Rare event computation in deterministic chaotic systems using genealogical particle analysis

TL;DR

This paper explores the application of genealogical particle analysis algorithms to estimate rare event probabilities in deterministic chaotic systems, demonstrating improved performance with time-dependent objectives in models like Lorenz '96.

Contribution

It introduces the use of genealogical particle analysis for rare event estimation in deterministic systems and shows how time-dependent objectives enhance estimator efficiency.

Findings

Successful application to Lorenz '96 model

Time-dependent objective functions improve estimation accuracy

Implementation issues are addressed using Ornstein-Uhlenbeck system

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.