We introduce a data-driven learning framework that assimilates two powerful
ideas: ideal large eddy simulation (LES) from turbulence closure modeling and
neural stochastic differential equations (SDE) for stochastic modeling. The
ideal LES models the LES flow by treating each full-order trajectory as a
random realization of the underlying dynamics, as such, the effect of
small-scales is marginalized to obtain the deterministic evolution of the LES
state. However, ideal LES is analytically intractable. In our work, we use a
latent neural SDE to model the evolution of the stochastic process and an
encoder-decoder pair for transforming between the latent space and the desired
ideal flow field. This stands in sharp contrast to other types of neural
parameterization of closure models where each trajectory is treated as a
deterministic realization of the dynamics. We show the effectiveness of our
approach (niLES - neural ideal LES) on a challenging chaotic dynamical system:
Kolmogorov flow at a Reynolds number of 20,000. Compared to competing methods,
our method can handle non-uniform geometries using unstructured meshes
seamlessly. In particular, niLES leads to trajectories with more accurate
statistics and enhances stability, particularly for long-horizon rollouts.

本文提出了一种基于数据打造的学习框架，将理想大涡模拟和神经随机微分方程相结合，应用在一种具有挑战性的混沌动力学系统 —— 雷诺数为 20000 的 Kolmogorov 流上，与其他方法相比，我们的 niLES 方法可以无缝处理非均匀几何结构，并可以处理更精确的统计数据和增强稳定性，特别是在长时间内的结果上.