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In this paper, we investigate meta-learning for combining forecasts generated by models of different types. While typical approaches for combining forecasts involve simple averaging, machine learning techniques enable more sophisticated…

Machine Learning · Computer Science 2025-04-15 Grzegorz Dudek

Recent studies have demonstrated that it is possible to combine machine learning with data assimilation to reconstruct the dynamics of a physical model partially and imperfectly observed. Data assimilation is used to estimate the system…

Machine Learning · Statistics 2022-10-26 Alban Farchi , Marcin Chrust , Marc Bocquet , Patrick Laloyaux , Massimo Bonavita

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…

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

The fusion between an inertial navigation system and global navigation satellite systems is regularly used in many platforms such as drones, land vehicles, and marine vessels. The fusion is commonly carried out in a model-based extended…

Systems and Control · Electrical Eng. & Systems 2022-09-05 Barak Or , Itzik Klein

Data assimilation is concerned with sequentially estimating a temporally-evolving state. This task, which arises in a wide range of scientific and engineering applications, is particularly challenging when the state is high-dimensional and…

Machine Learning · Statistics 2021-07-21 Yuming Chen , Daniel Sanz-Alonso , Rebecca Willett

We present a supervised learning method to learn the propagator map of a dynamical system from partial and noisy observations. In our computationally cheap and easy-to-implement framework a neural network consisting of random feature maps…

Machine Learning · Computer Science 2021-10-27 Georg A. Gottwald , Sebastian Reich

The idea of using machine learning (ML) methods to reconstruct the dynamics of a system is the topic of recent studies in the geosciences, in which the key output is a surrogate model meant to emulate the dynamical model. In order to treat…

Machine Learning · Statistics 2021-09-22 Alban Farchi , Patrick Laloyaux , Massimo Bonavita , Marc Bocquet

Data-driven methods have demonstrated strong predictive capabilities in fluid mechanics, yet most current applications still focus on simplified configurations, often characterised by statistical stationarity or limited temporal…

Fluid Dynamics · Physics 2025-11-21 Miguel M. Valero , Marcello Meldi

Data assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modeled on the basis of simple assumptions such as bias, white noise, first…

Chaotic Dynamics · Physics 2009-11-13 A. Carrassi , S. Vannitsem , C. Nicolis

Data assimilation (DA) aims at optimally merging observational data and model outputs to create a coherent statistical and dynamical picture of the system under investigation. Indeed, DA aims at minimizing the effect of observational and…

Data Analysis, Statistics and Probability · Physics 2022-01-05 Yumeng Chen , Alberto Carrassi , Valerio Lucarini

In the past couple of years, there is a proliferation in the use of machine learning approaches to represent subgrid scale processes in geophysical flows with an aim to improve the forecasting capability and to accelerate numerical…

Computational Physics · Physics 2021-04-13 Suraj Pawar , Omer San

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

4D-variational data assimilation is applied to the Lorenz '63 model to introduce a new method for parameter estimation in chaotic climate models. The approach aims to optimise an Earth system model (ESM), for which no adjoint exists, by…

Atmospheric and Oceanic Physics · Physics 2025-04-18 Philip David Kennedy , Abhirup Banerjee , Armin Köhl , Detlef Stammer

Marine biogeochemistry models are critical for forecasting, as well as estimating ecosystem responses to climate change and human activities. Data assimilation (DA) improves these models by aligning them with real-world observations, but…

Atmospheric and Oceanic Physics · Physics 2025-04-08 Ieuan Higgs , Ross Bannister , Jozef Skákala , Alberto Carrassi , Stefano Ciavatta

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

In recent years, there has been significant progress in the development of fully data-driven global numerical weather prediction models. These machine learning weather prediction models have their strength, notably accuracy and low…

Machine Learning · Statistics 2025-06-05 Alban Farchi , Marcin Chrust , Marc Bocquet , Massimo Bonavita

Satellite observations play a critical role in numerical weather prediction where they are assimilated through an observation operator that maps model states to radiances. In the traditional Ensemble Kalman Filter, these observations are…

Atmospheric and Oceanic Physics · Physics 2026-03-24 Gian Luca Buono , Stefanie Hollborn , Roland Potthast , Jörg Schäfer , Martin Simon

This paper is a contribution in the context of variational data assimilation combined with statistical learning. The framework of data assimilation traditionally uses data collected at sensor locations in order to bring corrections to a…

Numerical Analysis · Mathematics 2023-05-09 Amina Benaceur , Barbara Verfürth

Machine learning has opened new frontiers in purely data-driven algorithms for data assimilation in, and for forecasting of, dynamical systems; the resulting methods are showing some promise. However, in contrast to model-driven algorithms,…

Machine Learning · Statistics 2026-04-03 Edoardo Calvello , Elizabeth Carlson , Nikola Kovachki , Michael N. Manta , Andrew M. Stuart
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