Sent on behalf of the CMAI Colloquium.



Dear All,


The next CMAI Colloquium will be on



Friday February 05, 2021 at 10:00 am (Eastern Time) 


Prof. Georg Stadler

Courant Institute of Mathematical Sciences, 

New York University


Estimation of extreme event probabilities in systems governed by PDEs

Zoom Link:


We propose methods for the estimation of extreme event probabilities

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 function of the system state is at or above a threshold.

The proposed methods initially solve an optimization problem over the

set of parameters leading to events above a threshold.  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. Tsunamis

are typically caused by a sudden, unpredictable change of the ocean

floor elevation during an earthquake.  We model this change as random

process and use the one-dimensional shallow water equation to model

tsunamis. The PDE-constrained optimization problem arising in this

application is governed by the shallow water equation. This is joint

work with Shanyin Tong and Eric Vanden-Eijnden from NYU.





Harbir Antil

Director, Center for Mathematics and Artificial Intelligence (CMAI)
Associate Professor, Mathematical Sciences  
George Mason University

Fairfax, VA 22030  

Phone: (703) 993-5086

Fax:     (703) 993-1491