Numerical Analysis and Scientific Computing Seminar | Collin Victor, Exploring the Infinite Nudging Limit in Continuous Data Assimilation

Data assimilation is a class of techniques that integrates observational data with the underlying model to enhance predictions of dynamical systems. In this talk, I will discuss the Azouani-Olson-Titi (AOT) algorithm for continuous data assimilation algorithm, which includes a feedback-control term at the PDE level. I will focusing on the infinite nudging limit within this framework for the two-dimensional incompressible Navier-Stokes equations. I demonstrate that as the nudging parameter becomes exceedingly large, the nudging filter converges to the synchronization algorithm given by direct insertion of observational data into solution.

I will demonstrate the results of numerical experiments that support these theoretical findings, considering both deterministic observations and observations affected by stochastic noise and I will briefly compare performance with the Ensemble Kalman Filter (EnKF), a widely used data assimilation method based on the Kalman Filter. To address challenges posed by observational noise, I propose a simple adaptive strategy for selecting the nudging parameter, which shows improved performance over constant parameter approaches.