The Bleeps, the Sweeps, and the Creeps: Convergence Rates for Dynamic Observer Patterns via Data Assimilation for the 2D Navier-Stokes Equations

TL;DR

This paper explores how moving observers using the AOT data assimilation algorithm can significantly improve convergence rates for the 2D Navier-Stokes equations, with potential applications in real-world data collection.

Contribution

It introduces and tests novel movement patterns for observers in data assimilation, demonstrating substantial improvements over static observers.

Findings

Order-of-magnitude faster convergence with certain movement patterns

Comparison of different observer movement strategies

Potential for enhanced real-world data collection methods

Abstract

We adapt a continuous data assimilation scheme, known as the Azouani-Olson-Titi (AOT) algorithm, to the case of moving observers for the 2D incompressible Navier-Stokes equations. We propose and test computationally several movement patterns (which we refer to as "the bleeps, the sweeps and the creeps"), as well as Lagrangian motion and combinations of these patterns, in comparison with static (i.e. non-moving) observers. In several cases, order-of-magnitude improvements in terms of the time-to-convergence are observed. We end with a discussion of possible applications to real-world data collection strategies that may lead to substantial improvements in predictive capabilities.