In search of rogue waves: a novel proposal distribution for parallelized rejection sampling of the truncated KdV Gibbs measure

TL;DR

This paper introduces a new proposal distribution for rejection sampling of the truncated KdV Gibbs measure, significantly improving efficiency and enabling better parallelization for studying rogue wave statistics.

Contribution

A novel proposal distribution for rejection sampling of the TKdV Gibbs measure, enhancing sampling efficiency and parallelization capabilities.

Findings

Generated 1-6 orders of magnitude more accepted samples than naive methods.

Achieved better parallelization and uncorrelated sample generation.

Effectively captured extreme wave events in laboratory-relevant regimes.

Abstract

The Gibbs ensemble of the truncated KdV (TKdV) equation has been shown to accurately describe the anomalous wave statistics observed in laboratory experiments, in particular the emergence of extreme events. Here, we introduce a novel proposal distribution that facilitates efficient rejection sampling of the TKdV Gibbs measure. Within parameter regimes accessible to laboratory experiments and capable of producing extreme events, the proposal distribution generates 1-6 orders of magnitude more accepted samples than does a naive, uniform distribution. When equipped with the new proposal distribution, a simple rejection algorithm enjoys key advantages over a Markov chain Monte Carlo algorithm, include better parallelization properties and generation of uncorrelated samples.