相关论文: Continuous Data Assimilation For the 3D Ladyzhensk…

We introduce three new nonlinear continuous data assimilation algorithms. These models are compared with the linear continuous data assimilation algorithm introduced by Azouani, Olson, and Titi (AOT). As a proof-of-concept for these models,…

This paper is a contribution in the context of variational data assimilation combined with statistical learning. The framework of data assimilation traditionally uses data collected at sensor locations in order to bring corrections to a…

Data assimilation (DA) integrates observations with model forecasts to produce optimized atmospheric states, whose physical consistency is critical for stable weather forecasting and reliable climate research. Traditional Bayesian DA…

Analyzing the validity and success of a data assimilation algorithm when some state variable observations are not available is an important problem in meteorology and engineering. We present an improved data assimilation algorithm for…

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…

The paper deals with the existence and almost periodic homogenization of some model of generalized Navier-Stokes equations. We first establish an existence result for non-stationary Ladyzhenskaya equations with a given non constant density.…

This paper focuses on continuous data assimilation (CDA) for the Navier-Stokes equations with nonlinear slip boundary conditions. CDA methods are typically employed to recover the original system when initial data or viscosity coefficients…

Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weather and ocean forecasting. The approach involves a…

This paper is devoted to the problem of time parallelization of assimilation methods applying on unbounded time domain. In this way, we present a general procedure to couple the Luenberger observer with time parallelization algorithm. Our…

Data assimilation refers to the process of obtaining an estimate of a system's state using a model for the system's time evolution and a time series of measurements that are possibly noisy and incomplete. However, for practical reasons, the…

Data assimilation is a central problem in many geophysical applications, such as weather forecasting. It aims to estimate the state of a potentially large system, such as the atmosphere, from sparse observations, supplemented by prior…

We propose a numerical approximation method for the Cahn-Hilliard equations that incorporates continuous data assimilation in order to achieve long time accuracy. The method uses a C$^0$ interior penalty spatial discretization of the fourth…

Due to the chaotic nature of turbulence, statistical quantities are often more informative than pointwise characterizations. In this work, we consider the stochastic Ladyzhenskaya-Smagorinsky equation driven by space-time Gaussian noise on…

In this article we develop further an algorithm for data assimilation based upon a shadowing refinement technique [de Leeuw et al., SIAM J. Appl. Dyn. Sys., 17 (2018)] to take partial observations into account. Our method is based on…

This paper considers a nudging-based scheme for data assimilation for the two-dimensional (2D) Navier-Stokes equations (NSE) with periodic boundary conditions and studies the synchronization of the signal produced by this algorithm with the…

The Picard iteration for the Boussinesq model of natural convection can be an attractive solver because it stably decouples the fluid equations from the temperature equation (for contrast, the Newton iteration does not stably decouple).…

Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing…

Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a…

Data assimilation is uniquely challenging in weather forecasting due to the high dimensionality of the employed models and the nonlinearity of the governing equations. Although current operational schemes are used successfully, our…

We formulate a strong equivalence between machine learning, artificial intelligence methods and the formulation of statistical data assimilation as used widely in physical and biological sciences. The correspondence is that layer number in…