Sources and Sinks of Rare Trajectories in 2-Dimensional Velocity Fields Identified by Importance Sampling

TL;DR

This paper introduces a novel importance sampling method to better identify and analyze rare trajectories in 2D atmospheric flow fields, improving estimates of transition probabilities to target sets.

Contribution

It redefines importance sampling for rare event detection in flow dynamics and applies a transfer operator approach to reconstruct and analyze rare trajectories in atmospheric data.

Findings

Enhanced data sets of rare trajectories using importance sampling.

More accurate estimates of transition probabilities compared to standard methods.

Identification of initial conditions and most likely paths for rare events.

Abstract

We use importance sampling in a redefined way to highlight and investigate rare events in the form of trajectories trapped inside a target coherent set. We take a transfer operator approach to finding these sets on a reconstructed 2-dimensional flow of the atmosphere from wind velocity fields provided by the Portable University Model of the Atmosphere. Motivated by extreme value theory, we consider an observable $\phi(x) = -\log(d(x,\gamma))$ maximized at the center $\gamma$ of a chosen target coherent set, where it is rare for a particle to transition. We illustrate that importance sampling maximizing this observable provides an enriched data set of trajectories that experience such a rare event. Backwards reconstruction of these trajectories provides valuable information on initial conditions and most likely paths a trajectory will take. With this information, we are able to obtain more accurate estimates of rare transition probabilities compared to those of standard integration techniques.