Measuring the rogue wave pattern triggered from Gaussian perturbations by deep learning

TL;DR

This paper introduces a deep learning-based method to automatically detect rogue wave patterns triggered by Gaussian perturbations, demonstrating consistent visual patterns and providing a new dataset and metric for analysis.

Contribution

The authors develop RWD-Net for rogue wave detection, create the RWD-10K dataset with annotations, and propose the DRW metric to analyze rogue wave evolution.

Findings

Achieved 99.29% average precision in rogue wave detection.

Demonstrated similar visual patterns of rogue waves across different perturbations.

Provided statistical analysis of rogue wave density and evolution.

Abstract

Weak Gaussian perturbations on a plane wave background could trigger lots of rogue waves, due to modulational instability. Numerical simulations showed that these rogue waves seemed to have similar unit structure. However, to the best of our knowledge, there is no relative result to prove that these rogue waves have the similar patterns for different perturbations, partly due to that it is hard to measure the rogue wave pattern automatically. In this work, we address these problems from the perspective of computer vision via using deep neural networks. We propose a Rogue Wave Detection Network (RWD-Net) model to automatically and accurately detect RWs on the images, which directly indicates they have the similar computer vision patterns. For this purpose, we herein meanwhile have designed the related dataset, termed as Rogue Wave Dataset-$10$K (RWD-$10$K), which has $10,191$ RW images with bounding box annotations for each RW unit. In our detection experiments, we get $99.29\%$ average precision on the test splits of the RWD-$10$K dataset. Finally, we derive our novel metric, the density of RW units (DRW), to characterize the evolution of Gaussian perturbations and obtain the statistical results on them.