相关论文: Data Assimilation to the Primitive Equations in $H…

Modern weather and climate prediction models are based on a system of nonlinear partial differential equations called the primitive equations. Lie symmetries of the primitive equations with zero external heating rate are computed and the…

We consider data assimilation for the heat equation using a finite element space semi-discretization. The approach is optimization based, but the design of regularization operators and parameters rely on techniques from the theory of…

This paper is concerned with an initial-boundary value problem of the two-dimensional inhomogeneous primitive equations with density-dependent viscosity. The global well-posedness of strong solutions is established, provided the initial…

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-dimensional incompressible Navier--Stokes equations. Our model problem is…

An alternative data-driven modeling approach has been proposed and employed to gain fundamental insights into robot motion interaction with granular terrain at certain length scales. The approach is based on an integration of dimension…

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…

In this paper we consider the (simplified) 3-dimensional primitive equations with \emph{physical boundary conditions}. We show that the equations with constant forcing have a bounded absorbing ball in the $H^1$-norm and that a solution to…

We study Bayesian data assimilation (filtering) for time-evolution PDEs, for which the underlying forward problem may be very unstable or ill-posed. Such PDEs, which include the Navier-Stokes equations of fluid dynamics, are characterized…

This paper studies the role of sparse regularization in a properly chosen basis for variational data assimilation (VDA) problems. Specifically, it focuses on data assimilation of noisy and down-sampled observations while the state variable…

Covariance localization is a critical component of ensemble-based data assimilation (DA) and many current localization schemes simply dampen correlations as a function of distance. Increases in computational resources, broadening scope of…

Accurate weather and climate prediction relies on data assimilation (DA), which estimates the Earth system state by integrating observations with models. While exascale computing has significantly advanced earth simulation, scalable and…

In this paper, we improve the global existence result in [9] slightly. More precisely, the global existence of strong solutions to the primitive equations with only horizontal viscosity and diffusivity is obtained under the assumption of…

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…

Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the…

These notes provide a systematic mathematical treatment of the subject of data assimilation.

Data assimilation is a core component of numerical weather prediction systems. The large quantity of data processed during assimilation requires the computation to be distributed across increasingly many compute nodes, yet existing…

Research on Artificial Intelligence (AI)-based Data Assimilation (DA) is expanding rapidly. However, the absence of an objective, comprehensive, and real-world benchmark hinders the fair comparison of diverse methods. Here, we introduce…

Primal-dual algorithm (PDA) is a classic and popular scheme for convex-concave saddle point problems. It is universally acknowledged that the proximal terms in the subproblems about the primal and dual variables are crucial to the…

We show the local in time well-posedness of the Prandtl equation for data with Gevrey $2$ regularity in $x$ and $H^1$ regularity in $y$. The main novelty of our result is that we do not make any assumption on the structure of the initial…

This paper is concerned with the recovery of (approximate) solutions to parabolic problems from incomplete and possibly inconsistent observational data, given on a time-space cylinder that is a strict subset of the computational domain…