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 continuous data assimilation algorithm proposed by Azouani, Olson, and Titi
(AOT) in the context of an unknown viscosity. We determine the large-time error between the …

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

We study numerical schemes for incompressible Navier–Stokes equations using IMEX
temporal discretizations, finite element spatial discretizations, and equipped with continuous …

In this paper, the convergence of an algorithm for recovering the unknown kinematic
viscosity of a two-dimensional incompressible, viscous fluid is studied. The algorithm of …

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 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 …

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 …

We propose, analyze, and test a novel continuous data assimilation reduced order model
(DA-ROM) for simulating incompressible flows. While ROMs have a long history of success …

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