Estimation of extreme event probabilities in systems governed by PDEs (G. Stadler, Courant Institute, NYU)

Dez 01
01-12-2021 16:00 Uhr bis 17:00 Uhr

Estimation of extreme event probabilities in systems governed by PDEs

Speaker: Prof. Dr. Georg Stadler
Affiliation: Courant Institute for Mathematical Sciences, New York
University, USA, href=““““>Website

Meeting ID: 688 5113 6725
Passcode: 014980

Abstract: We propose methods for the estimation of extreme event
in complex systems governed by PDEs. Our approach is guided by ideas
from large deviation theory (LDT) and borrows methods from
PDE-constrained optimization. The systems under consideration involve
random parameters and we are interested in quantifying the probability
that a scalar quantity of interest is at or above a threshold. The
proposed methods initially solve an optimization problem over the set
of parameters leading to the extreme event. Based on solutions of this
PDE-constrained optimization problem, we propose (1) an importance
sampling method and (2) a method that uses curvature information of
the extreme event boundary to estimate small probabilities. We
illustrate the application of our approach to quantify the probability
of extreme tsunami events on shore, which results in a PDE-constrained
optimization problem governed by the shallow water equations. We study
the role of the nonlinearity in the equations for observing large
tsunamis and dominant mechanisms leading to large tsunamis on
shore. This is joint work with Shanyin Tong and Eric Vanden-Eijnden
from NYU.

Friedrich-Alexander-Universität Erlangen-Nürnberg