Rare event computation in deterministic chaotic systems using genealogical particle analysis

Abstract

In this paper we address the use of rare event computation techniques to estimate small over-threshold probabilities of observables in determin-istic dynamical systems. We demonstrate that the genealogical particle analysis algorithms can be successfully applied to a toy model of atmospheric dynamics, the Lorenz '96 model. We furthermore use the Ornstein-Uhlenbeck system to illustrate a number of implementation issues. We also show how a time-dependent objective function based on the fluctuation path to a high threshold can greatly improve the performance of the estimator compared to a fixed-in-time objective function.

References in corpus (6)

• On adaptive resampling strategies for sequential Monte Carlo methods
• A numerical approach to large deviations in continuous-time
• Genealogical particle analysis of rare events
• Probing rare physical trajectories with Lyapunov weighted dynamics
• Computing transition rates for the 1-D stochastic Ginzburg--Landau--Allen--Cahn equation for finite-amplitude noise with a rare event algorithm
• Harmonic Measure for Percolation and Ising Clusters Including Rare Events

Cited by in corpus (17)

• Numerical computation of rare events via large deviation theory
• Practical rare event sampling for extreme mesoscale weather
• Computing return times or return periods with rare event algorithms
• Applications of large deviation theory in geophysical fluid dynamics and climate science
• Extreme events in transitional turbulence
• Optimizing weighted ensemble sampling of steady states
• Application of Adaptive Multilevel Splitting to High-Dimensional Dynamical Systems
• A Large Deviation Theory-based Analysis of Heat Waves and Cold Spells in a Simplified Model of the General Circulation of the Atmosphere
• Large deviations in chaotic systems: exact results and dynamical phase transition
• Coupling rare event algorithms with data-based learned committor functions using the analogue Markov chain
• On a new class of score functions to estimate tail probabilities of some stochastic processes with Adaptive Multilevel Splitting
• An ergodic theorem for the weighted ensemble method
• A self-similarity principle for the computation of rare event probability
• Taming chaos to sample rare events: the effect of weak chaos
• Monte Carlo sampling in diffusive dynamical systems
• Remarkable similarities in distributions of dynamical observables in chaotic systems
• Adversarial sampling of unknown and high-dimensional conditional distributions