5 papers
Determining Modes, State Reconstruction, and Intertwinement: Existence of Self-Synchronizing Intertwinements
Elizabeth Carlson, Aseel Farhat, Vincent R. Martinez +1
In the companion paper of the authors, a general synchronization framework was developed in the paradigmatic context of the 2D Navier-Stokes equations that allows one to precisely…
On the inadequacy of nudging data assimilation algorithms for non-dissipative systems
Edriss S. Titi, Collin Victor
In this work, we study the applicability of the Azouani-Olson-Titi (AOT) nudging algorithm for continuous data assimilation to evolutionary dynamical systems that are not dissipati…
On the nudging approach to continuous data assimilation in the limit of infinite error feedback gain
Elizabeth Carlson, Aseel Farhat, Vincent R. Martinez +1
This article studies the intimate relationship between two filtering algorithms for continuous data assimilation, the synchronization filter and the nudging filter, in the paradigm…
Determining Modes, State Reconstruction, and Intertwinement: A Synchronization Framework
Elizabeth Carlson, Aseel Farhat, Vincent R. Martinez +1
This article studies the interrelation between the determining modes property in the two-dimensional (2D) Navier-Stokes equations (NSE) of incompressible fluids and the reconstruct…
An Assessment of Ensemble Kalman Filter and Azouani-Olson-Titi Algorithms for Data Assimilation: A Comparative Study
Ning Ning, Collin Victor
Continuous data assimilation (CDA) is a method that continuously integrates observational data into a dynamical system to improve model accuracy in real-time. The AOT algorithm is…