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The analysis of high-dimensional dynamical systems generally requires the integration of simulation data with experimental measurements. Experimental data often has substantial amounts of measurement noise that compromises the ability to…

Numerical Analysis · Mathematics 2019-10-02 Samuel Rudy , Steven Brunton , J. Nathan Kutz

Conventional recursive filtering approaches, designed for quantifying the state of an evolving uncertain dynamical system with intermittent observations, use a sequence of (i) an uncertainty propagation step followed by (ii) a step where…

Probability · Mathematics 2015-06-18 Wonjung Lee , Chris Farmer

Machine learning has emerged as a promising approach to path loss prediction, yet its effectiveness often degrades when measurement data are scarce. To address this limitation, we propose an ensemble-based machine learning framework that…

Signal Processing · Electrical Eng. & Systems 2026-05-26 Ahmed P. Mohamed , Byunghyun Lee , Yaguang Zhang , Christopher R. Anderson , David J. Love , James V. Krogmeier

With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…

Optimization and Control · Mathematics 2020-11-06 Shushu Zhang , Vivak Patel

Data assimilation (DA) is a key component of many forecasting models in science and engineering. DA allows one to estimate better initial conditions using an imperfect dynamical model of the system and noisy/sparse observations available…

Machine Learning · Computer Science 2023-02-01 Ashesh Chattopadhyay , Ebrahim Nabizadeh , Eviatar Bach , Pedram Hassanzadeh

A novel strategy is proposed to improve the accuracy of state estimation and reconstruction from low-fidelity models and sparse data from sensors. This strategy combines ensemble Data Assimilation (DA) and Machine Learning (ML) tools,…

Fluid Dynamics · Physics 2025-01-31 Miguel M. Valero , Marcello Meldi

Data assimilation (DA) estimates a dynamical system's state from noisy observations. Recent generative models like the ensemble score filter (EnSF) improve DA in high-dimensional nonlinear settings but are computationally expensive. We…

Machine Learning · Statistics 2025-09-30 Taos Transue , Bohan Chen , So Takao , Bao Wang

Robust integration of physical knowledge and data is key to improve computational simulations, such as Earth system models. Data assimilation is crucial for achieving this goal because it provides a systematic framework to calibrate model…

Computer Vision and Pattern Recognition · Computer Science 2024-06-14 Yongquan Qu , Juan Nathaniel , Shuolin Li , Pierre Gentine

An Ensemble of Data Assimilations (EDA) can provide valuable information on the analysis and short-range forecast uncertainties. The present ECMWF operational ocean analysis and reanalysis system, called ORAS5, produces an ensemble but does…

Atmospheric and Oceanic Physics · Physics 2024-07-08 Marcin Chrust , Anthony T. Weaver , Philip Browne , Hao Zuo , Magdalena Alonso Balmaseda

Reconstructing ocean dynamics from observational data is fundamentally limited by the sparse, irregular, and Lagrangian nature of spatial sampling, particularly in subsurface and remote regions. This sparsity poses significant challenges…

Atmospheric and Oceanic Physics · Physics 2025-07-10 Niloofar Asefi , Leonard Lupin-Jimenez , Tianning Wu , Ruoying He , Ashesh Chattopadhyay

Moment-based estimation filters have successfully aided spacecraft navigation for decades. However, future missions plan to venture into deep-space regimes with significant round-trip light-time telecommunication delays, operate in…

Earth and Planetary Astrophysics · Physics 2025-08-13 Benjamin L. Hanson , Todd A. Ely , Thomas R. Bewley , Aaron J. Rosengren

In this work, we aim at studying ensemble based optimal control strategies for data assimilation. Such formulation nicely combines the ingredients of ensemble Kalman filters and variational data assimilation (4DVar). In the same way as…

Mathematical Physics · Physics 2014-01-17 Yin Yang , Cordelia Robinson , Dominique Heitz , Etienne Mémin

We mathematically derive the sensitivity of data assimilation results for tsunami modelling, to perturbations in the observation operator. We consider results of variational data assimilation schemes on the one dimensional shallow water…

Numerical Analysis · Mathematics 2020-03-24 N. K. -R. Kevlahan , R. A. Khan

The accuracy of simulation-based forecasting in chaotic systems is heavily dependent on high-quality estimates of the system state at the time the forecast is initialized. Data assimilation methods are used to infer these initial conditions…

Machine Learning · Computer Science 2021-11-02 Michael McCabe , Jed Brown

Data assimilation (DA) provides a general framework for estimation in dynamical systems based on the concepts of Bayesian inference. This constitutes a common basis for the different linear and nonlinear filtering and smoothing techniques…

Optimization and Control · Mathematics 2023-03-08 Tarek Diaa-Eldeen , Marcus Krogh Nielsen , Carl Fredrik Berg , Morten Hovd , John Bagterp Jørgensen

Data assimilation of observational data into full atmospheric states is essential for weather forecast model initialization. Recently, methods for deep generative data assimilation have been proposed which allow for using new input data…

Particle filters are computational techniques for estimating the state of dynamical systems by integrating observational data with model predictions. This work introduces a class of Localized Particle Filters (LPFs) that exploit spatial…

Applications · Statistics 2025-07-10 Dan Crisan , Eliana Fausti

Data assimilation (DA) is a cornerstone of scientific and engineering applications, combining model forecasts with sparse and noisy observations to estimate latent system states. Classical high-dimensional DA methods, such as the ensemble…

Machine Learning · Statistics 2026-05-28 Martin Andrae , Erik Wikingsson , So Takao , Tomas Landelius , Fredrik Lindsten

To facilitate effective decision-making, precipitation datasets should include uncertainty estimates. Quantile regression with machine learning has been proposed for issuing such estimates. Distributional regression offers distinct…

Machine Learning · Computer Science 2025-01-07 Georgia Papacharalampous , Hristos Tyralis , Nikolaos Doulamis , Anastasios Doulamis

Since the start of the operational use of ensemble prediction systems, ensemble-based probabilistic forecasting has become the most advanced approach in weather prediction. However, despite the persistent development of the last three…

Applications · Statistics 2024-11-05 Sándor Baran , Mária Lakatos