Deep learning in turbulent convection networks

Abstract

We explore heat transport properties of turbulent Rayleigh–Bénard convection in horizontally extended systems by using deep-learning algorithms that greatly reduce the number of degrees of freedom. Particular attention is paid to the slowly evolving turbulent superstructures—so called because they are larger in extent than the height of the convection layer—which appear as temporal patterns of ridges of hot upwelling and cold downwelling fluid, including defects where the ridges merge or end. The machine-learning algorithm trains a deep convolutional neural network (CNN) with U-shaped architecture, consisting of a contraction and a subsequent expansion branch, to reduce the complex 3D turbulent superstructure to a temporal planar network in the midplane of the layer. This results in a data compression by more than five orders of magnitude at the highest Rayleigh number, and its application yields a discrete transport network with dynamically varying defect points, including points of locally enhanced heat flux or “hot spots.” One conclusion is that the fraction of heat transport by the superstructure decreases as the Rayleigh number increases (although they might remain individually strong), correspondingly implying the increased importance of small-scale background turbulence.

Machine learning for active matter

“…Machine learning appears to be ideally suited to solve this problem. For example, it has already been used to solve the difficult task of elucidating the intricate three-dimensional spatio-temporal patterns associated with turbulent flows 55 . Furthermore, machine learning can provide invaluable help to infer dynamic information and underlying models from static information 56,57 .…”

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“…It should be noted in this context that others have used spatial filtering (Green et al 2020) or time averaging (e.g. Pandey et al 2018;Fonda et al 2019) to extract the large-scale features in similar datasets.…”

Uniformly accurate machine learning-based hydrodynamic models for kinetic equations

“…This approach is conceptually simple and easy to implement. Ideas like this have been used in various problems, including the turbulence models [25,42,43].…”