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Solving Turbulent Rayleigh-Bénard Convection using Fourier Neural Operators

Michiel Straat, Thorben Markmann, Barbara Hammer

TL;DR

This work tackles predicting turbulent Rayleigh-Bénard convection dynamics with data-driven surrogates. It applies Fourier Neural Operator-3D to learn a spatiotemporal solution operator and compares it to Dynamic Mode Decomposition and Linearly Recurrent Autoencoder Network, using DNS as ground truth. FNO-3D delivers superior accuracy and zero-shot resolution generalization across moderate to high turbulence, while remaining substantially faster than Direct Numerical Simulations. The results suggest strong potential for flow control and parameter studies, with plans to extend to three-dimensional convection and integrate with model-based RL.

Abstract

We train Fourier Neural Operator (FNO) surrogate models for Rayleigh-Bénard 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.

Solving Turbulent Rayleigh-Bénard Convection using Fourier Neural Operators

TL;DR

This work tackles predicting turbulent Rayleigh-Bénard convection dynamics with data-driven surrogates. It applies Fourier Neural Operator-3D to learn a spatiotemporal solution operator and compares it to Dynamic Mode Decomposition and Linearly Recurrent Autoencoder Network, using DNS as ground truth. FNO-3D delivers superior accuracy and zero-shot resolution generalization across moderate to high turbulence, while remaining substantially faster than Direct Numerical Simulations. The results suggest strong potential for flow control and parameter studies, with plans to extend to three-dimensional convection and integrate with model-based RL.

Abstract

We train Fourier Neural Operator (FNO) surrogate models for Rayleigh-Bénard 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.

Paper Structure

This paper contains 9 sections, 1 equation, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Data generation using simulations
  4. Fourier Neural Operator
  5. Koopman architectures
  6. Dynamic Mode Decomposition
  7. Linearly Recurrent Autoencoder Network
  8. Results and Discussion
  9. Conclusion

Figures (2)

  • Figure 1: Left: A ground truth at $t=20$ from a random test starting point that we label $t=0$. Right: the field as predicted by FNO-3D. Color: temperature field, arrows: velocity field.
  • Figure 2: Evaluation of the three models as an average error \ref{['eq:NRSSE']} computed over 50 random starting points (10 random points in each of the 5 test episodes) for increasing Rayleigh number (see figure titles). The Cyan line for $Ra=5e6$ shows the same FNO model but evaluated on data with double the spatial resolution.