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A Bayesian data assimilation scheme is formulated for advection-dominated or hyperbolic evolutionary problems, and observations. The method is referred to as the dynamic likelihood filter because it exploits the model physics to dynamically…

Dynamical Systems · Mathematics 2017-04-26 Juan M. Restrepo

We explore the potential of three-dimensional data assimilation for assimilating sparsely-distributed 2-metre temperature observations across the coupled atmosphere-land interface into the soil moisture. Using idealised twin experiments…

Atmospheric and Oceanic Physics · Physics 2022-09-29 Tobias Finn , Gernot Geppert , Felix Ament

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

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

We show that modifying a Bayesian data assimilation scheme by incorporating kinematically-consistent displacement corrections produces a scheme that is demonstrably better at estimating partially observed state vectors in a setting where…

Data Analysis, Statistics and Probability · Physics 2016-12-06 W. Steven Rosenthal , Shankar C. Venkataramani , Arthur J. Mariano , Juan M. Restrepo

Reconstruction of turbulent flow based on data assimilation methods is of significant importance for improving the estimation of flow characteristics by incorporating limited observations. Existing works mainly focus on using only one…

Fluid Dynamics · Physics 2021-03-30 Xin-Lei Zhang , Heng Xiao , Guo-Wei He , Shi-Zhao Wang

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…

Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…

Machine Learning · Computer Science 2021-05-21 Thomas Frerix , Dmitrii Kochkov , Jamie A. Smith , Daniel Cremers , Michael P. Brenner , Stephan Hoyer

Data assimilation combines information from models, measurements, and priors to estimate the state of a dynamical system such as the atmosphere. The Ensemble Kalman filter (EnKF) is a family of ensemble-based data assimilation approaches…

Computational Engineering, Finance, and Science · Computer Science 2014-12-09 Ahmed Attia , Adrian Sandu

There has been a recent surge in development of accurate machine learning (ML) weather prediction models, but evaluation of these models has mainly been focused on medium-range forecasts, not their performance in cycling data assimilation…

Atmospheric and Oceanic Physics · Physics 2024-12-25 Laura C. Slivinski , Jeffrey S. Whitaker , Sergey Frolov , Timothy A. Smith , Niraj Agarwal

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

Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including…

Numerical Analysis · Mathematics 2025-06-03 J. A. Carrillo , F. Hoffmann , A. M. Stuart , U. Vaes

In applications such as free-space optical communication, a signal is often recovered after propagation through a turbulent medium. In this setting, it is common to assume that limited information is known about the turbulent medium, such…

Optics · Physics 2025-10-13 Anjali Nair , Qin Li , Samuel N. Stechmann

State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking…

Numerical Analysis · Mathematics 2025-09-08 Nazanin Abedini , Jana de Wiljes , Svetlana Dubinkina

Understanding and predicting people flow in urban areas is useful for decision-making in urban planning and marketing strategies. Traditional methods for understanding people flow can be divided into measurement-based approaches and…

Human-Computer Interaction · Computer Science 2024-01-18 Ryo Murata , Kenji Tanaka

Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as…

Numerical Analysis · Mathematics 2024-05-24 Iris Rammelmüller , Gottfried Hastermann , Jana de Wiljes

Accurate estimation and forecasting of energy consumption are important for power-system operation, planning, and demand-side management. In practice, however, complete and timely measurements may not always be available, and the observed…

Machine Learning · Computer Science 2026-05-29 Ruoyu Hu , Dahai Yu , Feng Bao , Guang Wang , Guannan Zhang

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

This paper proposes new methodology for sequential state and parameter estimation within the ensemble Kalman filter. The method is fully Bayesian and propagates the joint posterior density of states and parameters over time. In order to…

Methodology · Statistics 2016-11-14 Jonathan R. Stroud , Matthias Katzfuss , Christopher K. Wikle

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