{"paper":{"title":"Compressive sensing and low-rank libraries for classification of bifurcation regimes in nonlinear dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ido Bright, J. Nathan Kutz, Jonathan H. Tu, Steven L. Brunton","submitted_at":"2013-12-16T01:36:48Z","abstract_excerpt":"We show that for complex nonlinear systems, model reduction and compressive sensing strategies can be combined to great advantage for classifying, projecting, and reconstructing the relevant low-dimensional dynamics. $\\ell_2$-based dimensionality reduction methods such as the proper orthogonal decomposition are used to construct separate modal libraries and Galerkin models based on data from a number of bifurcation regimes. These libraries are then concatenated into an over-complete library, and $\\ell_1$ sparse representation in this library from a few noisy measurements results in correct ide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4221","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"}