{"paper":{"title":"A goal-oriented RBM-Accelerated generalized polynomial chaos algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Akil Narayan, Jiahua Jiang, Yanlai Chen","submitted_at":"2016-01-02T04:46:28Z","abstract_excerpt":"The non-intrusive generalized Polynomial Chaos (gPC) method is a popular computational approach for solving partial differential equations (PDEs) with random inputs. The main hurdle preventing its efficient direct application for high-dimensional input parameters is that the size of many parametric sampling meshes grows exponentially in the number of inputs (the \"curse of dimensionality\"). In this paper, we design a weighted version of the reduced basis method (RBM) for use in the non-intrusive gPC framework. We construct an RBM surrogate that can rigorously achieve a user-prescribed error tol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00137","kind":"arxiv","version":2},"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"}