{"paper":{"title":"Noisy dynamic simulations in the presence of symmetry: data alignment and model reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.comp-ph","authors_text":"Amit Singer, Benjamin E. Sonday, Ioannis G. Kevrekidis","submitted_at":"2011-04-05T03:05:07Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0725","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}