{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T21:40:14Z","timestamp":1791236414892,"version":"4.1.0"},"reference-count":55,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["VO2243\/2-1"],"award-info":[{"award-number":["VO2243\/2-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["AA4-5"],"award-info":[{"award-number":["AA4-5"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,4,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Model order reduction (MOR) methods that are designed to preserve structural features of a given full order model (FOM) often suffer from a lower accuracy when compared to their non-structure-preserving counterparts. In this paper, we present a framework for structure-preserving MOR, which allows us to compute structured reduced order models (ROMs) with a much higher accuracy. The framework is based on parameter optimization, i.e., the elements of the system matrices of the ROM are iteratively varied to minimize an objective functional that measures the difference between the FOM and the ROM. The structural constraints can be encoded in the parametrization of the ROM. The method only depends on frequency response data and can thus be applied to a wide range of dynamical systems. We illustrate the effectiveness of our method on a port-Hamiltonian and on a symmetric second-order system in a comparison with other structure-preserving MOR algorithms.<\/jats:p>","DOI":"10.1137\/20m1380235","type":"journal-article","created":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T04:01:31Z","timestamp":1682481691000},"page":"A502-A529","source":"Crossref","is-referenced-by-count":20,"title":["SOBMOR: Structured Optimization-Based Model Order Reduction"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8761-9217","authenticated-orcid":true,"given":"Paul","family":"Schwerdtner","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8491-1861","authenticated-orcid":true,"given":"Matthias","family":"Voigt","sequence":"additional","affiliation":[{"name":"UniDistance Suisse, 3900 Brig, Switzerland."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,4,26]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1086200"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718713"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611976083"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/040605552"},{"key":"ref5","unstructured":"C. Beattie  and \nP. Benner ,   \\(\\mathcal{H}_2\\)  -Optimality Conditions for Structured Dynamical Systems, Preprint MPIMD14-18, Max Planck Institute Magdeburg, 2014."},{"key":"ref6","unstructured":"C. Beattie , \nV. Mehrmann , and \nH. Xu , Port-Hamiltonian Realizations of Linear Time Invariant Systems, Preprint 23-2015, Institute of Mathematics, Technische Universit\u00e4t Berlin, 2015."},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1002\/pamm.201900224"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1080\/13873954.2013.794363"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2011.2161833"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(90)90037-U"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(90)90049-Z"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2008.12.029"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1137\/030601296"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2004.03.032"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2016.1208749"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1137\/090780201"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611975963"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-018-0969-z"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1137\/20M1346109"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1137\/130933228"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1137\/060666123"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2012.05.052"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1137\/120875752"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2013.09.032"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1145\/1132973.1132979"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1137\/080732717"},{"key":"ref27","first-page":"125","volume":"48","author":"Hauschild S.-A.","year":"2019","journal-title":"Control Cybernet."},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2008.2006160"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1007\/BF01386087"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1137\/20M1344184"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-27909-1_3"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/9.544000"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drv046"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.21105\/joss.00615"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1137\/0329065"},{"key":"ref36","doi-asserted-by":"crossref","unstructured":"H. K. F. Panzer , \nT. Wolf , and \nB. Lohmann ,   \\(H_2\\)   and   \\(H_\\infty\\)   error bounds for model order reduction of second order systems by Krylov subspace methods, in Proceedings of the 2013 European Control Conference, Z\u00fcrich, 2013, pp. 4484\u20134489.","DOI":"10.23919\/ECC.2013.6669657"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2010.937676"},{"key":"ref38","series-title":"proefschrift","volume-title":"Model Reduction of Port-Hamiltonian Systems","author":"Polyuga R. V.","year":"2010"},{"key":"ref39","unstructured":"R. V. Polyuga  and \nA. J. van der Schaft , Structure preserving model reduction of port-Hamiltonian systems, in Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems, 2008."},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1080\/13873950701844170"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRS.2006.881154"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1515\/9781400841059"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1515\/auto-2019-0027"},{"key":"ref44","unstructured":"B. Salimbahrami , Structure Preserving Order Reduction of Large Scale Second Order Models, Dissertation, Fakult\u00e4t f\u00fcr Maschinenwesen, Technische Universit\u00e4t M\u00fcnchen, 2005, https:\/\/mediatum.ub.tum.de\/doc\/601950\/00000941.pdf."},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2004.12.013"},{"key":"ref46","unstructured":"P. Schwerdtner , Port-Hamiltonian System Identification from Noisy Frequency Response Data, preprint, arXiv:2106.11355, 2021."},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2020.12.2482"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2018.11.086"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2021.11.069"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2004.07.006"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1137\/070683052"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1561\/2600000002"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2007.09.015"},{"key":"ref54","volume-title":"On Linear-Quadratic Optimal Control and Robustness of Differential-Algebraic Systems","author":"Voigt M.","year":"2015"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.3166\/ejc.16.401-406"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1380235","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:25:43Z","timestamp":1787333143000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1380235"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,26]]},"references-count":55,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,4,30]]}},"alternative-id":["10.1137\/20M1380235"],"URL":"https:\/\/doi.org\/10.1137\/20m1380235","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,26]]}}}