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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

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 an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Brian R. Hunt , Eric J. Kostelich , Istvan Szunyogh

Continuous data assimilation (CDA) is successfully implemented for the first time for efficient dynamical downscaling of a global atmospheric reanalysis. A comparison of the performance of CDA with the standard grid and spectral nudging…

Atmospheric and Oceanic Physics · Physics 2019-07-31 Srinivas Desamsetti , Hari Prasad Dasari , Sabique Langodan , Edriss S Titi , Omar Knio , Ibrahim Hoteit

There has been a recent surge in development of accurate machine learning (ML) weather prediction models, but evaluation of these models has mainly been focused on medium-range forecasts, not their performance in cycling data assimilation…

Atmospheric and Oceanic Physics · Physics 2024-12-25 Laura C. Slivinski , Jeffrey S. Whitaker , Sergey Frolov , Timothy A. Smith , Niraj Agarwal

We describe a new approach allowing for systematic causal attribution of weather and climate-related events, in near-real time. The method is purposely designed to facilitate its implementation at meteorological centers by relying on data…

Data Assimilation is a cornerstone of atmospheric system modeling, tasked with reconstructing system states by integrating sparse, noisy observations with prior estimation. While traditional approaches like variational and ensemble Kalman…

Machine Learning · Computer Science 2025-11-04 Hao Wang , Zixuan Weng , Jindong Han , Wei Fan , Hao Liu

Prediction of chaotic systems relies on a floating fusion of sensor data (observations) with a numerical model to decide on a good system trajectory and to compensate nonlinear feedback effects. Ensemble-based data assimilation (DA) is a…

Computational Engineering, Finance, and Science · Computer Science 2020-11-26 Sebastian Friedemann , Bruno Raffin

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

Data assimilation provides a systematic framework for combining dynamical models with partial and noisy observations to infer the evolving state of a system. In this work, we undertake a comparative study of Data Assimilation with Transfer…

Computational Engineering, Finance, and Science · Computer Science 2026-05-07 Emanuele Donno , Giovanni Conti , Paolo Oddo , Silvio Gualdi , Luca Mainetti , Giovanni Aloisio

Advances in data assimilation (DA) methods have greatly improved the accuracy of Earth system predictions. To fuse multi-source data and reconstruct the nonlinear evolution missing from observations, geoscientists are developing…

Atmospheric and Oceanic Physics · Physics 2024-12-19 Qingyu Zheng , Guijun Han , Wei Li , Lige Cao , Gongfu Zhou , Haowen Wu , Qi Shao , Ru Wang , Xiaobo Wu , Xudong Cui , Hong Li , Xuan Wang

Data assimilation (DA) has increasingly emerged as a critical tool for state estimation across a wide range of applications. It is significantly challenging when the governing equations of the underlying dynamics are unknown. To this end,…

Machine Learning · Computer Science 2026-01-13 Ziyi Wang , Lijian Jiang

We propose closed-form conditional diffusion models for data assimilation. Diffusion models use data to learn the score function (defined as the gradient of the log-probability density of a data distribution), allowing them to generate new…

Machine Learning · Statistics 2026-04-02 Brianna Binder , Agnimitra Dasgupta , Assad Oberai

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) plays a pivotal role in diverse applications, ranging from climate predictions and weather forecasts to trajectory planning for autonomous vehicles. A prime example is the widely used ensemble Kalman filter (EnKF),…

Dynamical Systems · Mathematics 2024-01-03 Mohamad Abed El Rahman Hammoud , Naila Raboudi , Edriss S. Titi , Omar Knio , Ibrahim Hoteit

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…

Machine Learning · Computer Science 2023-10-12 Salva Rühling Cachay , Bo Zhao , Hailey Joren , Rose Yu

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 (DA) is a computational tool that uses value from the model and the real measurement to arrive to an optimally acceptable value. Rather, this technique relies on the idea of Kalman gain. We point out that DA has two…

Optimization and Control · Mathematics 2020-12-15 Mohammad N. Murshed , Zarin Subah , M. Monir Uddin

We apply two data assimilation (DA) methods, a smoother and a filter, and a model-free machine learning (ML) shallow network to forecast two weakly turbulent systems. We analyse the effect of the spatial sparsity of observations on accuracy…

Fluid Dynamics · Physics 2024-07-16 Vikrant Gupta , Yuanqing Chen , Minping Wan

Despite advances in test-time scaling and diffusion finetuning, guidance for Auto-Regressive Diffusion Models (ARDMs) remains underexplored. We introduce an amortized framework that augments a pretrained ARDM with an offline-trained…

Machine Learning · Computer Science 2026-05-12 Prakhar Srivastava , Farrin Marouf Sofian , Francesco Immorlano , Kushagra Pandey , Stephan Mandt