{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:38:29Z","timestamp":1787330309106,"version":"build-2736575974"},"reference-count":52,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Germany\u2019s Excellence Strategy"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We present a novel physics-informed system identification method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the input, state, and output of a system in the time domain, we find a realization that approximates the data well while guaranteeing that the energy functional satisfies a dissipation inequality. To this end, we use the framework of port-Hamiltonian (pH) systems and modify the dynamic mode decomposition, respectively, operator inference, to be feasible for continuous-time pH systems. We propose an iterative numerical method to solve the corresponding least-squares minimization problem. We construct an effective initialization of the algorithm by studying the least-squares problem in a weighted norm, for which we present the analytical minimum-norm solution. The efficiency of the proposed method is demonstrated with several numerical examples.<\/jats:p>","DOI":"10.1137\/22m149329x","type":"journal-article","created":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T14:36:58Z","timestamp":1689172618000},"page":"A1690-A1710","source":"Crossref","is-referenced-by-count":16,"title":["Port-Hamiltonian Dynamic Mode Decomposition"],"prefix":"10.1137","volume":"45","author":[{"given":"Riccardo","family":"Morandin","sequence":"first","affiliation":[{"name":"Institute of Mathematics MA 4-5, Technical University Berlin, 10623 Berlin, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6734-9253","authenticated-orcid":true,"given":"Jonas","family":"Nicodemus","sequence":"additional","affiliation":[{"name":"Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart, 70569 Stuttgart, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4272-1079","authenticated-orcid":true,"given":"Benjamin","family":"Unger","sequence":"additional","affiliation":[{"name":"Stuttgart Center for Simulation Science (SC SimTech), University of Stuttgart, 70569 Stuttgart, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,7,11]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1080\/13873954.2021.1975137"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/ACC.2016.7524964"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974829.ch8"},{"key":"ref4","unstructured":"P. J. Baddoo , \nB. Herrmann , \nB. J. McKeon , \nJ. N. Kutz , and \nS. L. Brunton , Physics-Informed Dynamic Mode Decomposition (piDMD), 2021, https:\/\/royalsocietypublishing.org\/doi\/10.1098\/rspa.2022.0576."},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2018.11.013"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s00498-018-0223-3"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1553\/etna_vol56s28"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2020.104741"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-018-9592-x"},{"key":"ref10","author":"Borja P.","year":"2021","journal-title":"IEEE Trans. Automat. Control"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2021.07.022"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2022.110368"},{"key":"ref13","unstructured":"R. T. Q. Chen , \nY. Rubanova , \nJ. Bettencourt , and \nD. Duvenaud , Neural ordinary differential equations, in Proceedings of the 32nd Conference on Neural Information Processing Systems, NeurIPS, 2018; also available online from https:\/\/proceedings.neurips.cc\/paper\/2018\/file\/69386f6bb1dfed68692a24c8686939b9-Paper.pdf."},{"key":"ref14","unstructured":"K. Cherifi , \nV. Mehrmann , and \nK. Hariche , Numerical Methods to Compute a Minimal Realization of a Port-Hamiltonian System, http:\/\/arxiv.org\/abs\/1903.07042, 2019."},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479802402491"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2017.07.047"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2017.11.023"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2012.05.052"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/61.772353"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.3390\/math10030418"},{"key":"ref21","volume-title":"Matrix Nearness Problems and Applications","author":"Higham N. J.","year":"1988"},{"key":"ref22","doi-asserted-by":"crossref","unstructured":"B. Hillebrecht  and \nB. Unger , Certified machine learning: A posteriori error estimation for physics-informed neural networks, in Proceedings of the International Joint Conference on Neural Networks, IJCNN, 2022, pp. 1\u20138, https:\/\/doi.org\/10.1109\/IJCNN55064.2022.9892569.","DOI":"10.1109\/IJCNN55064.2022.9892569"},{"key":"ref23","unstructured":"B. Hillebrecht  and \nB. Unger , Certified Machine Learning: Rigorous A Posteriori Error Bounds for PDE Defined PINNs, http:\/\/arxiv.org\/abs\/2210.03426, 2022."},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-0399-1"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.2514\/3.20031"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1038\/s42254-021-00314-5"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2018.06.035"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974508"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2007.03.008"},{"key":"ref30","doi-asserted-by":"crossref","unstructured":"V. Mehrmann  and \nR. Morandin , Structure-preserving discretization for port-Hamiltonian descriptor systems, in Proceedings of the 58th IEEE Conference on Decision and Control, CDC, Nice, 2019, IEEE, pp. 6863\u20136868, https:\/\/doi.org\/10.1109\/CDC40024.2019.9030180.","DOI":"10.1109\/CDC40024.2019.9030180"},{"key":"ref31","unstructured":"V. Mehrmann  and \nB. Unger , Control of Port-Hamiltonian Differential-Algebraic Systems and Applications, http:\/\/arxiv.org\/abs\/2201.06590, 2022."},{"key":"ref32","doi-asserted-by":"crossref","unstructured":"T. Moser  and \nB. Lohmann , A new Riemannian framework for efficient   \\(\\mathcal{H}_2\\)  -optimal model reduction of port-Hamiltonian systems, in Proceedings of the 59th IEEE Conference on Decision and Control, CDC, 2020, pp. 5043\u20135049, https:\/\/doi.org\/10.1109\/CDC42340.2020.9304134.","DOI":"10.1109\/CDC42340.2020.9304134"},{"key":"ref33","series-title":"Appl. Optim. 87","volume-title":"Introductory Lectures on Convex Optimization: A Basic Course","author":"Nesterov Y.","year":"2003"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1137\/16M1094750"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2016.03.025"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2011.2128650"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2011.12.008"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1137\/15M1013857"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.10.045"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2017.2723259"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112010001217"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2016.09.007"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2017.09.030"},{"key":"ref44","unstructured":"P. Schwerdtner , Port-Hamiltonian System Identification from Noisy Frequency Response Data, https:\/\/arxiv.org\/abs\/2106.11355, 2021."},{"key":"ref45","unstructured":"P. Schwerdtner  and \nM. Voigt , SOBMOR: Structured Optimization-Based Model Order Reduction, https:\/\/arxiv.org\/abs\/2011.07567, 2020."},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2021.11.069"},{"key":"ref47","unstructured":"H. Sharma  and \nB. Kramer , Preserving Lagrangian Structure in Data-Driven Reduced-Order Modeling of Large-Scale Mechanical Systems, http:\/\/arxiv.org\/abs\/2203.06361, 2022."},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2021.133122"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.3934\/jcd.2014.1.391"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1561\/2600000002"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2022.09.089"},{"key":"ref52","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\/22M149329X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:56:21Z","timestamp":1787327781000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M149329X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,11]]},"references-count":52,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,8,31]]}},"alternative-id":["10.1137\/22M149329X"],"URL":"https:\/\/doi.org\/10.1137\/22m149329x","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,11]]}}}