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Related papers: Topological Approach for Data Assimilation

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Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as time evolves. Recently, a promising new algorithm for data…

Analysis of PDEs · Mathematics 2018-12-06 Adam Larios , Collin Victor

Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…

Algebraic Topology · Mathematics 2020-06-15 Chengyuan Wu , Carol Anne Hargreaves

We analyze the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of dynamics governed by the two-dimension…

Analysis of PDEs · Mathematics 2015-06-19 Hakima Bessaih , Eric Olson , E. S. Titi

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

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically…

Atmospheric and Oceanic Physics · Physics 2015-05-30 Jochen Bröcker , Ivan G. Szendro

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

In meteorology, engineering and computer sciences, data assimilation is routinely employed as the optimal way to combine noisy observations with prior model information for obtaining better estimates of a state, and thus better forecasts,…

Geophysics · Physics 2009-08-12 M. J. Werner , K. Ide , D. Sornette

Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using…

Numerical Analysis · Mathematics 2019-08-15 Sebastian Reich

A framework for data assimilation combining aspects of operator-theoretic ergodic theory and quantum mechanics is developed. This framework adapts the Dirac--von Neumann formalism of quantum dynamics and measurement to perform sequential…

Mathematical Physics · Physics 2019-09-18 Dimitrios Giannakis

Data assimilation is the process of fusing information from imperfect computer simulations with noisy, sparse measurements of reality to obtain improved estimates of the state or parameters of a dynamical system of interest. The data…

This paper contains the latest installment of the authors' project on developing ensemble based data assimilation methodology for high dimensional fluid dynamics models. The algorithm presented here is a particle filter that combines model…

Numerical Analysis · Mathematics 2020-04-22 Colin Cotter , Dan Crisan , Darryl Holm , Wei Pan , Igor Shevchenko

There is an urgent need to build models to tackle Indoor Air Quality issue. Since the model should be accurate and fast, Reduced Order Modelling technique is used to reduce the dimensionality of the problem. The accuracy of the model, that…

We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible…

Analysis of PDEs · Mathematics 2015-06-15 Abderrahim Azouani , Eric Olson , Edriss S. Titi

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

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

A simplified model of natural convection, similar to the Lorenz (1963) system, is compared to computational fluid dynamics simulations in order to test data assimilation methods and better understand the dynamics of convection. The…

Dynamical Systems · Mathematics 2012-04-23 Kameron Decker Harris , El Hassan Ridouane , Darren L. Hitt , Christopher M. Danforth

We present a convolution-based data assimilation method tailored to neuronal electrophysiology, addressing the limitations of traditional value-based synchronization approaches. While conventional methods rely on nudging terms and pointwise…

Neurons and Cognition · Quantitative Biology 2025-06-16 Dawei Li , Henry D. I. Abarbanel

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

The understanding of nonlinear, high dimensional flows, e.g, atmospheric and ocean flows, is critical to address the impacts of global climate change. Data Assimilation techniques combine physical models and observational data, often in a…

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