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Data-Driven Methods for Physics-Cons...

Dylewsky, Daniel.

Data-Driven Methods for Physics-Constrained Dynamical Systems.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Data-Driven Methods for Physics-Constrained Dynamical Systems.
Author:	Dylewsky, Daniel.
Published:	Ann Arbor : ProQuest Dissertations & Theses, 2020
Description:	127 p.
Notes:	Source: Dissertations Abstracts International, Volume: 82-05, Section: B.
Notes:	Advisor: Kutz, J. Nathan.
Contained By:	Dissertations Abstracts International82-05B.
Subject:	Applied mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28089805
ISBN:	9798684660610

Data-Driven Methods for Physics-Constrained Dynamical Systems.
Dylewsky, Daniel.

Data-Driven Methods for Physics-Constrained Dynamical Systems. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 127 p.

Source: Dissertations Abstracts International, Volume: 82-05, Section: B.

Thesis (Ph.D.)--University of Washington, 2020.

This item must not be sold to any third party vendors.

As the availability of large data sets has risen and computation has become cheaper, the field of dynamical systems analysis has placed increased emphasis on data-driven numerical methods for diagnostics, forecasting, and control of complex systems. Results from machine learning and statistics offer a broad suite of techniques with which to approach these tasks, often with great efficacy. With respect to time series data gathered from sequential measurements on a physical system, however, these generic methods often fail to account for important dynamical properties which are obscured if the data is treated as a collection of unordered snapshots without attention to coherence phenomena or symmetries. This thesis presents three methodological results designed to address particular problems in systems analysis by taking a physics inspired, dynamics focused approach. Chapter 3 offers a method for decomposition of data from systems in which different physics phenomena unfold simultaneously on highly disparate time scales by regressing separate local dynamical models for each scale component. Chapter 4 presents a novel representation for complex multidimensional time series as superpositions of simple constituent trajectories. It is shown that working in this representation, a large class of nonlinear, spectrally continuous systems can be effectively reproduced by actuated linear models. Finally, Chapter 5 introduces a dynamical alternative to existing methods for stability analysis of networked power systems. Instead of employing graph theory techniques directly on the topological structure of the power grid in question, a phenomenological graph representation learned directly from time series data is shown to offer greater practical insight into the structural basis for failure events. Taken together, these results contribute to a larger push toward effective data-driven analysis of physical systems which takes explicit account for geometry, scale, and coherence properties of observed dynamics.

ISBN: 9798684660610Subjects--Topical Terms:

377601
Applied mathematics.
Subjects--Index Terms:

Dynamic mode decomposition

Data-Driven Methods for Physics-Constrained Dynamical Systems.
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245 1 0 $a Data-Driven Methods for Physics-Constrained Dynamical Systems.
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300 $a 127 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-05, Section: B.
500 $a Advisor: Kutz, J. Nathan.
502 $a Thesis (Ph.D.)--University of Washington, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a As the availability of large data sets has risen and computation has become cheaper, the field of dynamical systems analysis has placed increased emphasis on data-driven numerical methods for diagnostics, forecasting, and control of complex systems. Results from machine learning and statistics offer a broad suite of techniques with which to approach these tasks, often with great efficacy. With respect to time series data gathered from sequential measurements on a physical system, however, these generic methods often fail to account for important dynamical properties which are obscured if the data is treated as a collection of unordered snapshots without attention to coherence phenomena or symmetries. This thesis presents three methodological results designed to address particular problems in systems analysis by taking a physics inspired, dynamics focused approach. Chapter 3 offers a method for decomposition of data from systems in which different physics phenomena unfold simultaneously on highly disparate time scales by regressing separate local dynamical models for each scale component. Chapter 4 presents a novel representation for complex multidimensional time series as superpositions of simple constituent trajectories. It is shown that working in this representation, a large class of nonlinear, spectrally continuous systems can be effectively reproduced by actuated linear models. Finally, Chapter 5 introduces a dynamical alternative to existing methods for stability analysis of networked power systems. Instead of employing graph theory techniques directly on the topological structure of the power grid in question, a phenomenological graph representation learned directly from time series data is shown to offer greater practical insight into the structural basis for failure events. Taken together, these results contribute to a larger push toward effective data-driven analysis of physical systems which takes explicit account for geometry, scale, and coherence properties of observed dynamics.
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650 4 $a Artificial intelligence. $3 194058
653 $a Dynamic mode decomposition
653 $a Dynamical systems
653 $a Koopman theory
653 $a Machine learning
653 $a Multiscale systems
653 $a Time series analysis
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710 2 $a University of Washington. $b Physics. $3 766113
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793 $a English
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