  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.
