{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T16:26:19Z","timestamp":1761582379169,"version":"3.37.3"},"reference-count":48,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"}],"funder":[{"name":"German Research Foundation on \u201cDamage Controlled Forming Processes\u201d","award":["TRR 188-278868966"],"award-info":[{"award-number":["TRR 188-278868966"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Access"],"published-print":{"date-parts":[[2024]]},"DOI":"10.1109\/access.2024.3465572","type":"journal-article","created":{"date-parts":[[2024,9,23]],"date-time":"2024-09-23T17:29:20Z","timestamp":1727112560000},"page":"137144-137161","source":"Crossref","is-referenced-by-count":3,"title":["Sobolev Neural Network With Residual Weighting as a Surrogate in Linear and Non-Linear Mechanics"],"prefix":"10.1109","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-2850-9495","authenticated-orcid":false,"given":"A. O. M.","family":"Kilicsoy","sequence":"first","affiliation":[{"name":"Chair for Reliability Engineering, Fakult&#x00E4;t Maschinenbau, Technical University Dortmund, Dortmund, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8759-6940","authenticated-orcid":false,"given":"J.","family":"Liedmann","sequence":"additional","affiliation":[{"name":"Lehrstuhl Baumechanik, Fakult&#x00E4;t Architektur und Bauingenieurwesen, Technical University Dortmund, Dortmund, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5083-0454","authenticated-orcid":false,"given":"M. A.","family":"Valdebenito","sequence":"additional","affiliation":[{"name":"Chair for Reliability Engineering, Fakult&#x00E4;t Maschinenbau, Technical University Dortmund, Dortmund, Germany"}]},{"given":"F.-J.","family":"Barthold","sequence":"additional","affiliation":[{"name":"Lehrstuhl Baumechanik, Fakult&#x00E4;t Architektur und Bauingenieurwesen, Technical University Dortmund, Dortmund, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3341-3410","authenticated-orcid":false,"given":"M. G. R.","family":"Faes","sequence":"additional","affiliation":[{"name":"Chair for Reliability Engineering, Fakult&#x00E4;t Maschinenbau, Technical University Dortmund, Dortmund, Germany"}]}],"member":"263","reference":[{"issue":"5","key":"ref1","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.compstruc.2006.10.009","article-title":"On the treatment of uncertainties in structural mechanics and analysis","volume":"85","author":"Schu\u00ebller","year":"2007","journal-title":"Comput. Struct."},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(96)01011-0"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(01)00248-1"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2023.112377"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.7712\/120223.10370.19940"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1615\/JMachLearnModelComput.2022046782"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1037\/h0042519"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1145\/3065386"},{"key":"ref9","article-title":"BERT: Pre-training of deep bidirectional transformers for language understanding","author":"Devlin","year":"2018","journal-title":"arXiv:1810.04805"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.5555\/2969033.2969125"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1038\/nature14539"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(89)90020-8"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110651"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.finel.2022.103904"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1186\/s40323-023-00243-1"},{"key":"ref16","article-title":"Large scale distributed deep networks","volume-title":"Advances in Neural Information Processing Systems","volume":"25","author":"Dean","year":"2012"},{"key":"ref17","article-title":"Adam: A method for stochastic optimization","author":"Kingma","year":"2014","journal-title":"arXiv:1412.6980"},{"key":"ref18","first-page":"799","article-title":"Training neural networks for and by interpolation","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Berrada"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2015.2487976"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/s11036-013-0489-0"},{"key":"ref21","article-title":"Physics informed deep learning (Part I): Data-driven solutions of nonlinear partial differential equations","author":"Raissi","year":"2017","journal-title":"arXiv:1711.10561"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.10.045"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/s11831-017-9226-3"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.probengmech.2020.103024"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-33287-6"},{"key":"ref26","article-title":"Sobolev training for neural networks","volume-title":"Advances in Neural Information Processing Systems","volume":"30","author":"Czarnecki","year":"2017"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1007\/s10994-020-05929-w"},{"key":"ref28","article-title":"Lipschitz regularized deep neural networks generalize and are adversarially robust","author":"Finlay","year":"2018","journal-title":"arXiv:1808.09540"},{"key":"ref29","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2022.114823","article-title":"Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems","volume":"393","author":"Yu","year":"2022","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1137\/19m1274067"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-020-02488-5"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1093\/imamat\/hxae011"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-23564-6_14"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-020-02492-9"},{"article-title":"Gradient-enhanced neural networks: Applications in linear and nonlinear mechanics","year":"2023","author":"Kilicsoy","key":"ref35"},{"key":"ref36","article-title":"Self-adaptive physics-informed neural networks using a soft attention mechanism","author":"McClenny","year":"2020","journal-title":"arXiv:2009.04544"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2020.12.028"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-56078-1"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-56865-7"},{"key":"ref40","volume-title":"The Finite Element Method: Solid Mechanics","volume":"2","author":"Zienkiewicz","year":"2000"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1016\/c2009-0-26332-x"},{"volume-title":"The Finite Element Method: Linear Static and Dynamic Finite Element Analysis","year":"2012","author":"Hughes","key":"ref42"},{"issue":"11","key":"ref43","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1016\/j.enganabound.2007.09.007","article-title":"Remarks on variational shape sensitivity analysis based on local coordinates","volume":"32","author":"Barthold","year":"2008","journal-title":"Eng. Anal. Boundary Elements"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1002\/pamm.201710340"},{"article-title":"Sensitivity analysis of elastoplastic structural response regarding geometry and external loads","volume-title":"Proc. 6th ECCM 7th ECFD","author":"Liedmann","key":"ref45"},{"key":"ref46","first-page":"24286","article-title":"One loss for all: Deep hashing with a single cosine similarity based learning objective","volume-title":"Advances in Neural Information Processing Systems","volume":"34","author":"Hoe","year":"2021"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-19309-5_55"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1109\/WACV45572.2020.9093286"}],"container-title":["IEEE Access"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/6287639\/10380310\/10685364.pdf?arnumber=10685364","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,10]],"date-time":"2024-10-10T11:21:20Z","timestamp":1728559280000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/10685364\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"references-count":48,"URL":"https:\/\/doi.org\/10.1109\/access.2024.3465572","relation":{},"ISSN":["2169-3536"],"issn-type":[{"type":"electronic","value":"2169-3536"}],"subject":[],"published":{"date-parts":[[2024]]}}}