Dynamics of a data-driven low-dimensional model of Rayleigh-Benard convection

Abstract: We present a multiscale, data-driven reduced-order framework for two-dimensional Rayleigh Benard convection in a square cell at high Rayleigh number, where the flow exhibits intermittent large-scale circulation reversals. Starting from direct numerical simulations using Nek5000, we extract a set of energy-ranked POD modes from the combined velocity and temperature fields. A Gaussian filter decomposes the temporal coefficients into low-frequency (slow) and high-frequency (fast) components, enabling a two-branch modeling strategy. Each branch is mapped into a latent representation using a nonlinear autoencoder and evolved via neural ODEs that incorporate time modulation. This strategy reduces the system from an original state space dimension of 10^5 to a compact 20-dimensional latent space while preserving the essential multiscale dynamics. Our model achieves accurate reconstruction of instantaneous flow structures, Reynolds stresses, energy autocorrelations and long-time quantities, such as angular momentum and wall observables. Furthermore, a waiting time analysis of flow reversals validates the statistical alignment of model prediction and DNS results. The explicit modeling of separate slow and fast branches yields significantly improved accuracy in both short-time flow structures and long-time reversal statistics, compared to single-branch alternatives. These results demonstrate the potential of multiscale latent models for capturing complex dynamics in turbulent flows.