{"paper":{"title":"The regularizing Levenberg-Marquardt scheme for history matching of petroleum reservoirs,","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Clint Dawson, Marco Iglesias","submitted_at":"2013-02-14T18:26:04Z","abstract_excerpt":"In this paper we study a history matching approach that consists of finding stable approximations to the problem of minimizing the weighted least-squares functional that penalizes the misfit between the reservoir model predictions $G(u)$ and noisy observations $y^{\\eta}$. In other words, we are interested in computing $u^{\\eta}\\equiv \\arg\\min_{u\\in X}\\frac{1}{2}\\vert\\vert \\Gamma^{-1/2}(y-G(u))\\vert\\vert_{Y}^{2} $ where $\\Gamma$ is the measurements error covariance, $Y$ is the observation space and $X$ is a set of admissible parameters. This is an ill-posed nonlinear inverse problem that we add"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3501","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"}