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Data assimilation in operator algebras

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Titel: Data assimilation in operator algebras
Autoren: David Freeman, Dimitrios Giannakis, Brian Mintz, Abbas Ourmazd, Joanna Slawinska
Quelle: Proc Natl Acad Sci U S A
Publication Status: Preprint
Verlagsinformationen: Proceedings of the National Academy of Sciences, 2023.
Publikationsjahr: 2023
Schlagwörter: Quantum Physics, FOS: Physical sciences, Mathematics - Statistics Theory, Statistics Theory (math.ST), Dynamical Systems (math.DS), Applications of functional analysis in probability theory and statistics, Nonlinear Sciences - Chaotic Dynamics, 01 natural sciences, Statistical aspects of big data and data science, 13. Climate action, Physics - Data Analysis, Statistics and Probability, Physical Sciences, FOS: Mathematics, Applications of operator theory in probability theory and statistics, Mathematics - Dynamical Systems, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Data Analysis, Statistics and Probability (physics.data-an), 0105 earth and related environmental sciences
Beschreibung: We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a nonabelian operator algebra, which provides a representation of observables by multiplication operators and probability densities by density operators (quantum states). In the algebraic approach, the forecast step of data assimilation is represented by a quantum operation induced by the Koopman operator of the dynamical system. Moreover, the analysis step is described by a quantum effect, which generalizes the Bayesian observational update rule. Projecting this formulation to finite-dimensional matrix algebras leads to computational schemes that are i) automatically positivity-preserving and ii) amenable to consistent data-driven approximation using kernel methods for machine learning. Moreover, these methods are natural candidates for implementation on quantum computers. Applications to the Lorenz 96 multiscale system and the El Niño Southern Oscillation in a climate model show promising results in terms of forecast skill and uncertainty quantification.
Publikationsart: Article
Other literature type
Dateibeschreibung: application/xml
Sprache: English
ISSN: 1091-6490
0027-8424
DOI: 10.1073/pnas.2211115120
DOI: 10.48550/arxiv.2206.13659
Zugangs-URL: https://pubmed.ncbi.nlm.nih.gov/36800390
http://arxiv.org/abs/2206.13659
Rights: CC BY NC ND
arXiv Non-Exclusive Distribution
URL: http://creativecommons.org/licenses/by-nc-nd/4.0/This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND) (http://creativecommons.org/licenses/by-nc-nd/4.0/) .
Dokumentencode: edsair.doi.dedup.....fa879b5f81ceee615a7a173f9d1d4c4d
Datenbank: OpenAIRE
Beschreibung
Abstract:We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a nonabelian operator algebra, which provides a representation of observables by multiplication operators and probability densities by density operators (quantum states). In the algebraic approach, the forecast step of data assimilation is represented by a quantum operation induced by the Koopman operator of the dynamical system. Moreover, the analysis step is described by a quantum effect, which generalizes the Bayesian observational update rule. Projecting this formulation to finite-dimensional matrix algebras leads to computational schemes that are i) automatically positivity-preserving and ii) amenable to consistent data-driven approximation using kernel methods for machine learning. Moreover, these methods are natural candidates for implementation on quantum computers. Applications to the Lorenz 96 multiscale system and the El Niño Southern Oscillation in a climate model show promising results in terms of forecast skill and uncertainty quantification.
ISSN:10916490
00278424
DOI:10.1073/pnas.2211115120