General audience seminar - Micha Chertkov (University of Arizona)

Traditional Large Eddy Simulations (LES) model turbulent flows using heuristics rooted in Eulerian truncation of the the Navier-Stocks (NS) equations which require assumptions about sub-grid scale impacts. We introduce an innovative Lagrangian approach, termed Lagrangian-LES, which evolves with turbulent flow particles. This method augments the Smooth Particle Hydrodynamics (SPH) formulation, leveraging Machine Learning (ML) to interpret Lagrangian data from Direct Numerical Simulation (DNS) of NS equations. L-LES offers explainable parameters, such as those for eddy-diffusivity, and uses Neural Networks (NN) to discern the effects of unresolved scales. With Differentiable Programming (DP) and Deep NN, we refine these parameters and functions, testing a variety of physics-informed loss functions. Our results demonstrate the L-LES's unique ability to depict turbulence efficiently and its proficiency in reproducing both Lagrangian and Eulerian flow statistics at the resolved scales. Based on collaborative work with Y. Tian, M. Woodward, M. Stepanov, C. Hyett, C. Fryer, and D. Livescu.