  We explore the generalization properties of an echo state network applied as
a reduced dynamical model to predict flux-driven two-dimensional turbulent
convection. To this end, we consider a convection domain at fixed height with a
variable ratio of buoyancy fluxes at the top and bottom boundaries, which break
the top-down symmetry in comparison to the standard Rayleigh-B\'enard case thus
leading to highly asymmetric mean and fluctuation profiles across the layer.
Our direct numerical simulation model describes a convective boundary layer in
a simple way. The data are used to train and test a recurrent neural network in
the form of an echo state network. The input to the echo state networks is
obtained in two different ways, either by a proper orthogonal decomposition or
by a convolutional autoencoder. In both cases, the echo state network
reproduces the turbulence dynamics and the statistical properties of the
buoyancy flux, and is able to model unseen data records with different flux
ratios.
