相关论文: Continuous data assimilation for the three-dimensi…

Data assimilation combines information from physical observations and numerical simulation results to obtain better estimates of the state and parameters of a physical system. A wide class of physical systems of interest have solutions that…

This work applies a continuous data assimilation scheme---a particular framework for reconciling sparse and potentially noisy observations to a mathematical model---to Rayleigh-B\'enard convection at infinite or large Prandtl numbers using…

We investigate the applicability of the data assimilation (DA) to large eddy simulations (LESs) based on the lattice Boltzmann method (LBM). We carry out the observing system simulation experiment of a two-dimensional (2D) forced isotropic…

This paper presents a new approach to verify accuracy of computational simulations. We develop mathematical theorems which can serve as robust a posteriori error estimation techniques to identify numerical pollution, check the performance…

Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…

This paper presents a novel centralized, variational data assimilation approach for calibrating transient dynamic models in electrical power systems, focusing on load model parameters. With the increasing importance of inverter-based…

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…

Data Assimilation (DA) plays a critical role in atmospheric science by reconstructing spatially continous estimates of the system state, which serves as initial conditions for scientific analysis. While recent advances in diffusion models…

We introduce a data assimilation strategy aimed at accurately capturing key non-Gaussian structures in probability distributions using a small ensemble size. A major challenge in statistical forecasting of nonlinearly coupled multiscale…

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…

Consider a continuous dynamical system for which partial information about its current state is observed at a sequence of discrete times. Discrete data assimilation inserts these observational measurements of the reference dynamical system…

This paper presents the formulation and analysis of a mixed finite element method for a hemivariational inequality arising from the stationary convective Brinkman-Forchheimer extended Darcy (CBFeD) equations. This model extends the…

Data assimilation is a fundamental task in updating forecasting models upon observing new data, with applications ranging from weather prediction to online reinforcement learning. Deep generative forecasting models (DGFMs) have shown…

We show how the 3DVAR data assimilation methodology can be used in the astrophysical context of a two-dimensional convection flow. We study the way this variational approach finds best estimates of the current state of the flow from a…

We adapt a previously introduced continuous in time data assimilation (downscaling) algorithm for the 2D Navier-Stokes equations to the more realistic case when the measurements are obtained discretely in time and may be contaminated by…

We introduce a Darcy-scale model to describe compressible multi-component flow in a fully saturated porous medium. In order to capture cross-diffusive effects between the different species correctly, we make use of the Maxwell--Stefan…

In this paper, we consider the generalized Forchheimer flows for slightly compressible fluids in porous media. Using Muskat's and Ward's general form of Forchheimer equations, we describe the flow of a single-phase fluid in $\mathbb R^d,…

This paper is concerned with the large-time behavior of solutions to the Cauchy problem on the two-fluid Euler-Maxwell system with collisions when initial data are around a constant equilibrium state. The main goal is the rigorous…

This paper develops a computational framework for optimizing the parameters of data assimilation systems in order to improve their performance. The approach formulates a continuous meta-optimization problem for parameters; the…

This paper develops the a priori analysis of a mixed finite element method for the filtration of an incompressible fluid through a non-deformable saturated porous medium with heterogeneous permeability. Flows are governed by the…