  Reservoir computing is applied to model the large-scale evolution and the
resulting low-order turbulence statistics of a two-dimensional turbulent
Rayleigh-B\'{e}nard convection flow at a Rayleigh number ${\rm Ra}=10^7$ and a
Prandtl number ${\rm Pr}=7$ in an extended domain with an aspect ratio of 6.
Our data-driven approach which is based on a long-term direct numerical
simulation of the convection flow comprises a two-step procedure. (1) Reduction
of the original simulation data by a Proper Orthogonal Decomposition (POD)
snapshot analysis and subsequent truncation to the first 150 POD modes which
are associated with the largest total energy amplitudes. (2) Setup and
optimization of a reservoir computing model to describe the dynamical evolution
of these 150 degrees of freedom and thus the large-scale evolution of the
convection flow. The quality of the prediction of the reservoir computing model
is comprehensively tested. At the core of the model is the reservoir, a very
large sparse random network charcterized by the spectral radius of the
corresponding adjacency matrix and a few further hyperparameters which are
varied to investigate the quality of the prediction. Our work demonstrates that
the reservoir computing model is capable to model the large-scale structure and
low-order statistics of turbulent convection which can open new avenues for
modeling mesoscale convection processes in larger circulation models.
