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Starting from limited measurements of a turbulent flow, data assimilation (DA) attempts to estimate all the spatio-temporal scales of motion. Success is dependent on whether the system is observable from the measurements, or how much of the…

Fluid Dynamics · Physics 2026-02-16 Andrew Cleary , Qi Wang , Tamer A. Zaki

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

The recent surge in machine learning (ML) methods for geophysical modeling has raised the question of how these methods might be applied to data assimilation (DA). We focus on diffusion modeling (a form of generative artificial…

Atmospheric and Oceanic Physics · Physics 2025-08-29 Daniel Hodyss , Matthias Morzfeld

Statistical Data Assimilation (SDA) is the transfer of information from field or laboratory observations to a user selected model of the dynamical system producing those observations. The data is noisy and the model has errors; the…

Computation · Statistics 2019-01-16 Adrian S. Wong , Kangbo Hao , Zheng Fang , Henry D. I. Abarbanel

This paper introduces a data assimilation (DA) framework based on the extended Kalman filter-cell transmission model, designed to assist jam-absorption driving (JAD) operation to alleviate sag traffic congestion. To ascertain and…

Systems and Control · Electrical Eng. & Systems 2024-09-09 Siyu Li , Ryosuke Nishi , Daichi Yanagisawa , Katsuhiro Nishinari

Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using…

Numerical Analysis · Mathematics 2019-08-15 Sebastian Reich

Variational Data Assimilation (DA) has enabled huge improvements in the skill of operational weather forecasting. In this study, we use a simple solar-wind propagation model to develop the first solar-wind variational DA scheme. This scheme…

Space Physics · Physics 2018-10-19 Matthew Lang , Mathew Owens

Data assimilation (DA) solves the inverse problem of inferring initial conditions given data and a model. Here we use biophysically motivated Hodgkin-Huxley (HH) models of avian HVCI neurons, experimentally obtained recordings of these…

Neurons and Cognition · Quantitative Biology 2016-08-17 Daniel Breen , Sasha Shirman , Eve Armstrong , Nirag Kadakia , Henry Abarbanel

Data assimilation (DA) is integrated with machine learning in order to perform entirely data-driven online state estimation. To achieve this, recurrent neural networks (RNNs) are implemented as surrogate models to replace key components of…

Data assimilation is a central problem in many geophysical applications, such as weather forecasting. It aims to estimate the state of a potentially large system, such as the atmosphere, from sparse observations, supplemented by prior…

Machine Learning · Computer Science 2024-06-24 Matthieu Blanke , Ronan Fablet , Marc Lelarge

Data Assimilation (DA) plays a critical role in atmospheric science by reconstructing spatially continous estimates of the system state, which serves as initial conditions for scientific analysis. While recent advances in diffusion models…

Machine Learning · Computer Science 2025-05-20 Hao Wang , Jindong Han , Wei Fan , Weijia Zhang , Hao Liu

Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing…

Machine Learning · Computer Science 2026-03-02 Anthony Frion , David S Greenberg

Obtaining accurate high-resolution representations of model outputs is essential to describe the system dynamics. In general, however, only spatially- and temporally-coarse observations of the system states are available. These observations…

Dynamical Systems · Mathematics 2022-11-08 Mohamad Abed El Rahman Hammoud , Olivier LeMaitre , Edriss S. Titi , Ibrahim Hoteit , Omar Knio

Dimensional analysis (DA) pays attention to fundamental physical dimensions such as length and mass when modelling scientific and engineering systems. It goes back at least a century to Buckingham's Pi theorem, which characterizes a…

Machine Learning · Computer Science 2023-12-19 G. Alexi Rodriguez-Arelis , William J. Welch

The majority of data assimilation (DA) methods in the geosciences are based on Gaussian assumptions. While these assumptions facilitate efficient algorithms, they cause analysis biases and subsequent forecast degradations. Non-parametric,…

Methodology · Statistics 2025-05-12 Hristo G. Chipilski

Data assimilation refers to the process of obtaining an estimate of a system's state using a model for the system's time evolution and a time series of measurements that are possibly noisy and incomplete. However, for practical reasons, the…

Chaotic Dynamics · Physics 2007-05-23 Matthew Cornick , Brian Hunt , Edward Ott , Michael F. Schatz

In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by…

Dynamical Systems · Mathematics 2017-07-31 Bart de Leeuw , Svetlana Dubinkina , Jason Frank , Andrew Steyer , Xuemin Tu , Erik Van Vleck

Data assimilation (DA) is a fundamental component of modern weather prediction, yet it remains a major computational bottleneck in machine learning (ML)-based forecasting pipelines due to reliance on traditional variational methods. Recent…

Machine Learning · Computer Science 2026-02-09 Ran Cheng , Lailai Zhu

The rapid rise of air pollution events necessitates accurate, real-time monitoring for informed mitigation strategies. Data Assimilation (DA) methods provide promising solutions, but their effectiveness hinges heavily on optimal measurement…

Robotics · Computer Science 2024-07-18 Ichrak Mokhtari , Walid Bechkit , Mohamed Sami Assenine , Hervé Rivano

Traditional data assimilation uses information obtained from the propagation of one physics-driven model and combines it with information derived from real-world observations in order to obtain a better estimate of the truth of some natural…

Computational Engineering, Finance, and Science · Computer Science 2022-10-24 Andrey A Popov , Adrian Sandu