English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We propose and compare methods for the analysis of extreme events in complexsystems governed by PDEs that involve random parameters, in situations where weare interested in quantifying the probability that a scalar function of thesystem's solution is above a threshold. If the threshold is large, thisprobability is small and its accurate estimation is challenging. To tackle thisdifficulty, we blend theoretical results from large deviation theory (LDT) withnumerical tools from PDE-constrained optimization. Our methods first computeparameters that minimize the LDT-rate function over the set of parametersleading to extreme events, using adjoint methods to compute the gradient ofthis rate function. The minimizers give information about the mechanism of theextreme events as well as estimates of their probability. We then propose aseries of methods to refine these estimates, either via importance sampling orgeometric approximation of the extreme event sets. Results are formulated forgeneral parameter distributions and detailed expressions are provided whenGaussian distributions. We give theoretical and numerical arguments showingthat the performance of our methods is insensitive to the extremeness of theevents we are interested in. We illustrate the application of our approach toquantify the probability of extreme tsunami events on shore. Tsunamis aretypically caused by a sudden, unpredictable change of the ocean floor elevationduring an earthquake. We model this change as a random process, which takesinto account the underlying physics. We use the one-dimensional shallow waterequation to model tsunamis numerically. In the context of this example, wepresent a comparison of our methods for extreme event probability estimation,and find which type of ocean floor elevation change leads to the largesttsunamis on shore.

Extreme event probability estimation using PDE-constrained optimization and large deviation theory, with application to tsunamis