# Direct data-driven forecast of local turbulent heat flux in Rayleigh-B'enard convection

arXiv: https://arxiv.org/abs/2202.13129 · HTML: https://mlsanity.com/paper/2202.13129/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 74 references that are in the map.
- First posted on arXiv 26 Feb 2022.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [Medical image denoising using convolutional denoising autoencoders](https://mlsanity.com/paper/1608.04667/) (2016)
- [Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics](https://mlsanity.com/paper/1912.11114/) (2019)
- [Reservoir computing approaches for representation and classification of multivariate time series](https://mlsanity.com/paper/1803.07870/) (2018)
- [Reservoir computing model of two-dimensional turbulent convection](https://mlsanity.com/paper/2001.10280/) (2020)
- [Gradient-free optimization of chaotic acoustics with reservoir computing](https://mlsanity.com/paper/2106.09780/) (2021)
- [Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models](https://mlsanity.com/paper/2201.03200/) (2022)

## Built on by (most cited first, 10 of 10)

- [Flipped Classroom: Effective Teaching for Time Series Forecasting](https://mlsanity.com/paper/2210.08959/) (2022)
- [Learning Closed-form Equations for Subgrid-scale Closures from High-fidelity Data: Promises and Challenges](https://mlsanity.com/paper/2306.05014/) (2023)
- [Learning a model is paramount for sample efficiency in reinforcement learning control of PDEs](https://mlsanity.com/paper/2302.07160/) (2023)
- [Koopman-Based Surrogate Modelling of Turbulent Rayleigh-B'enard Convection](https://mlsanity.com/paper/2405.06425/) (2024)
- [Deterministic Reservoir Computing for Chaotic Time Series Prediction](https://mlsanity.com/paper/2501.15615/) (2025)
- [Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoders](https://mlsanity.com/paper/2505.13569/) (2025)
- [Solving Partial Differential Equations with Equivariant Extreme Learning Machines](https://mlsanity.com/paper/2404.18530/) (2024)
- [Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical system](https://mlsanity.com/paper/2501.03070/) (2025)
- [A Physics-Informed Spatiotemporal Deep Learning Framework for Turbulent Systems](https://mlsanity.com/paper/2505.10919/) (2025)
- [Koopman-based surrogate modeling for reinforcement-learning-control of Rayleigh-Benard convection](https://mlsanity.com/paper/2603.28074/) (2026)

## Abstract (arXiv)

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'enard convection flow at Prandtl number rm Pr=7 and Rayleigh number rm Ra=107. 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.