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- W4300644013 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." @default.
- W4300644013 created "2022-10-03" @default.
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- W4300644013 date "2011-04-04" @default.
- W4300644013 modified "2023-09-28" @default.
- W4300644013 title "Noisy dynamic simulations in the presence of symmetry: data alignment and model reduction" @default.
- W4300644013 doi "https://doi.org/10.48550/arxiv.1104.0725" @default.
- W4300644013 hasPublicationYear "2011" @default.
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