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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

Data assimilation (DA) in the geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction, and is a crucial building block that has…

Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tuning and on employing an accurate model for the dynamics.…

Machine Learning · Statistics 2026-03-24 Melissa Adrian , Daniel Sanz-Alonso , Rebecca Willett

Particle filtering is a Bayesian inference method and a fundamental tool in state estimation for dynamic systems, but its effectiveness is often limited by the constraints of the initial prior distribution, a phenomenon we define as the…

Machine Learning · Statistics 2025-01-31 Yiwei Shi , Jingyu Hu , Yu Zhang , Mengyue Yang , Weinan Zhang , Cunjia Liu , Weiru Liu

Data assimilation (DA) is a fundamental computational technique that integrates numerical simulation models and observation data on the basis of Bayesian statistics. Originally developed for meteorology, especially weather forecasting, DA…

Motivated by non-linear, non-Gaussian, distributed multi-sensor/agent navigation and tracking applications, we propose a multi-rate consensus/fusion based framework for distributed implementation of the particle filter (CF/DPF). The CF/DPF…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-09-06 Arash Mohammadi , Amir Asif

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

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

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

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

The decentralized particle filter (DPF) was proposed recently to increase the level of parallelism of particle filtering. Given a decomposition of the state space into two nested sets of variables, the DPF uses a particle filter to sample…

Machine Learning · Statistics 2012-03-13 Mohamed Osama Ahmed , Pouyan T. Bibalan , Nando de Freitas , Simon Fauvel

Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation…

Optimization and Control · Mathematics 2013-08-06 C. E. A. Brett , K. F. Lam , K. J. H. Law , D. S. McCormick , M. R. Scott , A. M. Stuart

We show, using idealized models, that numerical data assimilation can be successful only if an effective dimension of the problem is not excessive. This effective dimension depends on the noise in the model and the data, and in physically…

Mathematical Physics · Physics 2015-06-15 Alexandre J. Chorin , Matthias Morzfeld

A method of data assimilation (DA) is employed to estimate electrophysiological parameters of neurons simultaneously with their synaptic connectivity in a small model biological network. The DA procedure is cast as an optimization, with a…

Neurons and Cognition · Quantitative Biology 2020-02-05 Eve Armstrong

Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation…

Optimization and Control · Mathematics 2011-10-13 C. E. A. Brett , K. F. Lam , K. J. H. Law , D. S. McCormick , M. R. Scott , A. M. Stuart

This paper presents the application of a particle filter for data assimilation in the context of puff-based dispersion models. Particle filters provide estimates of the higher moments, and are well suited for strongly nonlinear and/or…

Applications · Statistics 2011-07-11 Gabriel Terejanu , Yang Cheng , Tarunraj Singh , Peter D. Scott

Practical data assimilation algorithms often contain hyper-parameters, which may arise due to, for instance, the use of certain auxiliary techniques like covariance inflation and localization in an ensemble Kalman filter, the…

Computation · Statistics 2022-06-08 Xiaodong Luo , Chuan-An Xia

State estimation is crucial for the performance and safety of numerous robotic applications. Among the suite of estimation techniques, particle filters have been identified as a powerful solution due to their non-parametric nature. Yet, in…

Robotics · Computer Science 2024-04-23 Akhilan Boopathy , Aneesh Muppidi , Peggy Yang , Abhiram Iyer , William Yue , Ila Fiete

Implicit particle filters for data assimilation generate high-probability samples by representing each particle location as a separate function of a common reference variable. This representation requires that a certain underdetermined…

Numerical Analysis · Mathematics 2015-05-27 Matthias Morzfeld , Xuemin Tu , Ethan Atkins , Alexandre J. Chorin

The use of model order reduction techniques in combination with ensemble-based methods for estimating the state of systems described by nonlinear partial differential equations has been of great interest in recent years in the data…

Numerical Analysis · Mathematics 2024-12-18 Francesco A. B. Silva , Cecilia Pagliantini , Karen Veroy