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Contemporary data assimilation often involves more than a million prediction variables. Ensemble Kalman filters (EnKF) have been developed by geoscientists. They are successful indispensable tools in science and engineering, because they…

Data assimilation is a method of uncertainty quantification to estimate the hidden true state by updating the prediction owing to model dynamics with observation data. As a prediction model, we consider a class of nonlinear dynamical…

Data assimilation provides algorithms for widespread applications in various fields. It is of practical use to deal with a large amount of information in the complex system that is hard to estimate. Weather forecasting is one of the…

We consider the problem of selecting an optimal set of sensor precisions to estimate the states of a non-linear dynamical system using an Ensemble Kalman filter and an Unscented Kalman filter, which uses random and deterministic ensembles…

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,…

Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in…

Accurate data assimilation (DA) for systems with piecewise-smooth or discontinuous state variables remains a significant challenge, as conventional covariance-based ensemble Kalman filter approaches often fail to effectively balance…

Ensemble Kalman methods are widely used for state estimation in the geophysical sciences. Their success stems from the fact that they take an underlying (possibly noisy) dynamical system as a black box to provide a systematic,…

Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model…

Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state is high dimensional, ensemble Kalman filters are often the method of choice. This paper…

State estimation is a fundamental problem in control and signal processing, for which the Kalman Filter provides an optimal solution under linear dynamics, Gaussian noise, and known noise covariances. However, these assumptions often fail…

For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly time-sampled. We propose a continuous-discrete McKean--Vlasov…

Neural network (NN) ensembles can reduce large prediction variance of NN and improve prediction accuracy. For highly nonlinear problems with insufficient data set, the prediction accuracy of NN models becomes unstable, resulting in a…

The Ensemble Kalman filter is a sophisticated and powerful data assimilation method for filtering high dimensional problems arising in fluid mechanics and geophysical sciences. This Monte Carlo method can be interpreted as a mean-field…

There has been a recent surge in development of accurate machine learning (ML) weather prediction models, but evaluation of these models has mainly been focused on medium-range forecasts, not their performance in cycling data assimilation…

Ensemble methods have become ubiquitous for the solution of Bayesian inference problems. State-of-the-art Langevin samplers such as the Ensemble Kalman Sampler (EKS), Affine Invariant Langevin Dynamics (ALDI) or its extension using weighted…

This paper addresses the problem of steering a state distribution over a finite horizon in discrete time with output feedback. The incorporation of output feedback introduces additional challenges arising from the statistical coupling…

Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their mathematical foundations. As genetic-type…

Ensemble models often achieve higher accuracy than single learners, but their ability to maintain small generalization gaps is not always well understood. This study examines how ensembles balance accuracy and overfitting across four…

Assessing the validity of a real-world system with respect to given quality criteria is a common yet costly task in industrial applications due to the vast number of required real-world tests. Validating such systems by means of simulation…