Extreme events are short-lived episodes occurring due to exogenous causes or internal instabilities during which observables significantly depart from their mean values. A great deal of effort has been devoted to predicting and statistically quantifying extreme events because they can have catastrophic consequences (e.g., structural failure, rogue waves, extreme weather conditions, and market crashes). This is an arduous task because the systems that give rise to extreme events are most often highly complex and strongly nonlinear. This mini-symposium provides a venue to review the latest advances in the field.
16:30
- NEW - Sparse Methods for Bayesian Linear Regression
Samuel Rudy | Massachusetss Insitute of Technology | United States
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Authors:
Samuel Rudy | Massachusetss Insitute of Technology | United States
Themistoklis P. Sapsis | Massachusetts Institute of Technology | United States
We propose several adaptations of the Automatic Relevance Determination (ARD) method for Bayesian linear regression aimed at learning parsimonious models from high dimensional linear equations. We show that, in the orthogonal case, ARD includes a quantity of superfluous features that is independent of the error in the linear model. These non-zero coefficients are normally removed via magnitude-based thresholding or by passing an artificially large estimate of the linear model's error to the ARD algorithm. We rigorously show the effectiveness of each of these techniques in removing superfluous terms and introduce several alternatives using regularization or thresholding based on the learned posterior distribution from ARD. Relative merits of each technique are discussed.
17:00
- CANCELED - Estimation of Extreme Tsunami Waves Using Large Deviation Theory
Shanyin Tong | NYU Courant | United States
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Authors:
Shanyin Tong | NYU Courant | United States
Eric Vanden-Eijnden | NYU Courant | United States
Georg Stadler | NYU Courant | United States
Tsunami waves are caused by a sudden change of ocean depth (bathymetry) after an earthquake below the ocean floor. Since large tsunami waves are extreme events, they correspond to the tail part of a probability distribution, whose exploration would require impractically many samples of a Monte Carlo method. We use arguments and methods from large deviation theory to relate the probabilities of extreme events to the solutions of a one-parameter family of optimization problems. To model tsunami waves, we use the shallow water equations, which thus appear as PDE-constraints in this optimization problem. The optimization objective includes a term that measures how extreme the event is, and a term corresponding to the likelihood of bathymetry changes, which are modeled as a Gaussian random field. From large deviation theory, we know that the extreme event probability is log-asymptotic to the negative rate function at instantons (most probable points), which means that there is a prefactor needed to obtain the actual probability. We use first- and second-order information of the extreme event set to approximate the prefactor, thus removing the need of Monte Carlo sampling in our method. Numerical results with the 1D inviscid shallow water equation are presented.
17:30
Transition Probabilities of Noise-Induced Transitions of the Atlantic Ocean Circulation
Hendrik Dijkstra | Utrecht University | Netherlands
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Authors:
Daniele Castellana | Utrecht University | Netherlands
Hendrik Dijkstra | Utrecht University | Netherlands
Sven Baars | University of Groningen | Netherlands
Fred Wubs | University of Groningen | Netherlands
The Atlantic Meridional Overturning Circulation (AMOC) is considered to be a tipping element of the climate system. As it cannot be excluded that the AMOC is in a multiple regime, transitions can occur due to atmospheric noise between the present-day state and a weaker AMOC state. Using two models of different complexity, we present estimates of the transition probability of noise-induced transitions of the AMOC within a certain time period using methodology from large deviation theory. We find that there are two types of transitions, with a partial or full collapse of the AMOC, having different transition probabilities. For the present-day state, we estimate that the transition probabilities of the partial collapse over the next 100 years to be about 15%, with a high sensitivity of this probability to the surface freshwater noise amplitude.
18:00
A Large Deviation Theory-Based Analysis of Heat Waves and Cold Spells in a Simplified Model of the General Circulation of the Atmosphere
Vera Melinda Galfi | University of Hamburg | Germany
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Authors:
Vera Melinda Galfi | University of Hamburg | Germany
Valerio Lucarini | University of Reading | United Kingdom
Jeroen Wouters | University of Reading | United Kingdom
We study temporally persistent and spatially extended extreme events of temperature anomalies, i.e. heat waves and cold spells, using large deviation theory. To this end, we consider a simplified yet Earth-like general circulation model of the atmosphere and numerically estimate large deviation rate functions of near-surface temperature in the mid-latitudes. We find that, after a renormalization based on the integrated auto-correlation, the rate function obtained at a given latitude by looking locally in space at long time averages agrees with what is obtained, instead, by looking locally in time at large spatial averages along the latitude. This is a result of scale symmetry in the spatio-temporal turbulence and of the fact that advection is primarily zonal. This agreement hints at the universality of large deviations of the temperature field. Furthermore, we discover that the obtained rate function is able to describe the statistics of temporal averages of spatial averages performed over large spatial scales, thus allowing one to look into spatio-temporal large deviations. Finally, we find out that, as a result of a modification in the rate function, large deviations are relatively more likely to occur when looking at spatial averages performed over intermediate scales. This is due to the existence of weather patterns associated with the low-frequency variability of the atmosphere, which are responsible for extended and temporally persistent heat waves or cold spells.