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dc.contributor.authorAntunes Moreira, Hugo Goncalo
dc.date.accessioned2019-06-19T00:32:18Z
dc.date.available2019-06-19T00:32:18Z
dc.date.issued2019-06-19
dc.date.submitted2019-06-18T22:00:11Z
dc.identifier.urihttps://hdl.handle.net/1956/20227
dc.description.abstractData-driven schemes are in high demand, given the growing abundance and accessibility to large amounts of measurements from historical records, numerical simulations, and experimental data. However, despite the abundance of data, modeling high-dimensional complex dynamical systems remains a challenge. In this thesis we present a data-driven method for modeling dynamical systems called the Dynamic Mode Decomposition (DMD). This is a recent method that has first emerged in the fluid mechanics community as a tool for analyzing the dynamics of nonlinear systems. However, given its ability to provide an accurate decomposition of a complex system into spatiotemporal coherent structures, it gained popularity and interest from other fields where complex nonlinear processes cannot be accurately characterized by known governing equations, or that exhibit a rich multiscale dynamic properties. This method relies on the fact that many of these systems evolve on a low-dimensional attractor that may be characterized by dominant spatiotemporal coherent structures. The confidence that the DMD is useful to characterize non-linear dynamics is given by theoretical framework provided by Koopmans theory, which will also be presented in the thesis. Short examples are used to illustrate the DMD application and the Koopmans operator theory. Finally, two data-sets generated from two different fields (from a 2D ocean model, and a neuron strip experiment) are tested using the DMD. We will use the decomposition results to identify structures which we may relate to a physical phenomena, and discuss the performance.en_US
dc.language.isoeng
dc.publisherThe University of Bergenen_US
dc.subjectdata analysis
dc.subjectDynamical systems
dc.subjectmodeling
dc.titleDynamic Mode Decomposition and Koopman Operator (Data-Driven Modeling of Complex Dynamical Systems)
dc.typeMaster thesis
dc.date.updated2019-06-18T22:00:11Z
dc.rights.holderCopyright the Author. All rights reserveden_US
dc.description.degreeMaster's Thesis in Mathematicsen_US
dc.description.localcodeMAB399
dc.description.localcodeMAMN-MAB
dc.subject.nus753109
fs.subjectcodeMAB399
fs.unitcode12-11-0


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