# Fourier Neural Operators for Rayleigh-B'enard Convection

arXiv: https://arxiv.org/abs/2607.02088 · HTML: https://mlsanity.com/paper/2607.02088/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 14 references that are in the map.
- First posted on arXiv 2 Jul 2026.

## Builds on (most cited first, 5 of 5)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [TANTE: Time-Adaptive Operator Learning via Neural Taylor Expansion](https://mlsanity.com/paper/2502.08574/) (2025)
- [Solving Turbulent Rayleigh-B'enard Convection using Fourier Neural Operators](https://mlsanity.com/paper/2501.16209/) (2025)

## Abstract (arXiv)

We propose an improved Fourier Neural Operator (FNO) for modeling two-dimensional Rayleigh-B'enard convection by predicting time increments instead of full solutions, achieving higher accuracy than a standard FNO baseline. The resulting model is compact (314k parameters, 1.26 MB) and fast (7 ms inference), while maintaining similar accuracy as demonstrated in previous benchmarks. We show that although FNOs generalize to finer meshes, accuracy remains limited by the resolution of the training data.