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Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in…

Data Analysis, Statistics and Probability · Physics 2020-11-03 Alberto Carrassi , Marc Bocquet , Jonathan Demaeyer , Colin Grudzien , Patrick Raanes , Stephane Vannitsem

The use of machine learning (ML) models in meteorology has attracted significant attention for their potential to improve weather forecasting efficiency and accuracy. GraphCast and NeuralGCM, two promising ML-based weather models, are at…

Atmospheric and Oceanic Physics · Physics 2024-11-25 Xiaoxu Tian , Daniel Holdaway , Daryl Kleist

Weather forecasting has seen a shift in methods from numerical simulations to data-driven systems. While initial research in the area focused on deterministic forecasting, recent works have used diffusion models to produce skillful ensemble…

Machine Learning · Computer Science 2025-04-15 Martin Andrae , Tomas Landelius , Joel Oskarsson , Fredrik Lindsten

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

Data assimilation (DA) integrates observations with model forecasts to produce optimized atmospheric states, whose physical consistency is critical for stable weather forecasting and reliable climate research. Traditional Bayesian DA…

Atmospheric and Oceanic Physics · Physics 2026-03-05 Hang Fan , Lei Bai , Ben Fei , Yi Xiao , Kun Chen , Yubao Liu , Yongquan Qu , Fenghua Ling , Pierre Gentine

We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is in the form of noisy partial measurements of the past and present state of the dynamical system. Recently there have been several…

Machine Learning · Computer Science 2021-06-02 Alexander Wikner , Jaideep Pathak , Brian R. Hunt , Istvan Szunyogh , Michelle Girvan , Edward Ott

A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…

Data Analysis, Statistics and Probability · Physics 2012-04-11 Lewis Mitchell , Georg A. Gottwald

Data Assimilation (DA) plays a critical role in atmospheric science by reconstructing spatially continous estimates of the system state, which serves as initial conditions for scientific analysis. While recent advances in diffusion models…

Machine Learning · Computer Science 2025-05-20 Hao Wang , Jindong Han , Wei Fan , Weijia Zhang , Hao Liu

The large underlying assumption of climate models today relies on the basis of a "confident" initial condition, a reasonably plausible snapshot of the Earth for which all future predictions depend on. However, given the inherently chaotic…

Applications · Statistics 2025-06-03 Valerie Tsao , Nathaniel W. Chaney , Manolis Veveakis

Using simulations or experiments performed at some set of temperatures to learn about the physics or chemistry at some other arbitrary temperature is a problem of immense practical and theoretical relevance. Here we develop a framework…

Statistical Mechanics · Physics 2022-10-17 Yihang Wang , Lukas Herron , Pratyush Tiwary

Artificial intelligence (AI)-based weather prediction research is growing rapidly and has shown to be competitive with the advanced dynamic numerical weather prediction models. However, research combining AI-based weather prediction models…

Machine Learning · Computer Science 2025-10-16 Shunji Kotsuki , Kenta Shiraishi , Atsushi Okazaki

Uncertainty quantification is crucial to decision-making. A prominent example is probabilistic forecasting in numerical weather prediction. The dominant approach to representing uncertainty in weather forecasting is to generate an ensemble…

Machine Learning · Computer Science 2023-10-10 Lizao Li , Rob Carver , Ignacio Lopez-Gomez , Fei Sha , John Anderson

Learning physical dynamics from data is a fundamental challenge in machine learning and scientific modeling. Real-world observational data are inherently incomplete and irregularly sampled, posing significant challenges for existing…

Machine Learning · Computer Science 2026-05-04 Zihan Zhou , Chenguang Wang , Hongyi Ye , Yongtao Guan , Tianshu Yu

Data assimilation (DA) integrates observations with a dynamical model to estimate states of PDE-governed systems. Model-driven methods (e.g., Kalman, particle) presuppose full knowledge of the true dynamics, which is not always satisfied in…

Signal Processing · Electrical Eng. & Systems 2025-06-06 Siyi Chen , Yixuan Jia , Qing Qu , He Sun , Jeffrey A Fessler

Global medium-range weather forecasting is critical to decision-making across many social and economic domains. Traditional numerical weather prediction uses increased compute resources to improve forecast accuracy, but cannot directly use…

Data assimilation has become a key technique for combining physical models with observational data to estimate state variables. However, classical assimilation algorithms often struggle with the high nonlinearity present in both physical…

Machine Learning · Computer Science 2025-07-22 Zhuoyuan Li , Bin Dong , Pingwen Zhang

In recent years traditional numerical methods for accurate weather prediction have been increasingly challenged by deep learning methods. Numerous historical datasets used for short and medium-range weather forecasts are typically organized…

Machine Learning · Computer Science 2023-09-06 Andrea Asperti , Fabio Merizzi , Alberto Paparella , Giorgio Pedrazzi , Matteo Angelinelli , Stefano Colamonaco

Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data,…

Chaotic Dynamics · Physics 2025-04-09 Max M. Chumley , Firas A. Khasawneh

In recent years, the convergence of data-driven machine learning models with Data Assimilation (DA) offers a promising avenue for enhancing weather forecasting. This study delves into this emerging trend, presenting our methodologies and…

Atmospheric and Oceanic Physics · Physics 2024-01-17 Wenqi Wang , Jacob Bieker , Rossella Arcucci , César Quilodrán-Casas

Data assimilation (DA) improves prediction of chaotic systems by combining model forecasts with sparse, noisy observations. Many DA methods are inherently probabilistic, but accurate probabilistic DA is often computationally expensive…

Fluid Dynamics · Physics 2026-04-24 Aditya Sai Pranith Ayapilla , Kazuya Miyashita , Yuki Yasuda , Ryo Onishi