}nard convection flow at Prandtl number ${\rm Pr}=7$
and Rayleigh number ${\rm Ra}=10^7$. Two recurrent neural networks are applied
for the temporal advancement of flow data in the reduced latent data space, a
reservoir computing model in the form of an echo state network and a recurrent
gated unit. Thereby, the present 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 which suggests the present model might be applicable as a reduced
dynamical model that delivers transport fluxes and their variations to the
coarse grid cells of larger-scale computational models, such as global
circulation models for the atmosphere and ocean.
