Skip navigation
Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01736666898
Full metadata record
DC FieldValueLanguage
dc.contributor.advisorKevrekidis, Ioannis Gen_US
dc.contributor.authorDsilva, Carmeline Joanen_US
dc.contributor.otherChemical and Biological Engineering Departmenten_US
dc.date.accessioned2015-12-07T20:00:37Z-
dc.date.available2015-12-07T20:00:37Z-
dc.date.issued2015en_US
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp01736666898-
dc.description.abstractIn science and engineering, it is becoming increasingly common to explore and analyze large, complex data sets. Much of the data collected today is extremely high-dimensional, capturing detailed phenomena at the microscopic level. However, many systems exhibit coherent macroscopic dynamics described by only a few effective degrees of freedom, and uncovering those relevant degrees of freedom can aid in and accelerate modeling efforts. This dissertation addresses data collected from dynamical systems, with the goal of uncovering a parsimonious parameterization of the data which captures the governing macroscopic dynamics. We use diffusion maps, a manifold learning algorithm which is flexible enough to capture nonlinear structure in a data set, to analyze such data. However, traditional manifold learning algorithms, such as diffusion maps, must be modified to provide informative analysis of data from complex dynamical systems. This thesis work adapts the diffusion maps algorithm to address four issues which are prevalent throughout dynamical systems. We first analyze multiscale dynamical data, where slow dynamical modes are obscured by fast, large-magnitude noise. We then present a methodology for constructing consistent embeddings, so that data collected via different observations of the same underlying dynamical system can be merged and combined using a common low-dimensional description. Next, we discuss reconstructing the dynamics of a developmental process using fixed snapshots which must be both registered into a consistent frame of reference and temporally ordered. Finally, we present a method for extracting the true dimensionality of a data set, an essential task for reduced modeling in complex dynamical systems, using manifold learning.en_US
dc.language.isoenen_US
dc.publisherPrinceton, NJ : Princeton Universityen_US
dc.relation.isformatofThe Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: http://catalog.princeton.edu/en_US
dc.subject.classificationChemical engineeringen_US
dc.titleManifold Learning for Dynamical Systemsen_US
dc.typeAcademic dissertations (Ph.D.)en_US
pu.projectgrantnumber690-2143en_US
Appears in Collections:Chemical and Biological Engineering

Files in This Item:
File Description SizeFormat 
Dsilva_princeton_0181D_11442.pdf15.42 MBAdobe PDFView/Download


Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.