Title: Physics-informed neural networks for fluid and ice dynamics
Abstract: Physics-informed neural networks (PINNs) have recently emerged as a new class of numerical solver for partial differential equations which leverage deep neural networks constrained by equations. I’ll discuss two applications of PINNs in fluid dynamics developed in my group. The first concerns the search for self-similar blow-up solutions of the Euler equations. The second application uses PINNs as an inverse method in geophysics. Whether an inviscid incompressible fluid, described by the 3-dimensional Euler equations, can develop singularities in finite time is an open question in mathematical fluid dynamics. We employ PINNs to find a numerical self-similar blow-up solution for the incompressible 3-dimensional Euler equations with a cylindrical boundary. In the second part of the talk, I will discuss how PINNs trained with real world data from Antarctica can help discover flow laws that govern ice-shelf dynamics. These ice shelves play a role in slowing the flow of glaciers into the ocean, which impacts global sea level rise. However, the effective viscosity of the ice, a crucial material property, cannot be directly measured. By using PINNs to solve the governing equations for the ice shelves and invert for their effective viscosity, we were able to calculate flow laws that differ from those commonly assumed in climate simulations. This suggests the need to reassess the impact of these flow laws on sea level rise projections.