Poster publication: https://juser.fz-juelich.de/record/1059331

Fourier Neural Operators for Rayleigh–Bénard Convection ICCS 2026 Poster by Chelsea JohnThe International Conference on Computational Science (ICCS) 2026 was held in Hamburg, Germany, from 29th June to 1st July 2026, bringing together researchers to discuss advances in computational science, HPC, and AI. At the conference, we presented our poster, Fourier Neural Operators for Rayleigh–Bénard Convection, based on our paper published in the ICCS 2026 proceedings. We are delighted that the poster received the Best Poster Paper Award, recognising both the scientific contribution and its presentation.

Our work looks at two dimensional Rayleigh–Bénard convection (RBC), a classic fluid dynamics problem where a fluid is heated from below and cooled from above. As the temperature difference increases, the flow becomes turbulent and much harder to simulate accurately. Because of this, RBC has become a popular benchmark for testing new numerical methods, and we wanted to see how far machine learning could help speed up these simulations without sacrificing accuracy.

Recent advances in scientific machine learning have introduced Fourier Neural Operators (FNOs) as an efficient approach for learning solution operators of partial differential equations. Unlike traditional neural networks that are tied to a fixed computational mesh, FNOs learn mappings between function spaces using Fourier transforms, enabling them to generalise across different spatial resolutions while maintaining computational efficiency. This makes them attractive surrogate models for large-scale scientific simulations and promising building blocks for future HPC algorithms.

Our starting point was a simple question: does the model really need to predict the entire solution at every time step? Instead of asking the model to reconstruct the whole flow field, we trained it to predict only the changes between consecutive time steps. The next solution is then obtained by adding this predicted increment to the current state, much like a traditional numerical time integrator. It is a small change conceptually, but it turned out to make a surprisingly large difference.

Training on increments reduced the average prediction error from around 10-3 to 10-5, almost a two-order-of-magnitude improvement over the standard approach. We also experimented with the network architecture, replacing the linear lifting and projection layers with deeper one-dimensional convolutional layers and switching to a cosine learning-rate scheduler. Together, these changes gave us a model with just 314 772 parameters (1.26 MB) that performs inference in roughly 7 ms on a single NVIDIA A100 GPU, outperforming the baseline FNO. Training and evaluation were carried out using the PyTorch-based CFNO framework, available on GitHub.

We were also interested in how well the model generalises. One of the appealing features of neural operators is that they can be evaluated on spatial grids they were never trained on, and our experiments confirmed this. However, we also found an important limitation: simply running inference on a finer mesh does not produce a more accurate solution. The model remains fundamentally limited by the resolution of the data it learned from during training.

Overall, this work showed us that relatively modest changes to the training objective and network design can make a substantial difference. Rather than relying on larger models or more parameters, carefully choosing what the model learns proved to be much more effective. The resulting FNO is accurate, lightweight, and fast enough to be used as a surrogate model within larger HPC workflows, including space–time parallel methods such as Parareal.

Receiving the Best Poster Paper Award at ICCS 2026 was an encouraging recognition of this work and provided an excellent opportunity to discuss scientific machine learning with the broader computational science community. We thank the conference organisers and everyone who visited our poster for the engaging discussions, insightful questions, and valuable feedback.

This work is part of my PhD at the Technical University of Hamburg (TUHH) where my research explores the use of FNOs as surrogate models to accelerate and complement HPC-based numerical simulations.