Past Event: Oden Institute Seminar

Extreme Events in Complex Systems Involving Random Parameters

Georg Stadler, Courant Institute of Mathematical Sciences, New York University

Abstract

 Estimation of tail probabilities in systems that involve uncertain parameters or white noise forcing is important when these
unlikely events have severe consequences. Examples of such events are hurricanes, energy grid blackouts or failure of engineered
systems. After illustrating the challenges of estimating rare event probabilities, I will show a connection between extreme event
probability estimation and PDE-constrained optimization that is made precise by large deviation theory. The approach leads to practical
methods to estimate tail probabilities, and a novel class of challenging, large-scale constrained optimization problems. After 
showing examples governed by the shallow water and the Navier Stokes equations, I will end with an outlook towards using these methods for mitigation of extreme events, for monitoring failure probabilities in digital twins, and for tail-accurate model reduction.

Biography

Georg Stadler is a professor of Mathematics and Computer Science at New York University's Courant Institute of Mathematical
Sciences.  His research is in uncertainty quantification, rare event estimation, optimization under uncertainty and linear and nonlinear
scalable solvers.  This research is often driven by real world applications, primarily in climate, plasma physics and geodynamics.
Before joining the Courant Institute in 2014, he was a research scientist and postdoc at the Oden Institute at UT Austin. He obtained
a PhD in Mathematics from the University of Graz (Austria) under supervision of Karl Kunisch. His research is supported by NSF, ONR,
DOE and the Simons Foundation. Amongst his research recognitions are a Gordon Bell Award (2015), the Springer CSE prize (2011) and the SIAM CSE Best Paper Award (2019).