Related papers: A Closed-Form Nonlinear Data Assimilation Algorith…

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…

Many systems for which compressive sensing is used today are dynamical. The common approach is to neglect the dynamics and see the problem as a sequence of independent problems. This approach has two disadvantages. Firstly, the temporal…

Data assimilation (DA) provides a general framework for estimation in dynamical systems based on the concepts of Bayesian inference. This constitutes a common basis for the different linear and nonlinear filtering and smoothing techniques…

In this study, two classes of methods including statistical and variational data assimilation algorithms will be described. In statistical methods, the model state is updated sequentially based on the previous estimate. Variational methods,…

In the past couple of years, there is a proliferation in the use of machine learning approaches to represent subgrid scale processes in geophysical flows with an aim to improve the forecasting capability and to accelerate numerical…

This paper proposes new methodology for sequential state and parameter estimation within the ensemble Kalman filter. The method is fully Bayesian and propagates the joint posterior density of states and parameters over time. In order to…

A framework for deriving probabilistic data-driven closure models is proposed for coarse-grained numerical simulations of turbulence in statistically stationary state. The approach unites the ideal large-eddy simulation model and data…

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…

In this study, we explore data assimilation for the Stochastic Camassa-Holm equation through the application of the particle filtering framework. Specifically, our approach integrates adaptive tempering, jittering, and nudging techniques to…

Advances in data assimilation (DA) methods have greatly improved the accuracy of Earth system predictions. To fuse multi-source data and reconstruct the nonlinear evolution missing from observations, geoscientists are developing…

Traditional filtering algorithms for state estimation -- such as classical Kalman filtering, unscented Kalman filtering, and particle filters - show performance degradation when applied to nonlinear systems whose uncertainty follows…

In applications such as free-space optical communication, a signal is often recovered after propagation through a turbulent medium. In this setting, it is common to assume that limited information is known about the turbulent medium, such…

Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…

Data assimilation (DA) estimates the state of an evolving dynamical system from noisy, partial observations, and is widely used in scientific simulation as well as weather and climate science. In practice, filtering methods rely on…

Understanding and predicting people flow in urban areas is useful for decision-making in urban planning and marketing strategies. Traditional methods for understanding people flow can be divided into measurement-based approaches and…

We consider the problem of conditioning a geological process-based computer simulation, which produces basin models by simulating transport and deposition of sediments, to data. Emphasising uncertainty quantification, we frame this as a…

We develop a robust data fusion algorithm for field reconstruction of multiple physical phenomena. The contribution of this paper is twofold: First, we demonstrate how multi-spatial fields which can have any marginal distributions and…

Using a perturbation technique, we derive a new approximate filtering and smoothing methodology generalizing along different directions several existing approaches to robust filtering based on the score and the Hessian matrix of the…

Estimation of unsteady flow fields around flight vehicles may improve flow interactions and lead to enhanced vehicle performance. Although flow-field representations can be very high-dimensional, their dynamics can have low-order…

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…