{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:24:16Z","timestamp":1787340256531,"version":"3.56.0"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM\/ASA J. Uncertainty Quantification"],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>Computer models, or codes, are used to provide numerical solutions to mathematical models describing real-world problems. Some codes are computationally intensive, reflecting the complexities of mathematical models. Fast approximations, or surrogates, are often used to alleviate the computational burden. We propose multi-output physics-based Kriging surrogates for a class of finite element models, using code information about the underlying partial differential equation in a statistics framework. Specifically, the contribution of our paper consists in applying Kriging methods to deviation vectors of linearly transformed fine-mesh solutions retained on a coarse mesh, where the transformation is defined in terms of coarse-mesh stiffness matrices and load vectors. The accuracy of the surrogate is supported by a convergence result. We use Darcy's equation to illustrate the method. Based on a moderate sample of 50 inputs, the proposed finite element method deviation (FEM-dev) surrogate has a root mean square error lower by about 40% than its multi-output competitors, the direct regression and basis decomposition surrogates. In addition, it has prediction interval coverage closer to the nominal values than its competitors.<\/jats:p>","DOI":"10.1137\/16m1092489","type":"journal-article","created":{"date-parts":[[2017,8,24]],"date-time":"2017-08-24T12:56:55Z","timestamp":1503579415000},"page":"870-889","source":"Crossref","is-referenced-by-count":0,"title":["Physics-Based Kriging Surrogates for a Class of Finite Element Codes"],"prefix":"10.1137","volume":"5","author":[{"given":"A.","family":"Cesmelioglu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"Song","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D.","family":"Drignei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,8,24]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019155918070"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1214\/009053607000000163"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/130940517"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2009.08.006"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1198\/TECH.2010.10029"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1198\/016214506000000898"},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"A. Ern and J.L. Guermond,\n                      Theory and Practice of Finite Elements\n                      , Appl. Math. Sci. 159, Springer-Verlag, New York, 2004.","DOI":"10.1007\/978-1-4757-4355-5"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2007.1900"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/120876745"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.ast.2012.01.006"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.2514\/1.J051243"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1198\/016214507000000888"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/87.1.1"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2016.03.020"},{"key":"atypb15","first-page":"167","author":"Lax P.D.","year":"1954","journal-title":"NJ"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-016-0270-1"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1993.10485320"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1198\/106186008X384032"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177012413"},{"key":"atypb20","unstructured":"A. Saltelli, S. Tarantola, F. Campolongo, and M. Ratto,\n                      Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models\n                      , John Wiley & Sons, Chichester, UK, 2004."},{"key":"atypb21","doi-asserted-by":"crossref","unstructured":"T.J. Santner, B.J. Williams, and W.I. Notz,\n                      The Design and Analysis of Computer Experiments\n                      , Springer-Verlag, New York, 2003.","DOI":"10.1007\/978-1-4757-3799-8"},{"key":"atypb22","unstructured":"O. Schabenberger and C.A. Gotway,\n                      Statistical Methods for Spatial Data Analysis\n                      , Chapman and Hall\/CRC Press, Boca Raton, FL, 2005."}],"container-title":["SIAM\/ASA Journal on Uncertainty Quantification"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1092489","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:27:14Z","timestamp":1787336834000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1092489"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/16M1092489"],"URL":"https:\/\/doi.org\/10.1137\/16m1092489","relation":{},"ISSN":["2166-2525"],"issn-type":[{"value":"2166-2525","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}