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Accurate data assimilation (DA) for systems with piecewise-smooth or discontinuous state variables remains a significant challenge, as conventional covariance-based ensemble Kalman filter approaches often fail to effectively balance…

Numerical Analysis · Mathematics 2025-10-09 Tongtong Li , Anne Gelb , Yoonsang Lee

Continuous data assimilation (CDA) is a method that continuously integrates observational data into a dynamical system to improve model accuracy in real-time. The AOT algorithm is one of the most widely used methods in CDA due to its…

Optimization and Control · Mathematics 2024-07-25 Ning Ning , Collin Victor

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

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

This paper presents an approach for employing artificial neural networks (NN) to emulate an ensemble Kalman filter (EnKF) as a method of data assimilation. The assimilation methods are tested in the Simplified Parameterizations…

Artificial Intelligence · Computer Science 2014-07-17 Rosangela S. Cintra , Haroldo F. de Campos Velho

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

In numerical weather prediction (NWP), a large number of observations are used to create initial conditions for weather forecasting through a process known as data assimilation. An assessment of the value of these observations for NWP can…

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

Accurate time series forecasting is critical for a wide range of problems with temporal data. Ensemble modeling is a well-established technique for leveraging multiple predictive models to increase accuracy and robustness, as the…

Machine Learning · Computer Science 2023-04-11 Dimitris Bertsimas , Leonard Boussioux

Data assimilation (DA) plays a pivotal role in numerical weather prediction by systematically integrating sparse observations with model forecasts to estimate optimal atmospheric initial condition for forthcoming forecasts. Traditional…

Atmospheric and Oceanic Physics · Physics 2025-10-28 Jing-An Sun , Hang Fan , Junchao Gong , Ben Fei , Kun Chen , Fenghua Ling , Wenlong Zhang , Wanghan Xu , Li Yan , Pierre Gentine , Lei Bai

Data assimilation (DA) methods combine model predictions with observational data to improve state estimation in dynamical systems, inspiring their increasingly prominent role in geophysical and climate applications. Classical DA methods…

Numerical Analysis · Mathematics 2025-10-23 Lizuo Liu , Tongtong Li , Anne Gelb

Continuous data assimilation addresses time-dependent problems with unknown initial conditions by incorporating observations of the solution into a nudging term. For the prototypical heat equation with variable conductivity and the Neumann…

Numerical Analysis · Mathematics 2025-04-01 Vladimir Yushutin

Modeling strong gravitational lenses is prohibitively expensive for modern and next-generation cosmic survey data. Neural posterior estimation (NPE), a simulation-based inference (SBI) approach, has been studied as an avenue for efficient…

Instrumentation and Methods for Astrophysics · Physics 2024-10-23 Paxson Swierc , Marcos Tamargo-Arizmendi , Aleksandra Ćiprijanović , Brian D. Nord

Modeling strong gravitational lenses is computationally expensive for the complex data from modern and next-generation cosmic surveys. Deep learning has emerged as a promising approach for finding lenses and predicting lensing parameters,…

Instrumentation and Methods for Astrophysics · Physics 2025-01-08 Shrihan Agarwal , Aleksandra Ćiprijanović , Brian D. Nord

While machine learning-based weather prediction (MLWP) has achieved significant advancements, research on assimilating real observations or ensemble forecasts within MLWP models remains limited. We introduce ClimaX-LETKF, the first purely…

Machine Learning · Computer Science 2025-12-17 Akira Takeshima , Kenta Shiraishi , Atsushi Okazaki , Tadashi Tsuyuki , Shunji Kotsuki

Standard methods of data assimilation assume prior knowledge of a model that describes the system dynamics and an observation function that maps the model state to a predicted output. An accurate mapping from model state to observation…

Dynamical Systems · Mathematics 2019-05-22 Franz Hamilton , Tyrus Berry , Timothy Sauer

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 dominant approach for addressing unsupervised domain adaptation is to map data points for the source and the target domains into an embedding space which is modeled as the output-space of a shared deep encoder. The encoder is trained to…

Machine Learning · Computer Science 2022-09-30 Mohammad Rostami

The weather and climate domains are undergoing a significant transformation thanks to advances in AI-based foundation models such as FourCastNet, GraphCast, ClimaX and Pangu-Weather. While these models show considerable potential, they are…

Machine Learning · Computer Science 2024-07-18 Junqi Yin , Siming Liang , Siyan Liu , Feng Bao , Hristo G. Chipilski , Dan Lu , Guannan Zhang

Data assimilation is a method of uncertainty quantification to estimate the hidden true state by updating the prediction owing to model dynamics with observation data. As a prediction model, we consider a class of nonlinear dynamical…

Statistics Theory · Mathematics 2026-03-05 Kota Takeda , Takashi Sakajo