Computing return times or return periods with rare event algorithms

Abstract

The average time between two occurrences of the same event, referred to as its return time (or return period), is a useful statistical concept for practical applications. For instance insurances or public agency may be interested by the return time of a 10m flood of the Seine river in Paris. However, due to their scarcity, reliably estimating return times for rare events is very difficult using either observational data or direct numerical simulations. For rare events, an estimator for return times can be built from the extrema of the observable on trajectory blocks. Here, we show that this estimator can be improved to remain accurate for return times of the order of the block size. More importantly, we show that this approach can be generalised to estimate return times from numerical algorithms specifically designed to sample rare events. So far those algorithms often compute probabilities, rather than return times. The approach we propose provides a computationally extremely efficient way to estimate numerically the return times of rare events for a dynamical system, gaining several orders of magnitude of computational costs. We illustrate the method on two kinds of observables, instantaneous and time-averaged, using two different rare event algorithms, for a simple stochastic process, the Ornstein-Uhlenbeck process. As an example of realistic applications to complex systems, we finally discuss extreme values of the drag on an object in a turbulent flow.

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• Rare event algorithm study of extreme warm summers and heat waves over Europe
• Reinforcement learning of rare diffusive dynamics
• Applications of large deviation theory in geophysical fluid dynamics and climate science
• Extreme events in transitional turbulence
• Application of Adaptive Multilevel Splitting to High-Dimensional Dynamical Systems
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• Collapse of transitional wall turbulence captured using a rare events algorithm
• Do extreme events trigger turbulence decay? - a numerical study of turbulence decay time in pipe flows
• Data-driven methods to estimate the committor function in conceptual ocean models
• On a new class of score functions to estimate tail probabilities of some stochastic processes with Adaptive Multilevel Splitting
• Robust intra-model teleconnection patterns for extreme heatwaves
• A self-similarity principle for the computation of rare event probability
• Boosting Ensembles for Statistics of Tails at Conditionally Optimal Advance Split Times