We present a computational study of a simple finite-dimensional feedback control algorithm
for stabilizing solutions of infinite-dimensional dissipative evolution equations such as …

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 …

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 investigate the capabilities of Physics-Informed Neural Networks (PINNs) to reconstruct
turbulent Rayleigh–Bénard flows using only temperature information. We perform a …

In this article, we prove that data assimilation by feedback nudging can be achieved for the
three-dimensional quasi-geostrophic equation in a simplified scenario using only large …

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

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 …

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 …

Continuous data assimilation (CDA) is successfully implemented for the first time for efficient
dynamical downscaling of a global atmospheric reanalysis. A comparison of the …