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A Quantum Mechanical Approach for Data Assimilation in Climate Dynamics
  • Dimitrios Giannakis,
  • Joanna Slawinska,
  • Abbas Ourmazd
Dimitrios Giannakis
New York University

Corresponding Author:[email protected]

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Joanna Slawinska
University of Wisconsin-Milwaukee
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Abbas Ourmazd
University of Wisconsin-Milwaukee
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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 as an analog of probability distributions in Bayesian data assimilation. The framework is implemented in a fully empirical, data-driven manner by representing the evolution and measurement operators via matrices in a basis of kernel eigenfunctions learned from time-ordered observations. We discuss applications to data assimilation of Indo-Pacific SST and probabilistic forecasting of the Nino 3.4 index.