Lagrangian Large Eddy Simulations via Physics-Informed Machine Learning

In this work, we present a novel approach for developing particle-based Lagrangian turbulence models using Large Eddy Simulation (LES) heuristics within the framework of Physics-informed Machine Learning. We generalize the evolutionary equations of Lagrangian particles moving in weakly compressible turbulence with extended, physics-informed parameterization and functional freedom, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The sub-grid scale contributions are modeled separately with physical constraints to account for the effects from un-resolved scales. We build 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 trajectory, field, and statistics-based ones to embed physics into the learning. Through extensive analysis and validation, we demonstrate that our Lagrangian LES model successfully reproduces both Eulerian and unique Lagrangian turbulence structures and statistics across a wide range of turbulent Mach numbers.