A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete...

Area of Science:

• Dynamical systems
• Data analysis
• Numerical methods

Background:

• Identifying stable regions in phase space is crucial for understanding dynamical systems.
• Existing methods often require dense trajectory data and continuous observations.
• Real-world data frequently suffers from sparsity and observational gaps.

Purpose of the Study:

• To present a novel numerical method for identifying approximately retained regions in phase space.
• To address limitations of existing methods when dealing with sparse or incomplete trajectory data.
• To offer a computationally efficient and versatile approach applicable in any dimension.

Main Methods:

• The core methodology involves spatio-temporal clustering of trajectory data.
• This technique groups trajectories that maintain proximity over a specified time.
• The method is designed to be robust to missing data points.

Main Results:

• The numerical method successfully identifies regions of phase space that remain locally compact over time.
• Effective results were achieved even with a limited number of trajectories.
• The approach demonstrated resilience to gaps in trajectory observations.

Conclusions:

• The proposed spatio-temporal clustering method provides an effective way to analyze phase space dynamics.
• It offers a practical solution for systems with sparse or intermittently observed trajectories.
• The method is easy to implement, computationally fast, and broadly applicable across dimensions.