Detecting Lagrangian coherent structures from sparse and noisy trajectory data

TL;DR

This paper presents new methods for detecting Lagrangian Coherent Structures in sparse, noisy trajectory data from complex flows, applicable to fields like oceanography and biology, with validated results and accessible Python implementation.

Contribution

Introduces regularized least-squares and clustering techniques for identifying hyperbolic and elliptic LCSs in challenging data conditions, improving robustness and usability.

Findings

Accurate detection of LCSs in sparse, noisy datasets

Effective application to oceanographic and biological data

Provides a user-friendly Python implementation

Abstract

Many complex flows such as those arising from ocean plastics in geophysics or moving cells in biology are characterized by sparse and noisy trajectory datasets. We introduce techniques for identifying Lagrangian Coherent Structures (LCSs) of hyperbolic and elliptic nature in such datasets. Hyperbolic LCSs, which represent surfaces with maximal attraction or repulsion over a finite amount of time, are computed through a regularized least-squares approximation of the flow map gradient. Elliptic LCSs, which identify regions of coherent motion such as vortices and jets, are extracted using DBSCAN - a popular data clustering algorithm - combined with a systematic approach to choose parameters. We deploy these methods on various benchmark analytical flows and real-life experimental datasets ranging from oceanography to biology and show that they yield accurate results, despite sparse and noisy data. We also provide a lightweight computational implementation of these techniques as a user-friendly and straightforward Python code.