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
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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