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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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Abstract: We 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.
Publication Date: May-2013
Electronic Publication Date: 7-Mar-2013
Citation: Sonday, 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.2013.01.024
DOI: doi:10.1016/j.camwa.2013.01.024
ISSN: 0898-1221
Pages: 1535 - 1557
Type of Material: Journal Article
Version: Author's manuscript

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