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We introduce a data-driven learning framework that assimilates two powerfulideas: ideal large eddy simulation (LES) from turbulence closure modeling andneural stochastic differential equations (SDE) for stochastic modeling. Theideal LES models the LES flow by treating each full-order trajectory as arandom realization of the underlying dynamics, as such, the effect ofsmall-scales is marginalized to obtain the deterministic evolution of the LESstate. However, ideal LES is analytically intractable. In our work, we use alatent neural SDE to model the evolution of the stochastic process and anencoder-decoder pair for transforming between the latent space and the desiredideal flow field. This stands in sharp contrast to other types of neuralparameterization of closure models where each trajectory is treated as adeterministic realization of the dynamics. We show the effectiveness of ourapproach (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 meshesseamlessly. In particular, niLES leads to trajectories with more accuratestatistics and enhances stability, particularly for long-horizon rollouts.

Neural Ideal Large Eddy Simulation: Modeling Turbulence with Neural Stochastic Differential Equations