Reservoir computing of thermal convection: Random versus small-world networks

We study a classical two-dimensional thermal convection flow at a low Rayleigh number which is represented by an energy-conserving Lorenz-type model with eight degrees of freedom. This model accounts for the shear motion and tilted plumes in the flow. We employ a recurrent machine learning approach in the form of a reservoir computing model and test different reservoir architectures. In detail, small-world network architectures with different re-wiring probabilities are compared with conventional random network topology. It is found that similar prediction capabilities are obtained on the basis of the mean squared error or the prediction horizon.