{"paper":{"title":"Data Assimilation in Reduced Modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Albert Cohen, Guergana Petrova, Peter Binev, Przemyslaw Wojtaszczyk, Ronald DeVore, Wolfgang Dahmen","submitted_at":"2015-06-15T20:53:13Z","abstract_excerpt":"We consider the problem of optimal recovery of an element $u$ of a Hilbert space $\\mathcal{H}$ from $m$ measurements obtained through known linear functionals on $\\mathcal{H}$. Problems of this type are well studied \\cite{MRW} under an assumption that $u$ belongs to a prescribed model class, e.g. a known compact subset of $\\mathcal{H}$. Motivated by reduced modeling for parametric partial differential equations, this paper considers another setting where the additional information about $u$ is in the form of how well $u$ can be approximated by a certain known subspace $V_n$ of $\\mathcal{H}$ of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04770","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"}