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The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences,…

Numerical Analysis · Mathematics 2016-09-21 Claudia Schillings , Andrew M. Stuart

Variational inference (VI) combined with Bayesian nonlinear filtering produces state-of-the-art results for latent time-series modeling. A body of recent work has focused on sequential Monte Carlo (SMC) and its variants, e.g., forward…

Machine Learning · Statistics 2021-11-10 Tsuyoshi Ishizone , Tomoyuki Higuchi , Kazuyuki Nakamura

This work develops a new multifidelity ensemble Kalman filter (MFEnKF) algorithm based on linear control variate framework. The approach allows for rigorous multifidelity extensions of the EnKF, where the uncertainty in coarser fidelities…

Numerical Analysis · Mathematics 2020-07-03 Andrey A Popov , Changhong Mou , Traian Iliescu , Adrian Sandu

This paper uses a probabilistic approach to analyze the converge of an ensemble Kalman filter solution to an exact Kalman filter solution in the simplest possible setting, the scalar case, as it allows us to build upon a rich literature of…

Optimization and Control · Mathematics 2020-03-31 Andrey A Popov , Adrian Sandu

A modification scheme to the ensemble Kalman filter (EnKF) is introduced based on the concept of the unscented transform (Julier et al., 2000; Julier and Uhlmann, 2004), which therefore will be called the ensemble unscented Kalman filter…

Atmospheric and Oceanic Physics · Physics 2009-11-30 X. Luo , I. M. Moroz

The ensemble Kalman filter (EnKF) is widely used for data assimilation in high-dimensional systems, but its performance often deteriorates for strongly nonlinear dynamics due to the structural mismatch between the Kalman update and the…

Machine Learning · Computer Science 2026-04-30 Xin T. Tong , Yanyan Wang , Liang Yan

The iterative ensemble Kalman filter (IEnKF) in a deterministic framework was introduced in Sakov et al. (2012) to extend the ensemble Kalman filter (EnKF) and improve its performance in mildly up to strongly nonlinear cases. However, the…

Atmospheric and Oceanic Physics · Physics 2018-10-17 Pavel Sakov , Jean-Matthieu Haussaire , Marc Bocquet

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…

Probability · Mathematics 2017-05-26 Andrew J. Majda , Xin T. Tong

The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations…

Probability · Mathematics 2015-06-17 D. T. B. Kelly , K. J. H. Law , A. M. Stuart

Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman…

Numerical Analysis · Mathematics 2013-01-15 Sebastian Reich

This paper extends the Multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, Multilevel Monte Carlo is applied to a certain variant of the particle filter, the Ensemble Transform Particle Filter. A key…

Numerical Analysis · Mathematics 2016-02-24 Alastair Gregory , Colin Cotter , Sebastian Reich

State-of-the-art ensemble Kalman filtering (EnKF) algorithms require incorporating localization techniques to cope with the rank deficiency and the inherited spurious correlations in their error covariance matrices. Localization techniques…

Atmospheric and Oceanic Physics · Physics 2026-03-05 Boujemaa Ait-El-Fquih , Ibrahim Hoteit

We propose a Dynamical Low-Rank Ensemble Kalman Filter (DLR-ENKF) for efficient joint state-parameter estimation in high-dimensional dynamical systems. The method extends the DLR-ENKF formulation of arXiv:2509.11210 to the augmented…

Numerical Analysis · Mathematics 2026-02-09 Fabio Nobile , Sébastien Riffaud , Thomas Trigo Trindade

The use of model order reduction techniques in combination with ensemble-based methods for estimating the state of systems described by nonlinear partial differential equations has been of great interest in recent years in the data…

Numerical Analysis · Mathematics 2024-12-18 Francesco A. B. Silva , Cecilia Pagliantini , Karen Veroy

The intersection between classical data assimilation methods and novel machine learning techniques has attracted significant interest in recent years. Here we explore another promising solution in which diffusion models are used to…

Mathematical Physics · Physics 2024-04-02 Feng Bao , Hristo G. Chipilski , Siming Liang , Guannan Zhang , Jeffrey S. Whitaker

We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low…

Machine Learning · Statistics 2024-08-14 Feng Bao , Zezhong Zhang , Guannan Zhang

This study considers the data assimilation problem in coupled systems, which consists of two components (sub-systems) interacting with each other through certain coupling terms. A straightforward way to tackle the assimilation problem in…

Atmospheric and Oceanic Physics · Physics 2015-06-22 Xiaodong Luo , Ibrahim Hoteit

The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of…

Numerical Analysis · Mathematics 2019-11-28 Santiago Badia , Jerrad Hampton , Javier Principe

Data assimilation is concerned with sequentially estimating a temporally-evolving state. This task, which arises in a wide range of scientific and engineering applications, is particularly challenging when the state is high-dimensional and…

Machine Learning · Statistics 2021-07-21 Yuming Chen , Daniel Sanz-Alonso , Rebecca Willett

We discuss properties of hierarchical Bayesian inversion through the ensemble Kalman filter (EnKF). Our focus will be primarily on deriving continuous-time limits for hierarchical inversion in the linear case. An important characteristic of…

Numerical Analysis · Mathematics 2018-01-04 Neil K. Chada