Physics-informed neural networks for fluid dynamics.
Title: Physics-informed neural networks for fluid dynamics.
Speaker: Prof. Ching-Yao Lai (Princeton University)
Start Date/Time: 2022-8-3 / 10:30 (Taipei time)
End Date/Time: 2022-8-3 / 12:00
Host : Prof. Ying-Jer Kao (Department of Physics, NTU)
Onsite: NCTS Physics Lecture Hall, 4F, Chee-Chun Leung Cosmology Hall, NTU
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Abstract: Physics-informed neural networks (PINNs) have recently emerged as a new class of numerical solver for partial differential equations, leveraging deep neural networks constrained by equations. I'll discuss two applications of PINN 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 PINN 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 one of the most challenging problems in mathematical fluid dynamics (closely related to one of the seven Millennium Prize Problems). We employ PINN to discover a self-similar blow-up solution for the 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 PINN to solve the governing equations for ice shelves and invert for its viscosity. Our calculation yields new flow laws of ice shelves that are different from commonly assumed in climate simulations, and suggests the need for reassessing the impact of our finding on the future projection of sea-level rise.