Direct data-driven forecast of local turbulent heat flux in Rayleigh-B\'{e}nard convection

TL;DR

This paper introduces a data-driven machine learning model combining autoencoders and recurrent neural networks to accurately forecast local turbulent heat flux in Rayleigh-Bénard convection, capturing complex dynamics with high dimensionality reduction.

Contribution

It presents a novel modular ML framework that effectively models turbulent heat transfer dynamics using a reduced data representation and multiple neural network architectures.

Findings

Achieves high accuracy in first- and second-order heat flux statistics.

Successfully reproduces plume-mixing dynamics with some deviations.

Demonstrates noise resilience, suitable for larger-scale models.

Abstract

A combined convolutional autoencoder-recurrent neural network machine learning model is presented to analyse and forecast the dynamics and low-order statistics of the local convective heat flux field in a two-dimensional turbulent Rayleigh-B\'{e}nard convection flow at Prandtl number ${\rm Pr}=7$ and Rayleigh number ${\rm Ra}=10^7$. Two recurrent neural networks are applied for the temporal advancement of flow data in the reduced latent data space, a reservoir computing model in the form of an echo state network and a recurrent gated unit. Thereby, the present work exploits the modular combination of three different machine learning algorithms to build a fully data-driven and reduced model for the dynamics of the turbulent heat transfer in a complex thermally driven flow. The convolutional autoencoder with 12 hidden layers is able to reduce the dimensionality of the turbulence data to about 0.2 \% of their original size. Our results indicate a fairly good accuracy in the first- and second-order statistics of the convective heat flux. The algorithm is also able to reproduce the intermittent plume-mixing dynamics at the upper edges of the thermal boundary layers with some deviations. The same holds for the probability density function of the local convective heat flux with differences in the far tails. Furthermore, we demonstrate the noise resilience of the framework which suggests the present model might be applicable as a reduced dynamical model that delivers transport fluxes and their variations to the coarse grid cells of larger-scale computational models, such as global circulation models for the atmosphere and ocean.