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Data assimilation (DA) integrates numerical model forecasts with observations to achieve the optimal state estimation. Ensemble-based methods, such as the ensemble Kalman filter (EnKF), are widely used for state estimation for…

Atmospheric and Oceanic Physics · Physics 2026-05-25 Zhou Yao , Zhilin Li , Li Zhao , Zeng Liu , Zhaokuan Lu , Seungnam Kim , Guangyao Wang

Data assimilation (DA) plays a pivotal role in diverse applications, ranging from climate predictions and weather forecasts to trajectory planning for autonomous vehicles. A prime example is the widely used ensemble Kalman filter (EnKF),…

Dynamical Systems · Mathematics 2024-01-03 Mohamad Abed El Rahman Hammoud , Naila Raboudi , Edriss S. Titi , Omar Knio , Ibrahim Hoteit

Data assimilation (DA) aims at forecasting the state of a dynamical system by combining a mathematical representation of the system with noisy observations taking into account their uncertainties. State of the art methods are based on the…

Machine Learning · Computer Science 2023-05-26 Pierre Boudier , Anthony Fillion , Serge Gratton , Selime Gürol , Sixin Zhang

Data assimilation (DA) is a key component of many forecasting models in science and engineering. DA allows one to estimate better initial conditions using an imperfect dynamical model of the system and noisy/sparse observations available…

Machine Learning · Computer Science 2023-02-01 Ashesh Chattopadhyay , Ebrahim Nabizadeh , Eviatar Bach , Pedram Hassanzadeh

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

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

Recent advances in data assimilation (DA) have focused on developing more flexible approaches that can better accommodate nonlinearities in models and observations. However, it remains unclear how the performance of these advanced methods…

Atmospheric and Oceanic Physics · Physics 2025-05-08 Zixiang Xiong , Siming Liang , Feng Bao , Guannan Zhang , Hristo G. Chipilski

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…

Numerical Analysis · Mathematics 2025-10-09 Tongtong Li , Anne Gelb , Yoonsang Lee

Ensemble-based data assimilation (DA) methods have become increasingly popular due to their inherent ability to address nonlinear dynamic problems. However, these methods often face a trade-off between analysis accuracy and computational…

Machine Learning · Computer Science 2026-05-26 Zhilin Li , Zhou Yao , Xianglong Li , Zeng Liu , Zhaokuan Lu , Shanlin Xu , Seungnam Kim , Guangyao Wang

Data assimilation (DA) aims to optimally combine model forecasts and observations that are both partial and noisy. Multi-model DA generalizes the variational or Bayesian formulation of the Kalman filter, and we prove that it is also the…

Methodology · Statistics 2023-01-23 Eviatar Bach , Michael Ghil

Data assimilation (DA) integrates observations with model forecasts to produce optimized atmospheric states, whose physical consistency is critical for stable weather forecasting and reliable climate research. Traditional Bayesian DA…

Atmospheric and Oceanic Physics · Physics 2026-03-05 Hang Fan , Lei Bai , Ben Fei , Yi Xiao , Kun Chen , Yubao Liu , Yongquan Qu , Fenghua Ling , Pierre Gentine

Although data assimilation originates from control theory, the relationship between modern data assimilation methods in geoscience and model predictive control has not been extensively explored. In the present paper, I discuss that the…

Geophysics · Physics 2024-10-21 Yohei Sawada

There is an urgent need to build models to tackle Indoor Air Quality issue. Since the model should be accurate and fast, Reduced Order Modelling technique is used to reduce the dimensionality of the problem. The accuracy of the model, that…

Machine learning techniques have seen a tremendous rise in popularity in weather and climate sciences. Data assimilation (DA), which combines observations and numerical models, has great potential to incorporate machine learning and…

Machine Learning · Computer Science 2024-03-20 Feiyu Lu

Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a…

This paper presents an innovative Reduced-Order Model (ROM) for merging experimental and simulation data using Data Assimilation (DA) to estimate the "True" state of a fluid dynamics system, leading to more accurate predictions. Our…

Computational Engineering, Finance, and Science · Computer Science 2025-07-03 Paul Jeanney , Ashton Hetherington , Shady E. Ahmed , David Lanceta , Susana Saiz , José Miguel Perez , Soledad Le Clainche

Ensemble transform Kalman filtering (ETKF) data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliable state representations in dynamical systems. However, it is…

Numerical Analysis · Mathematics 2024-03-07 Tongtong Li , Anne Gelb , Yoonsang Lee

This paper presents an approach for employing artificial neural networks (NN) to emulate an ensemble Kalman filter (EnKF) as a method of data assimilation. The assimilation methods are tested in the Simplified Parameterizations…

Artificial Intelligence · Computer Science 2014-07-17 Rosangela S. Cintra , Haroldo F. de Campos Velho

We investigate the applicability of the data assimilation (DA) to large eddy simulations (LESs) based on the lattice Boltzmann method (LBM). We carry out the observing system simulation experiment of a two-dimensional (2D) forced isotropic…

Popular (ensemble) Kalman filter data assimilation (DA) approaches assume that the errors in both the a priori estimate of the state and those in the observations are Gaussian. For constrained variables, e.g. sea ice concentration or…

Machine Learning · Computer Science 2025-02-19 Ivo Pasmans , Yumeng Chen , Tobias Sebastian Finn , Marc Bocquet , Alberto Carrassi
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