Author ORCID Identifier

https://orcid.org/0000-0002-1588-0050

Date of Award

2026

Document Type

Thesis (Ph.D.)

Department or Program

Mathematics

First Advisor

Dimitrios Giannakis

Abstract

Quantum mechanics, as a mathematical system, can be understood as a generalization of classical probability theory. Quantum Mechanical Data Assimilation (QMDA) is a method in which classical dynamical systems are embedded into a quantum mechanical setting, with an associated data assimilation scheme leveraging the operator algebraic setting. In this dissertation, the algebraic structure underlying the operator theoretic formulation of QMDA is discussed. A procedure for closure of dynamical systems based on QMDA, known as Quantum Mechanical Closure (QMCl), is then constructed, and the procedures for constructing the quantum embeddings and implementing QMCl in practice are laid out and implemented for closures of the Lorenz 63’ and Lorenz 96’ systems. The QMCl methodology is then used for two parameterizations of a high-resolution, cloud-resolving atmosphere model. The first is a parameterization of the thermodynamic processes involved in cloud microphysics. The second is a coarse-graining of the high-resolution model. The results of these experiments are presented, and the parametrization schemes are analyzed on the basis of their ability to produce large-scale convective behavior similar to the high-resolution model.

Original Citation

Freeman, David, et al. "Data assimilation in operator algebras." Proceedings of the National Academy of Sciences 120.8 (2023): e2211115120.

Freeman, David C., Dimitrios Giannakis, and Joanna Slawinska. "Quantum mechanics for closure of dynamical systems." Multiscale Modeling & Simulation 22.1 (2024): 283-333.

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