Extreme Event Probability Estimation using PDE-Constrained Optimization and Large Deviation Theory, with Application to Tsunamis

Shanyin Tong (Courant Institute, NYU)

Extreme events like hurricanes, energy grid blackouts, dam breaks, earthquakes, and pandemics are infrequent, but have severe consequences. Because estimating the probability of such events can inform strategies that mitigate their effects, scientists must develop methods to study the distribution tail of these occurrences. However, calculating small probabilities is hard, particularly when involving complex dynamics and high-dimensional random variables. In this talk, I will discuss our proposed method overcoming these difficulties by using ideas from large deviation theory (LDT) to connect probability estimation with optimization, and illustrate its application to estimate the probability of large tsunami waves. The approach first computes the most important point in the extreme event set by solving a PDE-constrained optimization problem. This point and its local derivative information provide asymptotic estimations of the probability, they also inform the proposal distributions for importance sampling. I will also discuss the uses of these estimations for solving optimization under rare chance constraints, and constructing a low-dimensional subspace that dominates the probability.