High-fidelity direct numerical simulation of turbulent flows for most real-world applications remains an outstanding computational challenge. Several machine learning approaches have recently been proposed to alleviate the computational cost even though they become unstable or unphysical for long time predictions. We identify that the Fourier neural operator (FNO) based models combined with a partial differential equation (PDE) solver can accelerate fluid dynamic simulations and thus address computational expense of large-scale turbulence simulations. We treat the FNO model on the same footing as a PDE solver and answer important questions about the volume and temporal resolution of data required to build pre-trained models for turbulence. We also discuss the pitfalls of purely data-driven approaches that need to be avoided by the machine learning models to become viable and competitive tools for long time simulations of turbulence.

本研究解决了高保真直接数值模拟湍流流动的计算挑战，提出将傅里叶神经算子（FNO）与偏微分方程（PDE）求解器结合的方法。这种新颖的方法可以加速流体动力学模拟，显著降低大规模湍流模拟的计算成本，同时探讨了构建预训练模型所需的数据量和时间分辨率的问题。

用于二维湍流时空动态的傅里叶神经算子