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Estimating background-error covariances remains a core challenge in variational data assimilation (DA). Operational systems typically approximate these covariances by transformations that separate geostrophically balanced components from…

Atmospheric and Oceanic Physics · Physics 2026-01-21 Boštjan Melinc , Uroš Perkan , Žiga Zaplotnik

Fitting nonlinear dynamical models to sparse and noisy observations is fundamentally challenging. Identifying dynamics requires data assimilation (DA) to estimate system states, but DA requires an accurate dynamical model. To break this…

Machine Learning · Computer Science 2024-09-12 Vadim Zinchenko , David S. Greenberg

Lagrangian trajectories are widely used as observations for recovering the underlying flow field via Lagrangian data assimilation (DA). However, the strong nonlinearity in the observational process and the high dimensionality of the…

Fluid Dynamics · Physics 2024-02-06 Quanling Deng , Nan Chen , Samuel N. Stechmann , Jiuhua Hu

Unsupervised domain adaptation (UDA) is to make predictions for unlabeled data on a target domain, given labeled data on a source domain whose distribution shifts from the target one. Mainstream UDA methods learn aligned features between…

Computer Vision and Pattern Recognition · Computer Science 2020-03-20 Hui Tang , Ke Chen , Kui Jia

This paper proposes two practical implementations of Four-Dimensional Variational (4D-Var) Ensemble Kalman Filter (4D-EnKF) methods for non-linear data assimilation. Our formulations' main idea is to avoid the intrinsic need for adjoint…

Applications · Statistics 2023-05-05 Elias Nin-Ruiz , Jairo Diaz-Rodriguez

Global data assimilation enables weather forecasting at all scales and provides valuable data for studying the Earth system. However, the computational demands of physics-based algorithms used in operational systems limits the volume and…

Machine Learning · Computer Science 2024-07-17 Thomas J. Vandal , Kate Duffy , Daniel McDuff , Yoni Nachmany , Chris Hartshorn

Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model…

Numerical Analysis · Mathematics 2020-05-18 Melina A. Freitag

Data assimilation is the process of fusing information from imperfect computer simulations with noisy, sparse measurements of reality to obtain improved estimates of the state or parameters of a dynamical system of interest. The data…

Unlabeled data are increasingly prevalent in contemporary economic studies, yet their effective use for improving prediction remains challenging because the outcomes are often costly or even infeasible to observe. Machine learning methods…

Methodology · Statistics 2026-05-12 Fuzhi Xu , Xingyu Yan , Xinyu Zhang

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

Data assimilation techniques, such as ensemble Kalman filtering, have been shown to be a highly effective and efficient way to combine noisy data with a mathematical model to track and forecast dynamical systems. However, when dealing with…

Dynamical Systems · Mathematics 2023-05-17 Stephen A Falconer , David J. B. Lloyd , Naratip Santitissadeekorn

We propose a novel learning-based surrogate data assimilation (DA) model for efficient state estimation in a limited area. Our model employs a feedforward neural network for online computation, eliminating the need for integrating…

Numerical Analysis · Mathematics 2023-07-17 Wei Kang , Liang Xu , Hong Zhou

This paper addresses variational data assimilation from a learning point of view. Data assimilation aims to reconstruct the time evolution of some state given a series of observations, possibly noisy and irregularly-sampled. Using automatic…

Computational Physics · Physics 2021-11-10 Ronan Fablet , Bertrand Chapron , Lucas. Drumetz , Etienne Memin , Olivier Pannekoucke , Francois Rousseau

Ensemble weather predictions require statistical post-processing of systematic errors to obtain reliable and accurate probabilistic forecasts. Traditionally, this is accomplished with distributional regression models in which the parameters…

Machine Learning · Statistics 2019-04-01 Stephan Rasp , Sebastian Lerch

Distribution shift between train (source) and test (target) datasets is a common problem encountered in machine learning applications. One approach to resolve this issue is to use the Unsupervised Domain Adaptation (UDA) technique that…

In recent years, the convergence of data-driven machine learning models with Data Assimilation (DA) offers a promising avenue for enhancing weather forecasting. This study delves into this emerging trend, presenting our methodologies and…

Atmospheric and Oceanic Physics · Physics 2024-01-17 Wenqi Wang , Jacob Bieker , Rossella Arcucci , César Quilodrán-Casas

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

Covariance localization is a critical component of ensemble-based data assimilation (DA) and many current localization schemes simply dampen correlations as a function of distance. Increases in computational resources, broadening scope of…

Data Analysis, Statistics and Probability · Physics 2025-08-27 Shay Gilpin , Matthias Morzfeld , Kevin K. Lin

We consider unsupervised domain adaptation (UDA) for classification problems in the presence of missing data in the unlabelled target domain. More precisely, motivated by practical applications, we analyze situations where distribution…

Machine Learning · Computer Science 2021-09-21 Matthieu Kirchmeyer , Patrick Gallinari , Alain Rakotomamonjy , Amin Mantrach

Extreme precipitation wreaks havoc throughout the world, causing billions of dollars in damage and uprooting communities, ecosystems, and economies. Accurate extreme precipitation prediction allows more time for preparation and disaster…

Machine Learning · Computer Science 2022-02-01 Weichen Huang