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Related papers: Data Assimilation: A Mathematical Introduction

200 papers

This chapter provides various perspective on an important challenge in data assimilation: model error. While the overall goal is to understand the implication of model error of any type in data assimilation, we emphasize on the effect of…

Dynamical Systems · Mathematics 2015-07-02 John Harlim

A flexible representation of uncertainty that remains within the standard framework of probabilistic measure theory is presented along with a study of its properties. This representation relies on a specific type of outer measure that is…

Information Theory · Computer Science 2016-11-10 Jeremie Houssineau , Daniel E. Clark

In this study, we analyzed a continuous data assimilation scheme applied on a double-diffusive natural convection model. The algorithm is introduced with a first order backward Euler time scheme along with a finite element discretization in…

Numerical Analysis · Mathematics 2020-08-06 Mine Akbas , Aytekin Cibik

We show, using idealized models, that numerical data assimilation can be successful only if an effective dimension of the problem is not excessive. This effective dimension depends on the noise in the model and the data, and in physically…

Mathematical Physics · Physics 2015-06-15 Alexandre J. Chorin , Matthias Morzfeld

Nudging is a data assimilation method amenable to both analysis and implementation. It also has the (reported) advantage of being insensitive to model errors compared to other assimilation methods. However, nudging behavior in the presence…

Numerical Analysis · Mathematics 2025-04-24 Aytekin Çibik , Rui Fang , William Layton , Farjana Siddiqua

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

Data assimilation is a core component of numerical weather prediction systems. The large quantity of data processed during assimilation requires the computation to be distributed across increasingly many compute nodes, yet existing…

Machine Learning · Computer Science 2025-01-15 Oscar Key , So Takao , Daniel Giles , Marc Peter Deisenroth

The main phases of applied statistical work are discussed in general terms. The account starts with the clarification of objectives and proceeds through study design, measurement and analysis to interpretation. An attempt is made to extract…

Applications · Statistics 2009-09-29 D. R. Cox

The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…

Applications · Statistics 2016-07-19 Patrick S. Medina , R. W. Doerge

These informal notes deal with a number of questions related to sums and integrals in analysis.

Classical Analysis and ODEs · Mathematics 2010-08-17 Stephen Semmes

Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weather and ocean forecasting. The approach involves a…

Numerical Analysis · Mathematics 2026-04-30 I. Daužickaitė , M. A. Freitag , S. Gürol , A. S. Lawless , A. Ramage , J. A. Scott , J. M. Tabeart

This article develops a general framework for continuous deterministic data assimilation for semilinear parabolic equations by means of evolution equations. Introducing a nudged model driven by partial observations, the global…

Analysis of PDEs · Mathematics 2026-02-25 Gianmarco Del Sarto , Matthias Hieber , Filippo Palma , Tarek Zöchling

An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. We consider a nudging-based approach for data assimilation that constructs an approximate solution based on a…

Analysis of PDEs · Mathematics 2018-09-05 Michael S. Jolly , Vincent R. Martinez , Eric J. Olson , Edriss S. Titi

For the Research Topic Data Assimilation and Control: Theory and Applications in Life Sciences we first review the formulation of statistical data assimilation (SDA) and discuss algorithms for exploring variational approximations to the…

Neurons and Cognition · Quantitative Biology 2018-09-17 Anna Miller , Dawei Li , Jason Platt , Arij Daou , Daniel Margoliash , Henry Abarbanel

We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system…

Chaotic Dynamics · Physics 2009-11-13 Alberto Carrassi , Michael Ghil , Anna Trevisan , Francesco Uboldi

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

Using a very cheap Data Assimilation (DA) method, I show an alternative approach to classical DA for numerical climate models which produce a large amount of "big data". The problematic features of state-of-the-art high resolution Regional…

Applications · Statistics 2016-10-12 Bijan Fallah

The article is devoted to new mathematical methods for psychophysical filtering of experimental data and their processing.

General Mathematics · Mathematics 2007-05-23 Denis V. Juriev

We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a non-abelian operator algebra, which provides a representation of…

Statistics Theory · Mathematics 2023-03-29 David Freeman , Dimitrios Giannakis , Brian Mintz , Abbas Ourmazd , Joanna Slawinska

Data assimilation, in its most comprehensive form, addresses the Bayesian inverse problem of identifying plausible state trajectories that explain noisy or incomplete observations of stochastic dynamical systems. Various approaches have…

Machine Learning · Computer Science 2023-11-01 François Rozet , Gilles Louppe