Dynamically learning the parameters of a chaotic system using partial observations
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 …
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
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 …
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
This work applies a continuous data assimilation scheme---a framework for reconciling
sparse and potentially noisy observations to a mathematical model---to Rayleigh--Bénard …
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 …
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 …
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
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 …
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
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 …
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 …
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
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 …
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 …
potential, external time-dependent perturbations of an incompressible fluid from large-scale …