
Analysis and Simulation of Extremes and Rare Events in Complex Systems
Rare weather and climate events, such as heat waves and floods, can brin...
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Extreme event propagation using counterfactual theory and vine copulas
Understanding multivariate extreme events play a crucial role in managin...
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Optimization under rare chance constraints
Chance constraints provide a principled framework to mitigate the risk o...
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Orthounimodal Distributionally Robust Optimization: Representation, Computation and Multivariate Extreme Event Applications
This paper studies a basic notion of distributional shape known as ortho...
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Efficient computation of extreme excursion probabilities for dynamical systems
We develop a novel computational method for evaluating the extreme excur...
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Extreme events evaluation using CRPS distributions
Verification of ensemble forecasts for extreme events remains a challeng...
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Simulating flood event sets using extremal principal components
Hazard event sets, which correspond to a collection of synthetic flood e...
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Extreme event probability estimation using PDEconstrained optimization and large deviation theory, with application to tsunamis
We propose and compare 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 tools 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 solution is at or above a threshold. If this threshold is large, these probabilities are small and their accurate estimation is challenging. Our methods first compute parameters that minimize the LDTrate function over the set of parameters leading to extreme events. These solutions provide asymptotic information about small probability events. We propose a series of methods to refine these estimates, namely methods based on importance sampling and on geometric approximation of the extreme event sets. Results are formulated for general parameter distributions and detailed expressions are provided when the underlying distribution is Gaussian. We give theoretical and numerical arguments showing that the performance of our methods is insensitive to the extremeness of the events we are interested in. 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 a random process, which takes into account the underlying physics. We use the onedimensional shallow water equation to model tsunamis numerically. Adjoint methods are used to compute the derivatives needed to solve the LDToptimization problem. We present a comparison of the methods for extreme event probability estimation, and find which type of ocean floor elevation change leads to the largest tsunamis on shore.
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