Motivated by recent progress in data assimilation, we develop an algorithm to dynamically
learn the parameters of a chaotic system from partial observations. Under reasonable …

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 …

We study the use of the Azouani-Olson-Titi (AOT) continuous data assimilation algorithm to
recover solutions of the 3D Navier–Stokes equations modified to have finer-order fractional …

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 …

We introduce, analyze, and test an interpolation operator designed for use with continuous
data assimilation (DA) of evolution equations that are discretized spatially with the finite …

Data assimilation combines (imperfect) knowledge of a flow's physical laws with (noisy, time-
lagged, and otherwise imperfect) observations to produce a more accurate prediction of flow …

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 …

We analyze continuous data assimilation by nudging for the 3D Ladyzhenskaya equations.
The analysis provides conditions on the spatial resolution of the observed data that …

In this paper, we consider the analysis of a nudging based algorithm for data assimilation for
the three-dimensional Boussinesq system, which we call the AOT system. A rigorous …