Estimation of extreme event probabilities in complex systems
Georg Stadler (New York University)
I will discuss the estimation of tail probabilities in complex systems governed by PDEs. The approach is guided by ideas from large deviation theory and 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 solve an optimization problem over the set of parameters leading to an extreme event. This is followed by either importance sampling or exploration of the local curvature of the extreme event set around the optimizer. As application, we quantify the probability of extreme tsunami events on shore. Tsunamis are caused by a sudden, unpredictable change of the ocean floor elevation during an earthquake. We model this change as random field, and use a one-dimensional shallow water equation as simplified tsunami model. 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.