{"paper":{"title":"Bayesian Multiscale Finite Element Methods. Modeling missing subgrid information probabilistically","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"B. Mallick, N. Guha, S. W. Cheung, V. H. Hoang, W.T. Leung, Y. Efendiev","submitted_at":"2017-02-09T20:28:23Z","abstract_excerpt":"In this paper, we develop a Bayesian multiscale approach based on a multiscale finite element method. Because of scale disparity in many multiscale applications, computational models can not resolve all scales. Various subgrid models are proposed to represent un-resolved scales. Here, we consider a probabilistic approach for modeling un-resolved scales using the Multiscale Finite Element Method (cf., [1, 2]). By representing dominant modes using the Generalized Multiscale Finite Element, we propose a Bayesian framework, which provides multiple inexpensive (computable) solutions for a determini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02973","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"}