Estimation of extreme event probabilities in systems governed by PDEs

Speaker: Prof. Dr. Georg Stadler
Affiliation: Courant Institute of Mathematical Sciences, New York University (USA)
Organized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg (Germany)

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Meeting ID: 688 5113 6725 | PIN: 014980

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 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.

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