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Noisy dynamic simulations in the presence of symmetry: Data alignment and model reduction

Author(s): Sonday, Benjamin; Singer, Amit; Kevrekidis, Yannis G

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dc.contributor.authorSonday, Benjamin-
dc.contributor.authorSinger, Amit-
dc.contributor.authorKevrekidis, Yannis G-
dc.date.accessioned2019-08-29T17:01:57Z-
dc.date.available2019-08-29T17:01:57Z-
dc.date.issued2013-05en_US
dc.identifier.citationSonday, Benjamin, Singer, Amit, Kevrekidis, Ioannis G. (2013). Noisy dynamic simulations in the presence of symmetry: Data alignment and model reduction. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 65 (1535 - 1557. doi:10.1016/j.camwa.2013.01.024en_US
dc.identifier.issn0898-1221-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1mm9g-
dc.description.abstractWe process snapshots of trajectories of evolution equations with intrinsic symmetries, and demonstrate the use of recently developed eigenvector-based techniques to successfully quotient out the degrees of freedom associated with the symmetries in the presence of noise. Our illustrative examples include a one-dimensional evolutionary partial differential (the Kuramoto-Sivashinsky) equation with periodic boundary conditions, as well as a stochastic simulation of nematic liquid crystals which can be effectively modeled through a nonlinear Smoluchowski equation on the surface of a sphere. This is a useful first step towards data mining the symmetry-adjusted ensemble of snapshots in search of an accurate low-dimensional parametrization and the associated reduction of the original dynamical system. We also demonstrate a technique (Vector Diffusion Maps) that combines, in a single formulation, the symmetry removal step and the dimensionality reduction step. (C) 2013 Elsevier Ltd. All rights reserved.en_US
dc.format.extent1535 - 1557en_US
dc.language.isoen_USen_US
dc.relation.ispartofCOMPUTERS & MATHEMATICS WITH APPLICATIONSen_US
dc.rightsAuthor's manuscripten_US
dc.titleNoisy dynamic simulations in the presence of symmetry: Data alignment and model reductionen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1016/j.camwa.2013.01.024-
dc.date.eissued2013-03-07en_US
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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