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

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 modeling stochastic dynamical systems. ideal LES identifies the optimal reduced-order flow fields of the large-scale features by marginalizing out the effect of small-scales in stochastic turbulent trajectories. However, ideal LES is analytically intractable. In our work, we use a latent neural SDE to model the evolution of the stochastic process and a pair of encoder and decoder for transforming between the latent space and the desired optimal flow field. This stands in sharp contrast to other types of neural parameterization of the 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 systems: Kolmogorov flow at a Reynolds number of 20,000. Compared to prior works, our method is also able to handle non-uniform geometries and unstructured meshes. In particular, niLES leads to more accurate long term statistics, and is stable even when rolling out to long horizons.