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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.
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A quantum mechanical approach for data assimilation in climate dynamics
A framework for data assimilation in climate dynamics is presented, combining aspects of quantum mechanics, Koopman operator theory, and kernel methods for machine learning. This approach adapts the formalism of quantum dynamics and measurement to perform data assimilation (filtering), using the Koopman operator governing the evolution of observables as an analog of the Heisenberg operator in quantum mechanics, and a quantum mechanical density operator to represent the data assimilation state. The framework is implemented in a fully empirical, data-driven manner by representing the evolution and measurement operators via matrices in a basis learned from time-ordered observations. Applications to data assimilation of the Nino 3.4 index for the El Nino Southern Oscillation (ENSO) in a comprehensive climate model show promising results.
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- Award ID(s):
- 1842538
- PAR ID:
- 10111830
- Date Published:
- Journal Name:
- International Conference on Machine Learning Workshop on "Climate Change: How Can AI Help?"
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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