Ching-Yao Lai will speak at the Courant PIs Workshop on Wednesday, November 30th at 10:00am
Physics-informed neural networks for fluid and ice dynamics
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 discover a numerical self-similar blow-up solution for the incompressible 3-dimensional Euler equations with a cylindrical boundary. This new numerical framework is shown to be robust and readily adaptable to other fluid equations. 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. Ice shelves play a crucial role in slowing glacier flow into the ocean which impacts the global sea-level rise. The flow of glaciers is governed by the ice viscosity, a crucial material property that cannot be directly measured. We used PINNs to solve the governing equations for ice shelves and invert for their viscosity. Our calculation yields new flow laws of ice shelves that are different from those commonly assumed in climate simulations and suggests the need for reassessing the impact of flow laws on projections of sea-level rise.