Earth system models suffer from various structural and parametric errors in their
representation of nonlinear, multi‐scale processes, leading to uncertainties in their long …

Using limited observations of the velocity field of the two-dimensional Navier-Stokes
equations, we successfully reconstruct the steady body force that drives the flow. The …

This study undertakes the challenging task of unraveling the intricacies embedded in the
integrable Kuralay equation, a cornerstone in the field of mathematical physics. Specifically …

We study a nonlinear-nudging modification of the Azouani–Olson–Titi continuous data
assimilation (downscaling) algorithm for the 2D incompressible Navier–Stokes equations …

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 …

This article studies the interrelation between the determining modes property in the two-
dimensional (2D) Navier-Stokes equations (NSE) of incompressible fluids and the …

This article studies the intimate relationship between two filtering algorithms for continuous
data assimilation, the synchronization filter and the nudging filter, in the paradigmatic context …

Understanding the impact of model error on data assimilation is an important practical topic.
Model error in the subgrid scale is commonly seen in various applications as a natural …

We study different approaches to implementing sparse-in-time observations into the the
Azouani-Olson-Titi data assimilation algorithm. We propose a new method which introduces …

The Koopman operator presents an attractive approach to achieve global linearization of
nonlinear systems, making it a valuable method for simplifying the understanding of complex …