{"paper":{"title":"Manifold learning techniques and model reduction applied to dissipative PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"physics.comp-ph","authors_text":"Amit Singer, Benjamin E. Sonday, C. William Gear, Ioannis G. Kevrekidis","submitted_at":"2010-11-23T19:11:25Z","abstract_excerpt":"We link nonlinear manifold learning techniques for data analysis/compression with model reduction techniques for evolution equations with time scale separation. In particular, we demonstrate a `\"nonlinear extension\" of the POD-Galerkin approach to obtaining reduced dynamic models of dissipative evolution equations. The approach is illustrated through a reaction-diffusion PDE, and the performance of different simulators on the full and the reduced models is compared. We also discuss the relation of this nonlinear extension with the so-called \"nonlinear Galerkin\" methods developed in the context"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5197","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"}