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

Generalizability of reservoir computing for flux-driven two-dimensional convection