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 …
Parameter recovery for the 2 dimensional Navier--Stokes equations via continuous data assimilation
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 …
(AOT) in the context of an unknown viscosity. We determine the large-time error between the …
Super-Exponential Convergence Rate of a Nonlinear Continuous Data Assimilation Algorithm: The 2D Navier–Stokes Equation Paradigm
We study a nonlinear-nudging modification of the Azouani–Olson–Titi continuous data
assimilation (downscaling) algorithm for the 2D incompressible Navier–Stokes equations …
assimilation (downscaling) algorithm for the 2D incompressible Navier–Stokes equations …
Global in time stability and accuracy of IMEX-FEM data assimilation schemes for Navier–Stokes equations
A Larios, LG Rebholz, C Zerfas - Computer Methods in Applied Mechanics …, 2019 - Elsevier
We study numerical schemes for incompressible Navier–Stokes equations using IMEX
temporal discretizations, finite element spatial discretizations, and equipped with continuous …
temporal discretizations, finite element spatial discretizations, and equipped with continuous …
Convergence analysis of a viscosity parameter recovery algorithm for the 2D Navier–Stokes equations
VR Martinez - Nonlinearity, 2022 - iopscience.iop.org
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 …
viscosity of a two-dimensional incompressible, viscous fluid is studied. The algorithm of …
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 …
The bleeps, the sweeps, and the creeps: convergence rates for dynamic observer patterns via data assimilation for the 2D Navier–Stokes equations
We adapt a continuous data assimilation scheme, known as the Azouani–Olson–Titi (AOT)
algorithm, to the case of moving observers for the 2D incompressible Navier–Stokes …
algorithm, to the case of moving observers for the 2D incompressible Navier–Stokes …
Downscaling data assimilation algorithm with applications to statistical solutions of the Navier–Stokes equations
A Biswas, C Foias, CF Mondaini, ES Titi - … de l'Institut Henri Poincaré C …, 2019 - Elsevier
Based on a previously introduced downscaling data assimilation algorithm, which employs a
nudging term to synchronize the coarse mesh spatial scales, we construct a determining …
nudging term to synchronize the coarse mesh spatial scales, we construct a determining …
Continuous data assimilation reduced order models of fluid flow
We propose, analyze, and test a novel continuous data assimilation reduced order model
(DA-ROM) for simulating incompressible flows. While ROMs have a long history of success …
(DA-ROM) for simulating incompressible flows. While ROMs have a long history of success …
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 …