Data-driven discovery of reduced Lagrangian models of turbulence
Turbulence in fluids is a rich and ubiquitous physical phenomena and reducing its computational complexity remains an active research topic due to its many potential scientific and engineering impacts. The main objective of this work is to automatically discover the best fit Lagrangian model from turbulence data using a parameterized family of models (SPH and MD) along with modern machine learning tools (such as differentiable programming combined with deep learning). In this talk I will share my ongoing research (and some progress) on developing physics informed machine learning tools to solve this problem. I will discuss the necessary background in Lagrangian models such as Smooth Particle Hydrodynamics (SPH) and Molecular Dynamics (MD) for the description of fluid dynamics and turbulence. Next, I will discuss how we use differentiable programming to create an entire simulator that is consistent with automatic differentiation to achieve parameter estimation and the discovery of unknown functions (like a pairwise potential function). Essentially our methodology involves embedding neural networks within differentiable simulators (or integrators) which allows for the flexibility to encode as much or as little physical structure as we want. I will show some preliminary results that suggest that we can "learn" or discover certain physical parameters of our models from data, as well as unknown functions (such as a potential function or smoothing kernel by using neural networks as function approximators).