[{"file":[{"creator":"coffen","description":"The article shows how to learn models of dynamical systems\nfrom data which are governed by an unknown variational PDE. 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","date_updated":"2023-08-02T12:04:17Z","relation":"main_file","file_size":1938962,"access_level":"open_access","file_name":"LDensityLearning.pdf","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","content_type":"application/pdf","file_id":"46273"}],"date_created":"2023-02-16T11:32:48Z","type":"conference","keyword":["System identification","discrete Lagrangians","travelling waves"],"department":[{"_id":"636"}],"publication":"Geometric Science of Information","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."}],"related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/Christian-Offen/LagrangianDensityML"}]},"series_title":"Lecture Notes in Computer Science (LNCS)","language":[{"iso":"eng"}],"doi":"10.1007/978-3-031-38271-0_57","year":"2023","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","author":[{"id":"85279","full_name":"Offen, Christian","last_name":"Offen","first_name":"Christian","orcid":"0000-0002-5940-8057"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"}],"publication_identifier":{"eisbn":["978-3-031-38271-0"]},"publication_status":"published","date_updated":"2024-08-12T13:46:29Z","intvolume":"     14071","external_id":{"arxiv":["2302.08232 "]},"oa":"1","file_date_updated":"2023-08-02T12:04:17Z","citation":{"short":"C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric Science of Information, Springer, Cham., 2023, pp. 569–579.","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. Lecture Notes in Computer Science (LNCS). Springer, Cham., 2023. <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">https://doi.org/10.1007/978-3-031-38271-0_57</a>.","ieee":"C. Offen and S. 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>.","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2023). Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In F. Nielsen &#38; F. Barbaresco (Eds.), <i>Geometric Science of Information</i> (Vol. 14071, pp. 569–579). Springer, Cham. <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">https://doi.org/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)} }","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>","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>."},"quality_controlled":"1","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"page":"569-579","_id":"42163","publisher":"Springer, Cham.","user_id":"85279","ddc":["510"],"volume":14071,"editor":[{"full_name":"Nielsen, F","last_name":"Nielsen","first_name":"F"},{"full_name":"Barbaresco, F","last_name":"Barbaresco","first_name":"F"}],"status":"public","conference":{"end_date":"2023-09-01","name":"  GSI'23 6th International Conference on Geometric Science of Information","start_date":"2023-08-30","location":"Saint-Malo, Palais du Grand Large, France"},"has_accepted_license":"1"}]