Turbulent superstructures in Rayleigh-Bénard convection detected by deep learning

Turbulent convection in nature comprises vortices and plumes on many time and length scales that tend to assemble to gradually evolving large-scale patterns which are termed turbulent superstructures. These patterns appear in the form of ridge-like contours of hot upwelling and cold downwelling fluid. To detect them by machine learning techniques, we use a fully convolutional deep neural network that generates precise image segmentation from relatively small training sets. The neural network reduces the turbulent superstructures in an extended three-dimensional Rayleigh-Bénard convection layer to a planar network that connects defect points of the superstructure patterns. The dynamics of the network is manifest by the creation and annihilation of defects which determine the network topology. We estimate the fraction of heat transported across the network for varying Rayleigh numbers but fixed Prandtl number, and find the fraction to be significant.