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 …

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 develop an algorithm based on the nudging data assimilation scheme for the concurrent
(on-the-fly) estimation of scalar parameters for a system of evolutionary dissipative partial …

Based on a previously introduced downscaling data assimilation algorithm, which employs a
nudging term to synchronize the coarse mesh spatial scales, we construct a determining …

This work applies a continuous data assimilation scheme---a framework for reconciling
sparse and potentially noisy observations to a mathematical model---to Rayleigh--Bénard …

Our aim is to approximate a reference velocity field solving the two-dimensional Navier–
Stokes equations (NSE) in the absence of its initial condition by utilizing spatially discrete …

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

This paper considers continuous data assimilation (CDA) in partial differential equation
(PDE) discretizations where nudging parameters can be taken arbitrarily large. We prove …

In this article, we show that the continuous data assimilation algorithm is valid for the 3D
primitive equations of the ocean. Namely, the $ L^ 2$ norm of the assimilated solution …

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 …