collaborators

5 papers

math.AP2025

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…

math.OC2024

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…

math.AP2024

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…

math.AP2024

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…

math.OC2024

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…