{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,6]],"date-time":"2025-04-06T11:06:43Z","timestamp":1743937603862,"version":"3.38.0"},"reference-count":66,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,3,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this work, we analyze Parametrized Advection-Dominated distributed Optimal Control Problems with random inputs in a Reduced Order Model (ROM) context. All the simulations are initially based on a finite element method (FEM) discretization; moreover, a <jats:italic>space-time approach<\/jats:italic> is considered when dealing with unsteady cases. To overcome numerical instabilities that can occur in the optimality system for high values of the P\u00e9clet number, we consider a Streamline Upwind Petrov\u2013Galerkin technique applied in an optimize-then-discretize approach. We combine this method with the ROM framework in order to consider two possibilities of stabilization: Offline-Only stabilization and Offline-Online stabilization. Moreover we consider random parameters and we use a <jats:italic>weighted Proper Orthogonal Decomposition<\/jats:italic> algorithm in a partitioned approach to deal with the issue of uncertainty quantification. Several quadrature techniques are used to derive weighted ROMs: tensor rules, isotropic sparse grids, Monte-Carlo and quasi Monte-Carlo methods. We compare all the approaches analyzing relative errors between the FEM and ROM solutions and the computational efficiency based on the speedup-index.<\/jats:p>","DOI":"10.1515\/jnma-2023-0006","type":"journal-article","created":{"date-parts":[[2024,10,4]],"date-time":"2024-10-04T09:51:28Z","timestamp":1728035488000},"page":"1-35","source":"Crossref","is-referenced-by-count":2,"title":["Stabilized weighted reduced order methods for parametrized advection-dominated optimal control problems governed by partial differential equations with random inputs"],"prefix":"10.1515","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5845-8415","authenticated-orcid":false,"given":"Fabio","family":"Zoccolan","sequence":"first","affiliation":[{"name":"Institut de Math\u00e9matiques , \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne , 1015 Lausanne , Switzerland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1245-271X","authenticated-orcid":false,"given":"Maria","family":"Strazzullo","sequence":"additional","affiliation":[{"name":"DISMA , Politecnico di Torino , Corso Duca degli Abruzzi 24, 10129 Turin , Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0810-8812","authenticated-orcid":false,"given":"Gianluigi","family":"Rozza","sequence":"additional","affiliation":[{"name":"mathLab , Mathematics Area, SISSA , via Bonomea 265, I-34136 Trieste , Italy"}]}],"member":"374","published-online":{"date-parts":[[2024,10,7]]},"reference":[{"key":"2025022817485529880_j_jnma-2023-0006_ref_001","doi-asserted-by":"crossref","unstructured":"P. Benner, M. Ohlberger, A. Patera, G. Rozza, and K. Urban, Model Reduction of Parametrized Systems, Cham, Springer, 2017.","DOI":"10.1007\/978-3-319-58786-8"},{"key":"2025022817485529880_j_jnma-2023-0006_ref_002","doi-asserted-by":"crossref","unstructured":"J. S. Hesthaven, G. Rozza, and B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations, vol. 590, Heidelberg, Springer, 2016.","DOI":"10.1007\/978-3-319-22470-1"},{"key":"2025022817485529880_j_jnma-2023-0006_ref_003","doi-asserted-by":"crossref","unstructured":"A. Quarteroni, G. Rozza, and A. Manzoni, \u201cCertified reduced basis approximation for parametrized partial differential equations and applications,\u201d J. Math. Ind., vol.\u00a01, no.\u00a01, pp.\u00a01\u201349, 2011. https:\/\/doi.org\/10.1186\/2190-5983-1-3.","DOI":"10.1186\/2190-5983-1-3"},{"key":"2025022817485529880_j_jnma-2023-0006_ref_004","doi-asserted-by":"crossref","unstructured":"A. Quarteroni, et al.., Reduced Order Methods for Modeling and Computational Reduction, vol. 9, Berlin, Springer, 2014.","DOI":"10.1007\/978-3-319-02090-7"},{"key":"2025022817485529880_j_jnma-2023-0006_ref_005","doi-asserted-by":"crossref","unstructured":"A. Quarteroni, A. Manzoni, and F. Negri, Reduced Basis Methods for Partial Differential Equations: An Introduction, vol. 92, Heidelberg, Springer, 2015.","DOI":"10.1007\/978-3-319-15431-2"},{"key":"2025022817485529880_j_jnma-2023-0006_ref_006","doi-asserted-by":"crossref","unstructured":"L. Venturi, D. Torlo, F. Ballarin, and G. Rozza, \u201cWeighted reduced order methods for parametrized partial differential equations with random inputs,\u201d in Uncertainty Modeling for Engineering Applications, Cham, Springer, 2019, pp. 27\u201340.","DOI":"10.1007\/978-3-030-04870-9_2"},{"key":"2025022817485529880_j_jnma-2023-0006_ref_007","doi-asserted-by":"crossref","unstructured":"L. Venturi, F. Ballarin, and G. 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