Related papers: Continuous data assimilation for problems with lim…
An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. We consider a nudging-based approach for data assimilation that constructs an approximate solution based on a…
This paper considers continuous data assimilation (CDA) in partial differential equation (PDE) discretizations where nudging parameters can be taken arbitrarily large. We prove that long-time optimally accurate solutions are obtained for…
Continuous data assimilation (CDA) techniques, most notably the nudging approach proposed by Azouani, Olson, and Titi (AOT), have been shown to be very successful in deterministic frameworks for achieving long-time synchronization between…
Continuous data assimilation (CDA) nudges observational data into governing equations to recover the underlying flow and improve predictions. Existing rigorous CDA analyses focus primarily on incompressible flows, yet no physical flow is…
Motivated by the challenge of moment recovery in hydrodynamic approximation in kinetic theory, we propose a data-driven approach for the hydrodynamic models. Inspired by continuous data assimilation, our method introduces a relaxation-based…
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 on certain problems with recurring dominant structures, they tend…
The Gray--Scott model governs the interaction of two chemical species via a system of reaction-diffusion equations. Despite its simple form, it produces extremely rich patterns such as spots, stripes, waves, and labyrinths. That makes it…
We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible…
Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically…
In this paper we propose a continuous data assimilation (downscaling) algorithm for the B\'enard convection in porous media using only coarse mesh measurements of the temperature. In this algorithm, we incorporate the observables as a…
We introduce, analyze and test a new interpolation operator for use with continuous data assimilation (DA) of evolution equations that are discretized spatially with the finite element method. The interpolant is constructed as an…
We consider a finite element discretization for the reconstruction of the final state of the heat equation, when the initial data is unknown, but additional data is given in a sub domain in the space time. For the discretization in space we…
We study a continuous data assimilation (CDA) algorithm for a velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to the velocity and vorticity, and nudging applied to the velocity only. We prove…
In this study, we analyzed a continuous data assimilation scheme applied on a double-diffusive natural convection model. The algorithm is introduced with a first order backward Euler time scheme along with a finite element discretization in…
Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using…
Continuous data assimilation (CDA) methods, such as the nudging algorithm introduced by Azouani, Olson, and Titi (AOT), have proven to be highly effective in deterministic settings for asymptotically synchronizing approximate solutions with…
This article develops a general framework for continuous deterministic data assimilation for semilinear parabolic equations by means of evolution equations. Introducing a nudged model driven by partial observations, the global…
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-space configuration of the supplied flow. Here, we apply it…
Data assimilation combines (imperfect) knowledge of a flow's physical laws with (noisy, time-lagged, and otherwise imperfect) observations to produce a more accurate prediction of flow statistics. Assimilation by nudging (from 1964), while…
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 spatial scale observables on the dynamical boundary. On this…