Machine Learning Lagrangian Large Eddy Simulations with Smoothed Particle Hydrodynamics

In this work, we apply Physics-Informed Machine Learning to develop Lagrangian Large Eddy Simulation (LES) models for turbulent flows. We extend the weakly compressible Smoothed Particle Hydrodynamics (SPH) formalism using a broader set of parameterizations, by combining physics-based parameters and physics-inspired Neural Networks (NN) to describe the evolution of turbulence within the resolved range of scales. The sub-grid scale contributions, similar to those in LES, are modeled separately using NN with physical constraints to account for the effects from un-resolved scales. We construct the resulting model under the Differentiable Programming framework to facilitate efficient training and then train the model on a set of coarse-grained Lagrangian data extracted from fully-resolved Direct Numerical Simulations. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show, through a series of diagnostic tests, that the developed model is capable of reproducing flow structures at the resolved scale and important Lagrangian and Eulerian statistics of turbulent flows.