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This paper develops efficient ensemble Kalman filter (EnKF) implementations based on shrinkage covariance estimation. The forecast ensemble members at each step are used to estimate the background error covariance matrix via the…

Statistics Theory · Mathematics 2015-02-03 Elias D. Nino-Ruiz , Adrian Sandu

This paper presents the machine learning-based ensemble conditional mean filter (ML-EnCMF) -- a filtering method based on the conditional mean filter (CMF) previously introduced in the literature. The updated mean of the CMF matches that of…

Machine Learning · Computer Science 2022-08-02 Truong-Vinh Hoang , Sebastian Krumscheid , Hermann G. Matthies , Raúl Tempone

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 widely used to sample a probability density function (pdf) generated by a stochastic model conditioned by noisy data. This pdf can be either a joint posterior that describes the evolution of the state of…

Data Analysis, Statistics and Probability · Physics 2016-08-08 Matthias Morzfeld , Daniel Hodyss

Accurate modeling and prediction of complex physical systems often rely on data assimilation techniques to correct errors inherent in model simulations. Traditional methods like the Ensemble Kalman Filter (EnKF) and its variants as well as…

Machine Learning · Computer Science 2024-09-12 Phillip Si , Peng Chen

ICESEE (ICE Sheet statE and parameter Estimator) is a Python-based, open-source data assimilation framework designed for seamless integration with ice sheet and Earth system models. It implements a parallel Ensemble Kalman Filter (EnKF)…

Computational Complexity · Computer Science 2026-03-31 Brian Kyanjo , Talea L. Mayo , Alexander A. Robel

Working with a two-stage ice sheet model, we explore how statistical data assimilation methods can be used to improve predictions of glacier melt and relatedly, sea level rise. We find that the EnKF improves model runs initialized using…

Dynamical Systems · Mathematics 2023-05-23 Emily Corcoran , Logan Knudsen , Talea Mayo , Hannah Park-Kaufmann , Alexander Robel

Data assimilation (DA) for compressible flows with shocks is challenging because many classical DA methods generate spurious oscillations and nonphysical features near uncertain shocks. We focus here on the ensemble Kalman filter (EnKF). We…

Accurate and timely prediction of crop growth is of great significance to ensure crop yields and researchers have developed several crop models for the prediction of crop growth. However, there are large difference between the simulation…

Artificial Intelligence · Computer Science 2024-03-07 Siqi Zhou , Ling Wang , Jie Liu , Jinshan Tang

In many areas of science and engineering, it is a common task to infer physical fields from sparse observations. This paper presents the DAFI code intended as a flexible framework for two broad classes of such inverse problems: data…

Computational Physics · Physics 2020-12-07 Carlos A. Michelén Ströfer , Xin-Lei Zhang , Heng Xiao

We consider filtering in high-dimensional non-Gaussian state-space models with intractable transition kernels, nonlinear and possibly chaotic dynamics, and sparse observations in space and time. We propose a novel filtering methodology that…

Methodology · Statistics 2022-04-07 Alessio Spantini , Ricardo Baptista , Youssef Marzouk

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…

Statistics Theory · Mathematics 2026-03-05 Kota Takeda , Takashi Sakajo

The ensemble Kalman filter (EnKF) is a popular technique for performing inference in state-space models (SSMs), particularly when the dynamic process is high-dimensional. Unlike reweighting methods such as sequential Monte Carlo (SMC, i.e.…

The ensemble random forest filter (ERFF) is presented as an alternative to the ensemble Kalman filter (EnKF) for the purpose of inverse modeling. The EnKF is a data assimilation approach that forecasts and updates parameter estimates…

Machine Learning · Computer Science 2022-07-11 Vanessa A. Godoy , Gian F. Napa-García , J. Jaime Gómez-Hernández

Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in subsurface groundwater models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model's…

Data Analysis, Statistics and Probability · Physics 2015-11-09 Boujemaa Ait-El-Fquih , Mohamad El Gharamti , Ibrahim Hoteit

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

The accuracy of Earth system models is compromised by unknown and/or unresolved dynamics, making the quantification of systematic model errors essential. While a model parameter estimation, which allows parameters to change…

Methodology · Statistics 2023-10-04 Yohei Sawada , Le Duc

We explore the potential of Data-Assimilation (DA) within the multi-scale framework of a shell model of turbulence, with a focus on the Ensemble Kalman Filter (EnKF). The central objective is to understand how measuring mesoscales (i.e.,…

Fluid Dynamics · Physics 2026-01-15 Francesco Fossella , Luca Biferale , Alberto Carrassi , Massimo Cencini , Vikrant Gupta

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 present a practical implementation of the ensemble Kalman (EnKF) filter based on an iterative Sherman-Morrison formula. The new direct method exploits the special structure of the ensemble-estimated error covariance matrices in order to…

Numerical Analysis · Computer Science 2015-02-03 Elias D. Nino-Ruiz , Adrian Sandu , Jeffrey Anderson