Related papers: Extreme event probability estimation using PDE-con…
We discuss the use of likelihood asymptotics for inference on risk measures in univariate extreme value problems, focusing on estimation of high quantiles and similar summaries of risk for uncertainty quantification. We study whether…
Predicting the occurence of rare and extreme events in complex systems is a well-known problem in non-equilibrium physics. These events can have huge impacts on human societies. New approaches have emerged in the last ten years, which…
Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…
In this work we propose an adaptive multilevel version of subset simulation to estimate the probability of rare events for complex physical systems. Given a sequence of nested failure domains of increasing size, the rare event probability…
To advance automated detection of extreme weather events, which are increasing in frequency and intensity with climate change, we explore modifications to a novel light-weight Context Guided convolutional neural network architecture trained…
Extreme events are ubiquitous in a wide range of dynamical systems, including turbulent fluid flows, nonlinear waves, large scale networks and biological systems. Here, we propose a variational framework for probing conditions that trigger…
Real-time tsunami early warning relies on distributed sensor networks to infer seismic sources and seafloor motion. Optimizing these networks via Bayesian optimal experimental design (OED) is exceptionally challenging for systems governed…
Earth System Models (ESMs) are the state of the art for projecting the effects of climate change. However, longstanding uncertainties in their ability to simulate regional and local precipitation extremes and related processes inhibit…
Landslides plunging into lakes and reservoirs can result in extreme wave runup at shores. This phenomenon has claimed lives and caused damage to near-shore properties. Landslide tsunamis in lakes are different from typical earthquake…
Stretched exponential probability density functions (pdf), having the form of the exponential of minus a fractional power of the argument, are commonly found in turbulence and other areas. They can arise because of an underlying random…
Extreme events are occurrences whose magnitude and potential cause extensive damage on people, infrastructure, and the environment. Motivated by the extreme nature of the current global health landscape, which is plagued by the coronavirus…
Missing data occur in a variety of applications of extreme value analysis. In the block maxima approach to an extreme value analysis, missingness is often handled by either ignoring missing observations or dropping a block of observations…
We often rely on probabilistic measures -- e.g. event probability or expected time -- to characterize systems' safety. However, determining these quantities for extremely low-probability events is generally challenging, as standard safety…
Initially this paper reviews the mathematical issues surrounding the hydrostatic (HPE) and non-hydrostatic (NPE) primitive equations that have been used extensively in numerical weather prediction and climate modelling. Cao and Titi (2005,…
Extreme events occur in many spatially extended dynamical systems, often devastatingly affecting human life which makes their reliable prediction and efficient prevention highly desirable. We study the prediction and prevention of extreme…
Extreme value theory (EVT) is a statistical tool for analysis of extreme events. It has a strong theoretical background, however, we need to choose hyper-parameters to apply EVT. In recent studies of machine learning, techniques of choosing…
In this paper we develop a computationally efficient, two-population, time-dependent Fokker-Plank approach in the two dimensions of energy and angular momentum to study the rates of tidal disruption events (TDEs), extreme mass ratio…
Although the fundamental probabilistic theory of extremes has been well developed, there are many practical considerations that must be addressed in application. The contribution of this thesis is four-fold. The first concerns the choice of…
Our planet is facing increasingly frequent extreme events, which pose major risks to human lives and ecosystems. Recent advances in machine learning (ML), especially with foundation models (FMs) trained on extensive datasets, excel in…
The probability of rare and extreme events is an important quantity for design purposes. However, computing the probability of rare events can be expensive because only a few events, if any, can be observed. To this end, it is necessary to…