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Several variations of the Kalman filter algorithm, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are widely used in science and engineering applications. In this paper, we introduce two algorithms of…

Optimization and Control · Mathematics 2018-10-11 Wei Kang , Liang Xu

The forecasting skill of numerical weather prediction (NWP) models critically depends on the accurate initial conditions, also known as analysis, provided by data assimilation (DA). Traditional DA methods often face a trade-off between…

Atmospheric and Oceanic Physics · Physics 2024-11-28 Yanfei Xiang , Weixin Jin , Haiyu Dong , Mingliang Bai , Zuliang Fang , Pengcheng Zhao , Hongyu Sun , Kit Thambiratnam , Qi Zhang , Xiaomeng Huang

Data assimilation of atmospheric observations traditionally relies on variational and Kalman filter methods. Here, an alternative neural-network data assimilation (NNDA) with variational autoencoder (VAE) is proposed. The three-dimensional…

Atmospheric and Oceanic Physics · Physics 2024-04-29 Boštjan Melinc , Žiga Zaplotnik

Spatial reasoning in 3D scenes requires precise geometric calculations that challenge vision-language models. Visual programming addresses this by decomposing problems into steps calling specialized tools, yet existing methods rely on…

Computer Vision and Pattern Recognition · Computer Science 2025-12-25 Shengguang Wu , Xiaohan Wang , Yuhui Zhang , Hao Zhu , Serena Yeung-Levy

Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, but their application to the geosciences has been limited due to their inefficiency in high-dimensional systems in…

Applications · Statistics 2019-04-16 Peter Jan van Leeuwen , Hans R. Künsch , Lars Nerger , Roland Potthast , Sebastian Reich

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

The combined use of data from different sources can be critical in emergencies, where accurate models are needed to make real-time decisions, but high-fidelity representations and detailed information are simply unavailable. This study…

Systems and Control · Electrical Eng. & Systems 2025-01-07 Daniele Giovanni Gioia , Jacopo Bonari , Daniel Lichte , Alexander Popp

This paper is a contribution in the context of variational data assimilation combined with statistical learning. The framework of data assimilation traditionally uses data collected at sensor locations in order to bring corrections to a…

Numerical Analysis · Mathematics 2023-05-09 Amina Benaceur , Barbara Verfürth

Essential features of the Multigrid Ensemble Kalman Filter (G. Moldovan, G. Lehnasch, L. Cordier, M. Meldi, A multigrid/ensemble Kalman filter strategy for assimilation of unsteady flows, Journal of Computational Physics 443-110481)…

Fluid Dynamics · Physics 2022-10-20 Gabriel Moldovan , Guillaume Lehnasch , Laurent Cordier , Marcello Meldi

The emergence of data-driven computational materials science offers unprecedented opportunities to explore complex material landscapes, complementing experimental research with the discovery of novel compounds. To enable these developments,…

Materials Science · Physics 2026-04-30 Holger-Dietrich Saßnick , Joshua Edzards , Timo Reents , Caterina Cocchi

The article presents the torchosr package - a Python package compatible with PyTorch library - offering tools and methods dedicated to Open Set Recognition in Deep Neural Networks. The package offers two state-of-the-art methods in the…

Machine Learning · Computer Science 2024-02-12 Joanna Komorniczak , Pawel Ksieniewicz

Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous…

Computational Physics · Physics 2019-09-20 Hans Yu , Matthew P. Juniper , Luca Magri

Deep learning is widely used to predict complex dynamical systems in many scientific and engineering areas. However, the black-box nature of these deep learning models presents significant challenges for carrying out simultaneous data…

Machine Learning · Computer Science 2025-04-04 Chuanqi Chen , Nan Chen , Yinling Zhang , Jin-Long Wu

Deep learning methods have achieved a lot of success in various applications involving converting wearable sensor data to actionable health insights. A common application areas is activity recognition, where deep-learning methods still…

Signal Processing · Electrical Eng. & Systems 2024-07-09 Eun Som Jeon , Hongjun Choi , Ankita Shukla , Yuan Wang , Hyunglae Lee , Matthew P. Buman , Pavan Turaga

A data-driven method for improving the correlation estimation in serial ensemble Kalman filters is introduced. The method finds a linear map that transforms, at each assimilation cycle, the poorly estimated sample correlation into an…

Statistics Theory · Mathematics 2017-04-05 Michèle De La Chevrotière , John Harlim

Data assimilation (DA) combines partial observations with dynamical models to improve state estimation. Filter-based DA uses only past and present data and is the prerequisite for real-time forecasts. Smoother-based DA exploits both past…

Systems and Control · Electrical Eng. & Systems 2026-01-21 Marios Andreou , Nan Chen , Yingda Li

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

Four-dimensional variational data assimilation (4DVar) has become an increasingly important tool in data science with wide applications in many engineering and scientific fields such as geoscience1-12, biology13 and the financial…

Data Analysis, Statistics and Probability · Physics 2018-05-28 Xiangjun Tian , Aiguo Dai , Xiaobing Feng , Hongqin Zhang , Rui Han , Lu Zhang

A physics-based methodology for the determination of the localization function for the Ensemble Kalman Filter (EnKF) is proposed. The spatial features of such function evolve dynamically over time according to the relevant instantaneous…

Fluid Dynamics · Physics 2025-11-13 Sarp Er , Marcello Meldi

Marine biogeochemistry models are critical for forecasting, as well as estimating ecosystem responses to climate change and human activities. Data assimilation (DA) improves these models by aligning them with real-world observations, but…

Atmospheric and Oceanic Physics · Physics 2025-04-08 Ieuan Higgs , Ross Bannister , Jozef Skákala , Alberto Carrassi , Stefano Ciavatta
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