کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
468196 | 698196 | 2013 | 23 صفحه PDF | دانلود رایگان |
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.
Journal: Computers & Mathematics with Applications - Volume 65, Issue 10, May 2013, Pages 1535–1557