# Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models

arXiv: https://arxiv.org/abs/2201.03200 · HTML: https://mlsanity.com/paper/2201.03200/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 69 references that are in the map.
- First posted on arXiv 10 Jan 2022.

## Builds on (most cited first, 2 of 2)

- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Reservoir computing model of two-dimensional turbulent convection](https://mlsanity.com/paper/2001.10280/) (2020)

## Built on by (most cited first, 3 of 3)

- [Direct data-driven forecast of local turbulent heat flux in Rayleigh-B'enard convection](https://mlsanity.com/paper/2202.13129/) (2022)
- [SPINN: An Optimal Self-Supervised Physics-Informed Neural Network Framework](https://mlsanity.com/paper/2509.05886/) (2025)
- [Physics-Informed Neural Networks with Learnable Loss Balancing and Transfer Learning](https://mlsanity.com/paper/2605.05217/) (2026)

## Abstract (arXiv)

In this paper, we develop a multivariate regression model and a neural network model to predict the Reynolds number (Re) and Nusselt number in turbulent thermal convection. We compare their predictions with those of earlier models of convection: Grossmann-Lohse~[Phys. Rev. Lett. 86, 3316 (2001)], revised Grossmann-Lohse~[Phys. Fluids 33, 015113 (2021)], and Pandey-Verma [Phys. Rev. E 94, 053106 (2016)] models. We observe that although the predictions of all the models are quite close to each other, the machine learning models developed in this work provide the best match with the experimental and numerical results.