Synchronization to big data: Nudging the Navier-Stokes equations for data assimilation of turbulent flows

P Clark Di Leoni, A Mazzino, L Biferale - Physical Review X, 2020 - APS
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 …

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 …

Reconstruction of turbulent data with deep generative models for semantic inpainting from TURB-Rot database

M Buzzicotti, F Bonaccorso, PC Di Leoni, L Biferale - Physical Review Fluids, 2021 - APS
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 …

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 …

A computational study of a data assimilation algorithm for the two-dimensional Navier-Stokes equations

M Gesho, E Olson, ES Titi - Communications in Computational …, 2016 - cambridge.org
We study the numerical performance of a continuous data assimilation (downscaling)
algorithm, based on ideas from feedback control theory, in the context of the two …

Downscaling the 2D Bénard convection equations using continuous data assimilation

MU Altaf, ES Titi, T Gebrael, OM Knio, L Zhao… - Computational …, 2017 - Springer
We consider a recently introduced continuous data assimilation (CDA) approach for
downscaling a coarse resolution configuration of the 2D Bénard convection equations into a …

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 …