Nudging is an important data assimilation technique where partial field measurements are
used to control the evolution of a dynamical system and/or to reconstruct the entire phase …

We study the applicability of tools developed by the computer vision community for feature
learning and semantic image inpainting to perform data reconstruction of fluid turbulence …

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 …

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 …

Bayesian state estimation of a dynamical system utilising a stream of noisy measurements is
important in many geophysical and engineering applications. In these cases, nonlinearities …

Large eddy simulations of turbulent flows are powerful tools used in many engineering and
geophysical settings. Choosing the right value of the free parameters for their subgrid scale …