Attention-Enhanced Neural Network Models for Turbulence Simulation

TL;DR

This paper introduces an attention mechanism into neural network models for turbulence simulation, significantly improving their ability to generalize to chaotic flows and accurately predict turbulence statistics.

Contribution

The authors incorporate a visual attention module into the Fourier Neural Operator to enhance turbulence prediction, addressing the challenge of multi-scale flow structures.

Findings

40% error reduction in turbulence prediction

Improved generalization to higher Reynolds numbers

Accurate reconstruction of turbulence statistics and structures

Abstract

Deep neural network models have shown a great potential in accelerating the simulation of fluid dynamic systems. Once trained, these models can make inference within seconds, thus can be extremely efficient. However, they suffer from a generalization problem when the flow becomes chaotic and turbulent. One of the most important reasons is that, existing models lack the mechanism to handle the unique characteristic of turbulent flow: multi-scale flow structures are non-uniformly distributed and strongly nonequilibrium. In this work, we address this issue with the concept of visual attention: intuitively, we expect the attention module to capture the nonequilibrium of turbulence by automatically adjusting weights on different regions. We benchmark the performance improvement with a state of the art neural network model, the Fourier Neural Operator (FNO), on two-dimensional (2D) turbulence prediction task. Numerical experiments show that the attention-enhanced neural network model can generalize well on higher Reynolds numbers flow, and can accurately reconstruct a variety of statistics and instantaneous spatial structures of turbulence. The attention mechanism provides 40% error reduction with 1% increase of parameters, at the same level of computational cost.