Related papers: Adaptive tempering schedules with approximative in…

Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including…

Estimating the state of a dynamical system from partial and noisy observations is a ubiquitous problem in a large number of applications, such as probabilistic weather forecasting and prediction of epidemics. Particle filters are a widely…

We present a particle filtering algorithm for stochastic models on infinite dimensional state space, making use of Girsanov perturbations to nudge the ensemble of particles into regions of higher likelihood. We argue that the optimal…

Filtering in spatially-extended dynamical systems is a challenging problem with significant practical applications such as numerical weather prediction. Particle filters allow asymptotically consistent inference but require infeasibly large…

Data assimilation combines dynamical models with observations to improve state estimates. Ensemble filters sequentially assimilate observations by updating a set of samples over time, alternating between a forecast and an analysis step.…

For oceanographic applications, probabilistic forecasts typically have to deal with i) high-dimensional complex models, and ii) very sparse spatial observations. In search-and-rescue operations at sea, for instance, the short-term…

In this paper, we introduce a new, local formulation of the ensemble Kalman Filter approach for atmospheric data assimilation. Our scheme is based on the hypothesis that, when the Earth's surface is divided up into local regions of moderate…

The Ensemble Kalman filter and Ensemble square root filters are data assimilation methods used to combine high dimensional nonlinear models with observed data. These methods have proved to be indispensable tools in science and engineering…

This paper contains the latest installment of the authors' project on developing ensemble based data assimilation methodology for high dimensional fluid dynamics models. The algorithm presented here is a particle filter that combines model…

Artificial intelligence (AI)-based weather prediction research is growing rapidly and has shown to be competitive with the advanced dynamic numerical weather prediction models. However, research combining AI-based weather prediction models…

Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation…

Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation…

Bayesian filtering is a well-known problem that aims to estimate plausible states of a dynamical system from observations. Among existing approaches to solve this problem, particle filters are theoretically exact for non-linear dynamics and…

Ensemble data assimilation methods such as the Ensemble Kalman Filter (EnKF) are a key component of probabilistic weather forecasting. They represent the uncertainty in the initial conditions by an ensemble which incorporates information…

Assimilation of continuously streamed monitored data is an essential component of a digital twin; the assimilated data are used to ensure the digital twin is a true representation of the monitored system. One way this is achieved is by…

Ensemble forecasting is a technique devised to palliate sensitivity to initial conditions in nonlinear dynamical systems. The basic idea to avoid this sensitivity is to run the model many times under several slightly-different initial…

Particle filters are a powerful and flexible tool for performing inference on state-space models. They involve a collection of samples evolving over time through a combination of sampling and re-sampling steps. The re-sampling step is…

This survey paper is written with the intention of giving a mathematical introduction to filtering techniques for intermittent data assimilation, and to survey some recent advances in the field. The paper is divided into three parts. The…

Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally, our limited knowledge of the underlying processes.…

Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…