相关论文: A discrete data assimilation algorithm for the rec…

The Gray-Scott (GS) model represents the dynamics and steady state pattern formation in reaction-diffusion systems and has been extensively studied in the past. In this paper, we consider the effects of anomalous diffusion on pattern…

We consider the assimilation of Lagrangian data into a primitive equations circulation model of the ocean at basin scale. The Lagrangian data are positions of floats drifting at fixed depth. We aim at reconstructing the four-dimensional…

The Gray-Scott model can be thought of as an effective theory at large spatiotemporal scales coming from a more fundamental theory valid at shorter spatiotemporal scales. The more fundamental theory includes a composite molecule which is…

Inferring physical parameters of turbulent flows by assimilation of data measurements is an open challenge with key applications in meteorology, climate modeling and astrophysics. Up to now, spectral nudging was applied for empirical…

We introduce a continuous (downscaling) data assimilation algorithm for the 2D B\'enard convection problem using vorticity or local circulation measurements only. In this algorithm, a nudging term is added to the vorticity equation to…

Data assimilation has become a key technique for combining physical models with observational data to estimate state variables. However, classical assimilation algorithms often struggle with the high nonlinearity present in both physical…

Large Eddy Simulations of turbulent flows are powerful tools used in many engineering and geophysical settings. Choosing the right value of the free parameters for their subgrid scale models is a crucial task for which the current methods…

In this work, we study the applicability of the Azouani-Olson-Titi (AOT) nudging algorithm for continuous data assimilation to evolutionary dynamical systems that are not dissipative. Specifically, we apply the AOT algorithm to a partially…

The efficacy of a nudging data assimilation algorithm using higher order finite element interpolating operators is studied. Numerical experiments are presented for the 2D Navier-Stokes equations in two cases: shear flow in an annulus and a…

In atmospheric and turbulent flow modeling, Large Eddy Simulation (LES) is often used to reduce computational cost, while observational data typically originates from the underlying physical system. Motivated by this setting, we study a…

The generation of initial conditions via accurate data assimilation is crucial for weather forecasting and climate modeling. We propose DiffDA as a denoising diffusion model capable of assimilating atmospheric variables using predicted…

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…

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…

The requirements of modern sensing are rapidly evolving, driven by increasing demands for data efficiency, real-time processing, and deployment under limited sensing coverage. Complex physical systems are often characterized through the…

This article develops a novel data assimilation methodology, addressing challenges that are common in real-world settings, such as severe sparsity of observations, lack of reliable models, and non-stationarity of the system dynamics. These…

A novel method, based on the combination of data assimilation and machine learning is introduced. The new hybrid approach is designed for a two-fold scope: (i) emulating hidden, possibly chaotic, dynamics and (ii) predicting their future…

We study a nonlinear-nudging modification of the Azouani-Olson-Titi continuous data assimilation (downscaling) algorithm for the 2D incompressible Navier-Stokes equations. We give a rigorous proof that the nonlinear-nudging system is…

Many simulated complex systems that support persistent self-organizing patterns, i.e. gliders, have a 'state-plus-update' paradigm. This approach can be found in computational models of physics, continuous and neural cellular automata,…

We analyze continuous data assimilation by nudging for the 3D Ladyzhenskaya equations. The analysis provides conditions on the spatial resolution of the observed data that guarantee synchronization to the reference solution associated with…

Efficiently solving the continuous-time signal and discrete-time observation filtering problem for chaotic dynamical systems presents unique challenges in that the advected distribution between observations may encounter a separatrix…