# Solving Turbulent Rayleigh-B'enard Convection using Fourier Neural Operators

arXiv: https://arxiv.org/abs/2501.16209 · HTML: https://mlsanity.com/paper/2501.16209/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2025.

## Built on by (most cited first, 5 of 5)

- [Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoders](https://mlsanity.com/paper/2505.13569/) (2025)
- [Control of Rayleigh-B'enard Convection: Effectiveness of Reinforcement Learning in the Turbulent Regime](https://mlsanity.com/paper/2504.12000/) (2025)
- [A Physics-Informed Spatiotemporal Deep Learning Framework for Turbulent Systems](https://mlsanity.com/paper/2505.10919/) (2025)
- [Improving the Robustness of Control of Chaotic Convective Flows with Domain-Informed Reinforcement Learning](https://mlsanity.com/paper/2511.00272/) (2025)
- [Fourier Neural Operators for Rayleigh-B'enard Convection](https://mlsanity.com/paper/2607.02088/) (2026)

## Abstract (arXiv)

We train Fourier Neural Operator (FNO) surrogate models for Rayleigh-B'enard Convection (RBC), a model for convection processes that occur in nature and industrial settings. We compare the prediction accuracy and model properties of FNO surrogates to two popular surrogates used in fluid dynamics: the Dynamic Mode Decomposition and the Linearly-Recurrent Autoencoder Network. We regard Direct Numerical Simulations (DNS) of the RBC equations as the ground truth on which the models are trained and evaluated in different settings. The FNO performs favorably when compared to the DMD and LRAN and its predictions are fast and highly accurate for this task. Additionally, we show its zero-shot super-resolution ability for the convection dynamics. The FNO model has a high potential to be used in downstream tasks such as flow control in RBC.