A discrete data assimilation scheme for the solutions of the two-dimensional Navier--Stokes equations and their statistics

C Foias, CF Mondaini, ES Titi - SIAM Journal on Applied Dynamical Systems, 2016 - SIAM
We adapt a previously introduced continuous in time data assimilation (downscaling)
algorithm for the two-dimensional Navier--Stokes equations to the more realistic case when …

Finite determining parameters feedback control for distributed nonlinear dissipative systems-a computational study

E Lunasin, ES Titi - arXiv preprint arXiv:1506.03709, 2015 - arxiv.org
We present a computational study of a simple finite-dimensional feedback control algorithm
for stabilizing solutions of infinite-dimensional dissipative evolution equations such as …

Dynamically learning the parameters of a chaotic system using partial observations

E Carlson, J Hudson, A Larios, VR Martinez… - arXiv preprint arXiv …, 2021 - arxiv.org
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 …

Parameter recovery for the 2 dimensional Navier--Stokes equations via continuous data assimilation

E Carlson, J Hudson, A Larios - SIAM Journal on Scientific Computing, 2020 - SIAM
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 …

Data assimilation algorithm for 3D Bénard convection in porous media employing only temperature measurements

A Farhat, E Lunasin, ES Titi - Journal of Mathematical Analysis and …, 2016 - Elsevier
In this paper we propose a continuous data assimilation (downscaling) algorithm for the
Bénard convection in porous media using only discrete spatial-mesh measurements of the …

On the Charney conjecture of data assimilation employing temperature measurements alone: the paradigm of 3D planetary geostrophic model

A Farhat, E Lunasin, ES Titi - Mathematics of Climate and Weather …, 2016 - degruyter.com
Analyzing the validity and success of a data assimilation algorithmwhen some state variable
observations are not available is an important problem in meteorology and engineering. We …

Efficient dynamical downscaling of general circulation models using continuous data assimilation

S Desamsetti, HP Dasari, S Langodan… - Quarterly Journal of …, 2019 - Wiley Online Library
Continuous data assimilation (CDA) is successfully implemented for the first time for efficient
dynamical downscaling of a global atmospheric reanalysis. A comparison of the …

A data assimilation algorithm for the subcritical surface quasi-geostrophic equation

MS Jolly, VR Martinez, ES Titi - Advanced Nonlinear Studies, 2017 - degruyter.com
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 …

Continuous data assimilation for a 2D Bénard convection system through horizontal velocity measurements alone

A Farhat, E Lunasin, ES Titi - Journal of Nonlinear Science, 2017 - Springer
In this paper we propose a continuous data assimilation (downscaling) algorithm for a two-
dimensional Bénard convection problem. Specifically we consider the two-dimensional …

Super-Exponential Convergence Rate of a Nonlinear Continuous Data Assimilation Algorithm: The 2D Navier–Stokes Equation Paradigm

E Carlson, A Larios, ES Titi - Journal of Nonlinear Science, 2024 - Springer
We study a nonlinear-nudging modification of the Azouani–Olson–Titi continuous data
assimilation (downscaling) algorithm for the 2D incompressible Navier–Stokes equations …