Sent on behalf of the CMAI Colloquium.

Dear All,
The next CMAI Colloquium will be on
Date: 
Friday February 05, 2021 at 10:00 am (Eastern Time) 
Speaker: 
Courant Institute of Mathematical Sciences, New York University 
Title: 
Estimation of extreme event probabilities in systems governed by PDEs 
Zoom Link: 

Abstract: 
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 PDEconstrained 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 PDEconstrained 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 onedimensional shallow water equation to model tsunamis. The PDEconstrained optimization problem arising in this application is governed by the shallow water equation. This is joint work with Shanyin Tong and Eric VandenEijnden from NYU. 
Best,
CMAI Team
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Harbir Antil
Director, Center for Mathematics and Artificial Intelligence (CMAI)
Associate Professor, Mathematical Sciences
George Mason University
Fairfax, VA 22030
Phone: (703) 9935086
Fax: (703) 9931491