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 …

Data assimilation with model error: Analytical and computational study for Sabra shell model

N Chen, A Farhat, E Lunasin - Physica D: Nonlinear Phenomena, 2023 - Elsevier
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 …

Data assimilation in large Prandtl Rayleigh--Bénard convection from thermal measurements

A Farhat, NE Glatt-Holtz, VR Martinez… - SIAM Journal on Applied …, 2020 - SIAM
This work applies a continuous data assimilation scheme---a framework for reconciling
sparse and potentially noisy observations to a mathematical model---to Rayleigh--Bénard …

Continuous data assimilation with blurred-in-time measurements of the surface quasi-geostrophic equation

MS Jolly, VR Martinez, EJ Olson, ES Titi - Chinese Annals of Mathematics …, 2019 - Springer
An intrinsic property of almost any physical measuring device is that it makes observations
which are slightly blurred in time. The authors consider a nudging-based approach for data …

Fully discrete numerical schemes of a data assimilation algorithm: uniform-in-time error estimates

HA Ibdah, CF Mondaini, ES Titi - IMA Journal of Numerical …, 2020 - academic.oup.com
Our aim is to approximate a reference velocity field solving the two-dimensional Navier–
Stokes equations (NSE) in the absence of its initial condition by utilizing spatially discrete …

On the infinite-nudging limit of the nudging filter for continuous data assimilation

E Carlson, A Farhat, VR Martinez, C Victor - arXiv preprint arXiv …, 2024 - arxiv.org
This article studies the intimate relationship between two filtering algorithms for continuous
data assimilation, the synchronization filter and the nudging filter, in the paradigmatic context …

Identifying the body force from partial observations of a two-dimensional incompressible velocity field

A Farhat, A Larios, VR Martinez, JP Whitehead - Physical Review Fluids, 2024 - APS
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 …

Determining the viscosity of the Navier–Stokes equations from observations of finitely many modes

A Biswas, J Hudson - Inverse Problems, 2023 - iopscience.iop.org
In this work, we ask and answer the question: when is the viscosity of a fluid uniquely
determined from spatially sparse measurements of its velocity field? We pose the question …

Identifying the body force from partial observations of a 2D incompressible velocity field

A Farhat, A Larios, VR Martinez… - arXiv preprint arXiv …, 2023 - arxiv.org
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 …

On the reconstruction of unknown driving forces from low-mode observations in the 2D Navier–Stokes equations

VR Martinez - Proceedings of the Royal Society of Edinburgh …, 2022 - cambridge.org
This article is concerned with the problem of determining an unknown source of non-
potential, external time-dependent perturbations of an incompressible fluid from large-scale …