Data assimilation in operator algebras
Category
Published on
Type
journal-article
Author
David Freeman and Dimitrios Giannakis and Brian Mintz and Abbas Ourmazd and Joanna Slawinska
Citation
Freeman, D., Giannakis, D., Mintz, B., Ourmazd, A., & Slawinska, J. (2023). Data assimilation in operator algebras. Proceedings of the National Academy of Sciences, 120(8). https://doi.org/10.1073/pnas.2211115120
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.
DOI
Funding
NSF-STC Biology with X-ray Lasers (NSF-1231306)
