Attention-enhanced neural network models for turbulence simulation

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