Dimitrios Giannakis (Courant Institute of Mathematical Sciences, New York University); Joanna Slawinska (University of Wisconsin-Milwaukee); Abbas Ourmazd (University of Wisconsin-Milwaukee)
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 Dirac-von Neumann formalism of quantum dynamics and measurement to perform data assimilation (filtering) of climate dynamics, 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, using kernel methods for machine learning to represent 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.