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We turn the group of all\r\n$C^\\infty$-diffeomorphisms of $M$ into a regular Lie group.","lang":"eng"}],"date_created":"2022-12-22T07:45:13Z","type":"journal_article","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"status":"public","page":"343-358","_id":"34805","publisher":"Heldermann","user_id":"178","volume":30,"citation":{"ieee":"H. Glöckner, “Diffeomorphism groups of convex polytopes,” <i>Journal of Convex Analysis</i>, vol. 30, no. 1, pp. 343–358, 2023.","apa":"Glöckner, H. (2023). Diffeomorphism groups of convex polytopes. <i>Journal of Convex Analysis</i>, <i>30</i>(1), 343–358.","chicago":"Glöckner, Helge. “Diffeomorphism Groups of Convex Polytopes.” <i>Journal of Convex Analysis</i> 30, no. 1 (2023): 343–58.","short":"H. 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Rather\nthan employing reduction techniques, we learn a discrete field theory\ngoverned by a discrete Lagrangian density Ld that is modelled as a neural network. Careful regularisation of the loss function for training Ld is\nnecessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of\nthe discrete Euler–Lagrange equations. Secondly, we develop a method to\nfind solutions to machine learned discrete field theories which constitute\ntravelling waves of the underlying continuous PDE.","date_created":"2023-08-02T12:04:17Z","creator":"coffen"}],"department":[{"_id":"636"}],"type":"conference","keyword":["System identification","discrete Lagrangians","travelling waves"],"publication":"Geometric Science of Information","related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/Christian-Offen/LagrangianDensityML"}]},"abstract":[{"lang":"eng","text":"The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that is modelled as a neural network. Careful regularisation of the loss function for training $L_d$ is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler--Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE."}],"language":[{"iso":"eng"}],"series_title":"Lecture Notes in Computer Science (LNCS)","doi":"10.1007/978-3-031-38271-0_57","author":[{"first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian","id":"85279"},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"}],"publication_identifier":{"eisbn":["978-3-031-38271-0"]},"year":"2023","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","intvolume":"     14071","date_updated":"2024-08-12T13:46:29Z","publication_status":"published","external_id":{"arxiv":["2302.08232 "]},"oa":"1","citation":{"chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” In <i>Geometric Science of Information</i>, edited by F Nielsen and F Barbaresco, 14071:569–79. 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Ober-Blöbaum, “Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves,” in <i>Geometric Science of Information</i>, Saint-Malo, Palais du Grand Large, France, 2023, vol. 14071, pp. 569–579, doi: <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>.","ama":"Offen C, Ober-Blöbaum S. Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In: Nielsen F, Barbaresco F, eds. <i>Geometric Science of Information</i>. Vol 14071. Lecture Notes in Computer Science (LNCS). Springer, Cham.; 2023:569-579. doi:<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>","bibtex":"@inproceedings{Offen_Ober-Blöbaum_2023, series={Lecture Notes in Computer Science (LNCS)}, title={Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves}, volume={14071}, DOI={<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>}, booktitle={Geometric Science of Information}, publisher={Springer, Cham.}, author={Offen, Christian and Ober-Blöbaum, Sina}, editor={Nielsen, F and Barbaresco, F}, year={2023}, pages={569–579}, collection={Lecture Notes in Computer Science (LNCS)} }","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” <i>Geometric Science of Information</i>, edited by F Nielsen and F Barbaresco, vol. 14071, Springer, Cham., 2023, pp. 569–79, doi:<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>."},"file_date_updated":"2023-08-02T12:04:17Z","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"quality_controlled":"1","_id":"42163","publisher":"Springer, Cham.","page":"569-579","editor":[{"full_name":"Nielsen, F","first_name":"F","last_name":"Nielsen"},{"full_name":"Barbaresco, F","first_name":"F","last_name":"Barbaresco"}],"volume":14071,"ddc":["510"],"user_id":"85279","conference":{"start_date":"2023-08-30","name":"  GSI'23 6th International Conference on Geometric Science of Information","location":"Saint-Malo, Palais du Grand Large, France","end_date":"2023-09-01"},"status":"public","has_accepted_license":"1"},{"user_id":"89059","publisher":"University of Engineering and Technology, Lahore","_id":"55584","language":[{"iso":"eng"}],"series_title":"Planning in Germany and Pakistan:  Responding Challenges of Climate Change through Intercultural Dialogue","date_updated":"2024-08-13T07:57:33Z","title":"Decarbonisation and extension of existing district heating systems in German cities","status":"public","year":"2023","author":[{"last_name":"Divkovic","first_name":"Denis","full_name":"Divkovic, Denis","id":"89059"},{"id":"86954","full_name":"Meschede, Henning","last_name":"Meschede","first_name":"Henning","orcid":"0000-0002-1538-089X"}],"type":"misc","place":"Islamabad, Pakistan","date_created":"2024-08-13T07:56:52Z","supervisor":[{"full_name":"Meschede, Henning","last_name":"Meschede","orcid":"0000-0002-1538-089X","first_name":"Henning","id":"86954"}],"citation":{"mla":"Divkovic, Denis, and Henning Meschede. <i>Decarbonisation and Extension of Existing District Heating Systems in German Cities</i>. University of Engineering and Technology, Lahore, 2023.","ama":"Divkovic D, Meschede H. <i>Decarbonisation and Extension of Existing District Heating Systems in German Cities</i>. University of Engineering and Technology, Lahore; 2023.","bibtex":"@book{Divkovic_Meschede_2023, place={Islamabad, Pakistan}, series={Planning in Germany and Pakistan:  Responding Challenges of Climate Change through Intercultural Dialogue}, title={Decarbonisation and extension of existing district heating systems in German cities}, publisher={University of Engineering and Technology, Lahore}, author={Divkovic, Denis and Meschede, Henning}, year={2023}, collection={Planning in Germany and Pakistan:  Responding Challenges of Climate Change through Intercultural Dialogue} }","apa":"Divkovic, D., &#38; Meschede, H. (2023). <i>Decarbonisation and extension of existing district heating systems in German cities</i>. University of Engineering and Technology, Lahore.","ieee":"D. Divkovic and H. 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