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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

Data assimilation is the process to fuse information from priors, observations of nature, and numerical models, in order to obtain best estimates of the parameters or state of a physical system of interest. Presence of large errors in some…

Numerical Analysis · Mathematics 2015-11-06 Vishwas Rao , Adrian Sandu , Michael Ng , Elias Nino-Ruiz

Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi-scale processes, leading to uncertainties in their long-term projections. The effects of many of these errors (particularly…

Computational Physics · Physics 2024-02-19 Rambod Mojgani , Ashesh Chattopadhyay , Pedram Hassanzadeh

The nudging data assimilation algorithm is a powerful tool used to forecast phenomena of interest given incomplete and noisy observations. Machine learning is becoming increasingly popular in data assimilation given its ease of computation…

Numerical Analysis · Mathematics 2021-11-24 Harbir Antil , Rainald Löhner , Randy Price

Machine learning techniques have seen a tremendous rise in popularity in weather and climate sciences. Data assimilation (DA), which combines observations and numerical models, has great potential to incorporate machine learning and…

Machine Learning · Computer Science 2024-03-20 Feiyu Lu

Data assimilation (DA) is widely used to combine physical knowledge and observations. It is nowadays commonly used in geosciences to perform parametric calibration. In a context of climate change, old calibrations can not necessarily be…

Machine Learning · Statistics 2021-06-23 Rem-Sophia Mouradi , Cédric Goeury , Olivier Thual , Fabrice Zaoui , Pablo Tassi

Inferring the state and unknown parameters of a network of coupled oscillators is of utmost importance. This task is made harder when only partial and noisy observations are available, which is a typical scenario in realistic…

Adaptation and Self-Organizing Systems · Physics 2025-04-07 Lauren D. Smith , Georg A. Gottwald

For oceanographic applications, probabilistic forecasts typically have to deal with i) high-dimensional complex models, and ii) very sparse spatial observations. In search-and-rescue operations at sea, for instance, the short-term…

Applications · Statistics 2023-02-15 Florian Beiser , Håvard Heitlo Holm , Jo Eidsvik

Ensemble Kalman methods were initially developed to solve nonlinear data assimilation problems in oceanography, but are now popular in applications far beyond their original use cases. Of particular interest is climate model calibration. As…

Data Analysis, Statistics and Probability · Physics 2025-11-21 Rebecca Gjini , Matthias Morzfeld , Oliver R. A. Dunbar , Tapio Schneider

Adaptive spatial meshing has proven invaluable for the accurate, efficient computation of solutions of time dependent partial differential equations. In a DA context the use of adaptive spatial meshes addresses several factors that place…

Numerical Analysis · Mathematics 2025-02-17 Jeremiah Buenger , Weizhang Huang , Erik Van Vleck

We explore the potential of Data-Assimilation (DA) within the multi-scale framework of a shell model of turbulence, with a focus on the Ensemble Kalman Filter (EnKF). The central objective is to understand how measuring mesoscales (i.e.,…

Fluid Dynamics · Physics 2026-01-15 Francesco Fossella , Luca Biferale , Alberto Carrassi , Massimo Cencini , Vikrant Gupta

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

A hybrid data assimilation algorithm is developed for complex dynamical systems with partial observations. The method starts with applying a spectral decomposition to the entire spatiotemporal fields, followed by creating a machine learning…

Computational Physics · Physics 2022-12-27 Changhong Mou , Leslie M. Smith , Nan Chen

This work integrates ensemble-based data assimilation (DA) with the energy-aware hybrid modeling approach, applied to a three-layer quasi-geostrophic (QG) model of the Gulf Stream flow. Building on prior DA success in the QG channel regime,…

Fluid Dynamics · Physics 2025-09-03 Igor Shevchenko , Dan Crisan

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

Ensemble data assimilation techniques form an indispensable part of numerical weather prediction. As the ensemble size grows and model resolution increases, the amount of required storage becomes a major issue. Data compression schemes may…

Data augmentation, by the introduction of auxiliary variables, has become an ubiquitous technique to improve convergence properties, simplify the implementation or reduce the computational time of inference methods such as Markov chain…

Methodology · Statistics 2020-09-30 Maxime Vono , Nicolas Dobigeon , Pierre Chainais

Using a very cheap Data Assimilation (DA) method, I show an alternative approach to classical DA for numerical climate models which produce a large amount of "big data". The problematic features of state-of-the-art high resolution Regional…

Applications · Statistics 2016-10-12 Bijan Fallah

The growing deployment of low-cost, distributed sensor networks in environmental and biomedical domains has enabled continuous, large-scale health monitoring. However, these systems often face challenges related to degraded data quality…

Machine Learning · Computer Science 2025-08-07 Keivan Faghih Niresi , Ismail Nejjar , Olga Fink

Today's ocean numerical prediction skills depend on the availability of in-situ and remote ocean observations at the time of the predictions only. Because observations are scarce and discontinuous in time and space, numerical models are…

Signal Processing · Electrical Eng. & Systems 2022-06-06 Ali Muhamed Ali , Hanqi Zhuang , Yu Huang , Ali K. Ibrahim , Ali Salem Altaher , Laurent Chérubin