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AMS Special Seminar Series | Florian Schäfer

February 27 @ 10:00 am - 11:00 am

Location: Clark 110

When: February 27th at 10:00 a.m.

Title: Toward Information Geometric Mechanics

Abstract: Shock waves in high-speed gas dynamics cause severe numerical difficulties for classical solvers and scientific machine learning. This talk begins with the observation that shock formation arises from the flow map reaching the boundary of the manifold of diffeomorphisms. We modify its geometry such that geodesics approach but never reach the boundary. The resulting information geometric regularization (IGR) has smooth solutions while avoiding the excessive dissipation of viscous regularizations, accelerating and simplifying the simulation of flows with shocks. We prove the existence of global strong IGR solutions in the unidimensional pressureless case and illustrate its practical utility on multidimensional examples with complex shock interactions.

The modified geometry of the diffeomorphism manifold is the information geometry of the mass density. The last part of the talk explains how this observation motivates information geometric mechanics that views the solutions of continuum mechanical PDEs as parameters of probability distributions originating from statistical physics. Replacing the Euclidean geometry of individual particles with the information geometry of statistical families promises performant numerical methods that preserve the positivity of densities and energies and readily integrate with scientific machine learning.

Bio: Florian Schäfer is an assistant professor in the School of Computational Science and Engineering at Georgia Tech. Prior to joining Georgia Tech, he received his PhD in applied and computational mathematics at Caltech, working with Houman Owhadi. Before that, he received Bachelor’s and Master’s degrees in Mathematics at the University of Bonn. His research solves fundamental problems in computational science and engineering using insights from statistics and decision theory.

Zoom link: https://wse.zoom.us/j/92755277282?pwd=iULpLaFnWAcWl6tQYUbeyZaN3zwBzn.1

Details

Date:
February 27
Time:
10:00 am - 11:00 am
Event Category:

Venue

Clark 110
3400 North Charles Street
Baltimore, Maryland 21218 + Google Map