{"paper":{"title":"Hessian-based sampling for high-dimensional model reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Omar Ghattas, Peng Chen","submitted_at":"2018-09-26T22:25:50Z","abstract_excerpt":"In this work we develop a Hessian-based sampling method for the construction of goal-oriented reduced order models with high-dimensional parameter inputs. Model reduction is known very challenging for high-dimensional parametric problems whose solutions also live in high-dimensional manifolds. However, the manifold of some quantity of interest (QoI) depending on the parametric solutions may be low-dimensional. We use the Hessian of the QoI with respect to the parameter to detect this low-dimensionality, and draw training samples by projecting the high-dimensional parameter to a low-dimensional"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10255","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"}