Fourier Neural Operators for Rayleigh-Bénard Convection

2026-07-02

AI Summary

This work addresses the challenge of balancing accuracy and computational efficiency in modeling two-dimensional Rayleigh–Bénard convection by proposing a lightweight Fourier Neural Operator (FNO) architecture based on temporal increment prediction. Instead of predicting the full solution directly, the model forecasts the state increment, substantially reducing its complexity. The resulting network contains only 314k parameters (1.26 MB) and achieves a single inference time of 7 milliseconds. While maintaining accuracy comparable to existing methods, the approach significantly lowers computational overhead, offering a novel pathway toward efficient, high-fidelity simulations in fluid dynamics.

Abstract

We propose an improved Fourier Neural Operator (FNO) for modeling two-dimensional Rayleigh-Bénard 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.

Problem

• Fourier Neural Operators
• Rayleigh-Bénard Convection
• resolution limitation
• mesh generalization
• prediction accuracy

Innovation

• Fourier Neural Operator
• Rayleigh-Bénard convection
• time-increment prediction
• mesh generalization
• data resolution limit