[{"article_type":"original","intvolume":"        34","publication_status":"published","date_updated":"2024-08-12T13:45:43Z","publication_identifier":{"issn":["1054-1500"]},"author":[{"full_name":"Offen, Christian","last_name":"Offen","first_name":"Christian","orcid":"0000-0002-5940-8057","id":"85279"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494"}],"title":"Learning of discrete models of variational PDEs from data","year":"2024","doi":"10.1063/5.0172287","language":[{"iso":"eng"}],"article_number":"013104","related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/DLNN_pde","description":"GitHub"}]},"abstract":[{"lang":"eng","text":"We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train a neural network model of a discrete Lagrangian density such that the discrete Euler--Lagrange equations are consistent with the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian densities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for the training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers guarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical simulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory such as travelling waves. This is possible even when travelling waves are not present in the training data. This is compared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces containing structurally simple solutions when these are not present in the training data. Ideas are demonstrated on examples based on the wave equation and the Schrödinger equation. "}],"issue":"1","publication":"Chaos","department":[{"_id":"636"}],"type":"journal_article","date_created":"2023-08-10T08:24:48Z","file":[{"date_created":"2024-01-09T10:48:38Z","creator":"coffen","content_type":"application/pdf","file_id":"50376","title":"Accepted Manuscript Chaos","access_level":"open_access","file_size":13222105,"file_name":"Accepted manuscript with AIP banner CHA23-AR-01370.pdf","date_updated":"2024-01-09T10:48:38Z","relation":"main_file"},{"file_name":"LDensityPDE_AIP.pdf","access_level":"open_access","file_size":12960884,"relation":"main_file","date_updated":"2024-01-09T11:19:49Z","file_id":"50390","content_type":"application/pdf","title":"Learning of discrete models of variational PDEs from data","creator":"coffen","date_created":"2024-01-09T11:19:49Z","description":"We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train\na neural network model of a discrete Lagrangian density such that the discrete Euler–Lagrange equations are consistent\nwith the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian\ndensities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for\nthe training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers\nguarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical\nsimulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory\nsuch as travelling waves. This is possible even when travelling waves are not present in the training data. This is\ncompared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces\ncontaining structurally simple solutions when these are not present in the training data. Ideas are demonstrated on\nexamples based on the wave equation and the Schrödinger equation."}],"has_accepted_license":"1","status":"public","volume":34,"user_id":"85279","ddc":["510"],"_id":"46469","publisher":"AIP Publishing","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"quality_controlled":"1","citation":{"short":"C. Offen, S. Ober-Blöbaum, Chaos 34 (2024).","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” <i>Chaos</i> 34, no. 1 (2024). <a href=\"https://doi.org/10.1063/5.0172287\">https://doi.org/10.1063/5.0172287</a>.","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2024). Learning of discrete models of variational PDEs from data. <i>Chaos</i>, <i>34</i>(1), Article 013104. <a href=\"https://doi.org/10.1063/5.0172287\">https://doi.org/10.1063/5.0172287</a>","ieee":"C. Offen and S. Ober-Blöbaum, “Learning of discrete models of variational PDEs from data,” <i>Chaos</i>, vol. 34, no. 1, Art. no. 013104, 2024, doi: <a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>.","ama":"Offen C, Ober-Blöbaum S. Learning of discrete models of variational PDEs from data. <i>Chaos</i>. 2024;34(1). doi:<a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>","bibtex":"@article{Offen_Ober-Blöbaum_2024, title={Learning of discrete models of variational PDEs from data}, volume={34}, DOI={<a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>}, number={1013104}, journal={Chaos}, publisher={AIP Publishing}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2024} }","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” <i>Chaos</i>, vol. 34, no. 1, 013104, AIP Publishing, 2024, doi:<a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>."},"file_date_updated":"2024-01-09T11:19:49Z","oa":"1","external_id":{"arxiv":["2308.05082 "]}},{"keyword":["System identification","inverse problem of variational calculus","Gaussian process","Lagrangian learning","physics informed machine learning","geometry aware learning"],"type":"preprint","department":[{"_id":"636"}],"file":[{"description":"We introduce a method based on Gaussian process regression to identify discrete\nvariational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a geometric machine learning technique in the sense that the variational structure of the true field theory is reflected in the data-driven model by design.\nWe provide a rigorous convergence statement of the method.\nThe proof circumvents challenges posed by the ambiguity of discrete Lagrangian densities in the inverse problem of variational calculus.\nMoreover, our method can be used to quantify model uncertainty in the equations of motions and any linear observable of the discrete field theory.\nThis is illustrated on the example of the discrete wave equation and Schrödinger equation.\nThe article constitutes an extension of our previous article for the data-driven identification of (discrete) Lagrangians for variational dynamics from an ode setting to the setting of discrete pdes.","date_created":"2024-07-10T13:39:32Z","creator":"coffen","title":"Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification","file_id":"55160","content_type":"application/pdf","relation":"main_file","date_updated":"2024-07-10T13:39:32Z","file_name":"L_Collocation.pdf","access_level":"open_access","file_size":4569314}],"date_created":"2024-07-10T13:43:50Z","related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/Lagrangian_GP_PDE","description":"GitHub"}]},"abstract":[{"text":"We introduce a method based on Gaussian process regression to identify discrete variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a geometric machine learning technique in the sense that the variational structure of the true field theory is reflected in the data-driven model by design. We provide a rigorous convergence statement of the method. The proof circumvents challenges posed by the ambiguity of discrete Lagrangian densities in the inverse problem of variational calculus.\r\nMoreover, our method can be used to quantify model uncertainty in the equations of motions and any linear observable of the discrete field theory. This is illustrated on the example of the discrete wave equation and Schrödinger equation.\r\nThe article constitutes an extension of our previous article  arXiv:2404.19626 for the data-driven identification of (discrete) Lagrangians for variational dynamics from an ode setting to the setting of discrete pdes.","lang":"eng"}],"language":[{"iso":"eng"}],"publication_status":"submitted","date_updated":"2024-08-12T13:43:32Z","title":"Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification","year":"2024","author":[{"orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen","full_name":"Offen, Christian","id":"85279"}],"oa":"1","external_id":{"arxiv":["2407.07642"]},"project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"file_date_updated":"2024-07-10T13:39:32Z","citation":{"chicago":"Offen, Christian. “Machine Learning of Discrete Field Theories with Guaranteed Convergence and Uncertainty Quantification,” n.d.","short":"C. Offen, (n.d.).","ieee":"C. Offen, “Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification.” .","apa":"Offen, C. (n.d.). <i>Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification</i>.","bibtex":"@article{Offen, title={Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification}, author={Offen, Christian} }","ama":"Offen C. Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification.","mla":"Offen, Christian. <i>Machine Learning of Discrete Field Theories with Guaranteed Convergence and Uncertainty Quantification</i>."},"user_id":"85279","ddc":["510"],"page":"28","_id":"55159","has_accepted_license":"1","status":"public"},{"citation":{"mla":"Maslovskaya, Sofya, and Sina Ober-Blöbaum. “Symplectic Methods in Deep Learning.” <i>IFAC-PapersOnLine</i>, vol. 58, no. 17, Elsevier BV, 2024, pp. 85–90, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">10.1016/j.ifacol.2024.10.118</a>.","bibtex":"@inproceedings{Maslovskaya_Ober-Blöbaum_2024, title={Symplectic Methods in Deep Learning}, volume={58}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">10.1016/j.ifacol.2024.10.118</a>}, number={17}, booktitle={IFAC-PapersOnLine}, publisher={Elsevier BV}, author={Maslovskaya, Sofya and Ober-Blöbaum, Sina}, year={2024}, pages={85–90} }","ama":"Maslovskaya S, Ober-Blöbaum S. Symplectic Methods in Deep Learning. In: <i>IFAC-PapersOnLine</i>. Vol 58. Elsevier BV; 2024:85-90. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">10.1016/j.ifacol.2024.10.118</a>","ieee":"S. Maslovskaya and S. Ober-Blöbaum, “Symplectic Methods in Deep Learning,” in <i>IFAC-PapersOnLine</i>, 2024, vol. 58, no. 17, pp. 85–90, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">10.1016/j.ifacol.2024.10.118</a>.","apa":"Maslovskaya, S., &#38; Ober-Blöbaum, S. (2024). Symplectic Methods in Deep Learning. <i>IFAC-PapersOnLine</i>, <i>58</i>(17), 85–90. <a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">https://doi.org/10.1016/j.ifacol.2024.10.118</a>","chicago":"Maslovskaya, Sofya, and Sina Ober-Blöbaum. “Symplectic Methods in Deep Learning.” In <i>IFAC-PapersOnLine</i>, 58:85–90. Elsevier BV, 2024. <a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">https://doi.org/10.1016/j.ifacol.2024.10.118</a>.","short":"S. Maslovskaya, S. Ober-Blöbaum, in: IFAC-PapersOnLine, Elsevier BV, 2024, pp. 85–90."},"_id":"59791","publisher":"Elsevier BV","page":"85-90","volume":58,"user_id":"87909","status":"public","date_created":"2025-05-05T09:21:13Z","department":[{"_id":"636"}],"type":"conference","issue":"17","publication":"IFAC-PapersOnLine","language":[{"iso":"eng"}],"doi":"10.1016/j.ifacol.2024.10.118","author":[{"id":"87909","first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya"},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494"}],"publication_identifier":{"issn":["2405-8963"]},"year":"2024","title":"Symplectic Methods in Deep Learning","intvolume":"        58","date_updated":"2025-05-05T09:22:27Z","publication_status":"published"},{"date_created":"2025-05-05T09:42:19Z","type":"preprint","department":[{"_id":"636"}],"citation":{"ieee":"F. Jean and S. Maslovskaya, “Inverse optimal control problem in the non autonomous linear-quadratic case.” 2024.","apa":"Jean, F., &#38; Maslovskaya, S. (2024). <i>Inverse optimal control problem in the non autonomous linear-quadratic case</i>.","chicago":"Jean, Frédéric, and Sofya Maslovskaya. “Inverse Optimal Control Problem in the Non Autonomous Linear-Quadratic Case,” 2024.","short":"F. Jean, S. Maslovskaya, (2024).","mla":"Jean, Frédéric, and Sofya Maslovskaya. <i>Inverse Optimal Control Problem in the Non Autonomous Linear-Quadratic Case</i>. 2024.","bibtex":"@article{Jean_Maslovskaya_2024, title={Inverse optimal control problem in the non autonomous linear-quadratic case}, author={Jean, Frédéric and Maslovskaya, Sofya}, year={2024} }","ama":"Jean F, Maslovskaya S. Inverse optimal control problem in the non autonomous linear-quadratic case. Published online 2024."},"language":[{"iso":"eng"}],"_id":"59801","user_id":"87909","title":"Inverse optimal control problem in the non autonomous linear-quadratic case","year":"2024","status":"public","author":[{"full_name":"Jean, Frédéric","first_name":"Frédéric","last_name":"Jean"},{"first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","id":"87909"}],"date_updated":"2025-05-05T09:43:05Z"},{"abstract":[{"text":"By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system will behave in time. If the dynamics exhibit additional symmetries, then the motion fulfils additional conservation laws, such as conservation of energy (time invariance), momentum (translation invariance), or angular momentum (rotational invariance). To learn a system representation, one could learn the discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function Ld which defines them. Based on ideas from Lie group theory, in this work we introduce a framework to learn a discrete Lagrangian along with its symmetry group from discrete observations of motions and, therefore, identify conserved quantities. The learning process does not restrict the form of the Lagrangian, does not require velocity or momentum observations or predictions and incorporates a cost term which safeguards against unwanted solutions and against potential numerical issues in forward simulations. The learnt discrete quantities are related to their continuous analogues using variational backward error analysis and numerical results demonstrate the improvement such models can have both qualitatively and quantitatively even in the presence of noise.","lang":"eng"}],"related_material":{"link":[{"relation":"software","url":"https://github.com/yanalish/SymDLNN","description":"GitHub"}]},"publication":"IFAC-PapersOnLine","issue":"2","type":"conference","department":[{"_id":"636"}],"file":[{"title":"Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery","file_id":"44037","content_type":"application/pdf","relation":"main_file","date_updated":"2023-04-17T08:05:55Z","file_name":"LNN_project.pdf","access_level":"open_access","file_size":576115,"description":"By one of the most fundamental principles in physics, a dynamical system will\nexhibit those motions which extremise an action functional. This leads to the formation of\nthe Euler-Lagrange equations, which serve as a model of how the system will behave in time.\nIf the dynamics exhibit additional symmetries, then the motion fulfils additional conservation\nlaws, such as conservation of energy (time invariance), momentum (translation invariance), or\nangular momentum (rotational invariance). To learn a system representation, one could learn\nthe discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function\nLd which defines them. Based on ideas from Lie group theory, we introduce a framework to learn\na discrete Lagrangian along with its symmetry group from discrete observations of motions and,\ntherefore, identify conserved quantities. The learning process does not restrict the form of the\nLagrangian, does not require velocity or momentum observations or predictions and incorporates\na cost term which safeguards against unwanted solutions and against potential numerical issues\nin forward simulations. The learnt discrete quantities are related to their continuous analogues\nusing variational backward error analysis and numerical results demonstrate the improvement\nsuch models can have both qualitatively and quantitatively even in the presence of noise.","date_created":"2023-04-17T08:05:55Z","creator":"coffen"}],"date_created":"2022-11-23T08:17:10Z","publication_status":"published","date_updated":"2023-12-29T14:26:00Z","intvolume":"        56","title":"Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery","year":"2023","author":[{"last_name":"Lishkova","first_name":"Yana","full_name":"Lishkova, Yana"},{"first_name":"Paul","last_name":"Scherer","full_name":"Scherer, Paul"},{"first_name":"Steffen","last_name":"Ridderbusch","full_name":"Ridderbusch, Steffen"},{"full_name":"Jamnik, Mateja","last_name":"Jamnik","first_name":"Mateja"},{"last_name":"Liò","first_name":"Pietro","full_name":"Liò, Pietro"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"id":"85279","first_name":"Christian","last_name":"Offen","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian"}],"doi":"10.1016/j.ifacol.2023.10.1457","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S2405896323018657"}],"language":[{"iso":"eng"}],"quality_controlled":"1","file_date_updated":"2023-04-17T08:05:55Z","citation":{"mla":"Lishkova, Yana, et al. “Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery.” <i>IFAC-PapersOnLine</i>, vol. 56, no. 2, Elsevier, 2023, pp. 3203–10, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>.","bibtex":"@inproceedings{Lishkova_Scherer_Ridderbusch_Jamnik_Liò_Ober-Blöbaum_Offen_2023, title={Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery}, volume={56}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>}, number={2}, booktitle={IFAC-PapersOnLine}, publisher={Elsevier}, author={Lishkova, Yana and Scherer, Paul and Ridderbusch, Steffen and Jamnik, Mateja and Liò, Pietro and Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={3203–3210} }","ama":"Lishkova Y, Scherer P, Ridderbusch S, et al. Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery. In: <i>IFAC-PapersOnLine</i>. Vol 56. Elsevier; 2023:3203-3210. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>","ieee":"Y. Lishkova <i>et al.</i>, “Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery,” in <i>IFAC-PapersOnLine</i>,  Yokohama, Japan, 2023, vol. 56, no. 2, pp. 3203–3210, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>.","apa":"Lishkova, Y., Scherer, P., Ridderbusch, S., Jamnik, M., Liò, P., Ober-Blöbaum, S., &#38; Offen, C. (2023). Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery. <i>IFAC-PapersOnLine</i>, <i>56</i>(2), 3203–3210. <a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">https://doi.org/10.1016/j.ifacol.2023.10.1457</a>","chicago":"Lishkova, Yana, Paul Scherer, Steffen Ridderbusch, Mateja Jamnik, Pietro Liò, Sina Ober-Blöbaum, and Christian Offen. “Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery.” In <i>IFAC-PapersOnLine</i>, 56:3203–10. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">https://doi.org/10.1016/j.ifacol.2023.10.1457</a>.","short":"Y. Lishkova, P. Scherer, S. Ridderbusch, M. Jamnik, P. Liò, S. Ober-Blöbaum, C. Offen, in: IFAC-PapersOnLine, Elsevier, 2023, pp. 3203–3210."},"oa":"1","external_id":{"arxiv":["2211.10830"]},"has_accepted_license":"1","status":"public","conference":{"end_date":"2023-07-14","name":"The 22nd World Congress of the International Federation of Automatic Control","start_date":"2023-07-09","location":" Yokohama, Japan"},"user_id":"85279","ddc":["510"],"volume":56,"page":"3203-3210","publisher":"Elsevier","_id":"34135"},{"date_updated":"2024-08-12T13:46:29Z","publication_status":"published","intvolume":"     14071","year":"2023","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","publication_identifier":{"eisbn":["978-3-031-38271-0"]},"author":[{"id":"85279","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen"},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"}],"doi":"10.1007/978-3-031-38271-0_57","series_title":"Lecture Notes in Computer Science (LNCS)","language":[{"iso":"eng"}],"related_material":{"link":[{"url":"https://github.com/Christian-Offen/LagrangianDensityML","relation":"software","description":"GitHub"}]},"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."}],"publication":"Geometric Science of Information","type":"conference","keyword":["System identification","discrete Lagrangians","travelling waves"],"department":[{"_id":"636"}],"file":[{"title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","file_id":"46273","content_type":"application/pdf","relation":"main_file","date_updated":"2023-08-02T12:04:17Z","file_name":"LDensityLearning.pdf","access_level":"open_access","file_size":1938962,"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","creator":"coffen"}],"date_created":"2023-02-16T11:32:48Z","has_accepted_license":"1","status":"public","conference":{"location":"Saint-Malo, Palais du Grand Large, France","start_date":"2023-08-30","name":"  GSI'23 6th International Conference on Geometric Science of Information","end_date":"2023-09-01"},"ddc":["510"],"user_id":"85279","editor":[{"first_name":"F","last_name":"Nielsen","full_name":"Nielsen, F"},{"last_name":"Barbaresco","first_name":"F","full_name":"Barbaresco, F"}],"volume":14071,"page":"569-579","_id":"42163","publisher":"Springer, Cham.","quality_controlled":"1","project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"file_date_updated":"2023-08-02T12:04:17Z","citation":{"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>.","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>.","short":"C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric Science of Information, Springer, Cham., 2023, pp. 569–579.","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>","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>."},"oa":"1","external_id":{"arxiv":["2302.08232 "]}},{"page":"114780","publisher":"Elsevier","_id":"29240","ddc":["510"],"user_id":"85279","volume":421,"status":"public","has_accepted_license":"1","external_id":{"arxiv":["2112.12619"]},"oa":"1","file_date_updated":"2022-06-28T15:25:50Z","citation":{"bibtex":"@article{Ober-Blöbaum_Offen_2023, title={Variational Learning of Euler–Lagrange Dynamics from Data}, volume={421}, DOI={<a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>}, journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier}, author={Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={114780} }","ama":"Ober-Blöbaum S, Offen C. Variational Learning of Euler–Lagrange Dynamics from Data. <i>Journal of Computational and Applied Mathematics</i>. 2023;421:114780. doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>","mla":"Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” <i>Journal of Computational and Applied Mathematics</i>, vol. 421, Elsevier, 2023, p. 114780, doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>.","chicago":"Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” <i>Journal of Computational and Applied Mathematics</i> 421 (2023): 114780. <a href=\"https://doi.org/10.1016/j.cam.2022.114780\">https://doi.org/10.1016/j.cam.2022.114780</a>.","short":"S. Ober-Blöbaum, C. Offen, Journal of Computational and Applied Mathematics 421 (2023) 114780.","ieee":"S. Ober-Blöbaum and C. Offen, “Variational Learning of Euler–Lagrange Dynamics from Data,” <i>Journal of Computational and Applied Mathematics</i>, vol. 421, p. 114780, 2023, doi: <a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>.","apa":"Ober-Blöbaum, S., &#38; Offen, C. (2023). Variational Learning of Euler–Lagrange Dynamics from Data. <i>Journal of Computational and Applied Mathematics</i>, <i>421</i>, 114780. <a href=\"https://doi.org/10.1016/j.cam.2022.114780\">https://doi.org/10.1016/j.cam.2022.114780</a>"},"quality_controlled":"1","language":[{"iso":"eng"}],"doi":"10.1016/j.cam.2022.114780","title":"Variational Learning of Euler–Lagrange Dynamics from Data","year":"2023","publication_identifier":{"issn":["0377-0427"]},"author":[{"id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"id":"85279","orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen","full_name":"Offen, Christian"}],"date_updated":"2023-08-10T08:42:39Z","publication_status":"epub_ahead","intvolume":"       421","article_type":"original","file":[{"title":"Variational Learning of Euler–Lagrange Dynamics from Data","content_type":"application/pdf","file_id":"32274","date_updated":"2022-06-28T15:25:50Z","relation":"main_file","access_level":"open_access","file_size":3640770,"file_name":"ShadowLagrangian_revision1_journal_style_arxiv.pdf","description":"The principle of least action is one of the most fundamental physical principle. It says that among all possible motions\nconnecting two points in a phase space, the system will exhibit those motions which extremise an action functional.\nMany qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equa-\ntions, are related to the existence of an action functional. Incorporating variational structure into learning algorithms\nfor dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features\nwith the exact physical system. In this paper we show how to incorporate variational principles into trajectory predic-\ntions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position\ndata of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no\nprior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward\nerror analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the\nlearned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,\nwe introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of\nvariational backward error analysis. (3) Finally, we introduce a method to perform system identification from position\nobservations only, based on variational backward error analysis.","date_created":"2022-06-28T15:25:50Z","creator":"coffen"}],"date_created":"2022-01-11T13:24:00Z","keyword":["Lagrangian learning","variational backward error analysis","modified Lagrangian","variational integrators","physics informed learning"],"type":"journal_article","department":[{"_id":"636"}],"publication":"Journal of Computational and Applied Mathematics","related_material":{"link":[{"url":"https://github.com/Christian-Offen/LagrangianShadowIntegration","relation":"software"}]},"abstract":[{"text":"The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exhibit those motions which extremise an action functional. Many qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equations, are related to the existence of an action functional. Incorporating variational structure into learning algorithms for dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features with the exact physical system. In this paper we show how to incorporate variational principles into trajectory predictions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position data of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no prior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward error analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the learned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,\r\nwe introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of variational backward error analysis. (3) Finally, we introduce a method to perform system identification from position observations only, based on variational backward error analysis.","lang":"eng"}]},{"quality_controlled":"1","file_date_updated":"2022-08-12T16:48:59Z","citation":{"short":"R. McLachlan, C. Offen, Journal of Geometric Mechanics 15 (2023) 98–115.","chicago":"McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate Symplectic Methods.” <i>Journal of Geometric Mechanics</i> 15, no. 1 (2023): 98–115. <a href=\"https://doi.org/10.3934/jgm.2023005\">https://doi.org/10.3934/jgm.2023005</a>.","ieee":"R. McLachlan and C. Offen, “Backward error analysis for conjugate symplectic methods,” <i>Journal of Geometric Mechanics</i>, vol. 15, no. 1, pp. 98–115, 2023, doi: <a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>.","apa":"McLachlan, R., &#38; Offen, C. (2023). Backward error analysis for conjugate symplectic methods. <i>Journal of Geometric Mechanics</i>, <i>15</i>(1), 98–115. <a href=\"https://doi.org/10.3934/jgm.2023005\">https://doi.org/10.3934/jgm.2023005</a>","bibtex":"@article{McLachlan_Offen_2023, title={Backward error analysis for conjugate symplectic methods}, volume={15}, DOI={<a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>}, number={1}, journal={Journal of Geometric Mechanics}, publisher={AIMS Press}, author={McLachlan, Robert and Offen, Christian}, year={2023}, pages={98–115} }","ama":"McLachlan R, Offen C. Backward error analysis for conjugate symplectic methods. <i>Journal of Geometric Mechanics</i>. 2023;15(1):98-115. doi:<a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>","mla":"McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate Symplectic Methods.” <i>Journal of Geometric Mechanics</i>, vol. 15, no. 1, AIMS Press, 2023, pp. 98–115, doi:<a href=\"https://doi.org/10.3934/jgm.2023005\">10.3934/jgm.2023005</a>."},"oa":"1","external_id":{"arxiv":["2201.03911"]},"has_accepted_license":"1","status":"public","ddc":["510"],"user_id":"85279","volume":15,"page":"98-115","_id":"29236","publisher":"AIMS Press","abstract":[{"text":"The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analysis. If the original and modified equation share structural properties, then the exact and approximate solution share geometric features such as the existence of conserved quantities. Conjugate symplectic methods preserve a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian system. We show how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures. In contrast to other approaches, our backward error analysis method does not rely on an ansatz but computes the structures systematically, provided that a variational formulation of the method is known. The technique is illustrated on the example of symmetric linear multistep methods with matrix coefficients.","lang":"eng"}],"related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/BEAConjugateSymplectic"}]},"publication":"Journal of Geometric Mechanics","issue":"1","type":"journal_article","keyword":["variational integrators","backward error analysis","Euler--Lagrange equations","multistep methods","conjugate symplectic methods"],"department":[{"_id":"636"}],"file":[{"date_created":"2022-08-12T16:48:59Z","description":"The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analysis. If the original and modified equation share structural properties, then the exact and approximate solution share geometric features such as the existence of conserved quantities. Conjugate symplectic methods preserve a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian system. We show how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures. In contrast to other approaches, our backward error analysis method does not rely on an ansatz but computes the structures systematically, provided that a variational formulation of the method is known. The technique is illustrated on the example of symmetric linear multistep methods with matrix coefficients.","creator":"coffen","file_id":"32801","content_type":"application/pdf","title":"Backward error analysis for conjugate symplectic methods","file_name":"BEA_MultiStep_Matrix.pdf","access_level":"open_access","file_size":827030,"relation":"main_file","date_updated":"2022-08-12T16:48:59Z"}],"date_created":"2022-01-11T12:48:39Z","date_updated":"2023-08-10T08:40:30Z","publication_status":"published","intvolume":"        15","article_type":"original","year":"2023","title":"Backward error analysis for conjugate symplectic methods","author":[{"first_name":"Robert","last_name":"McLachlan","full_name":"McLachlan, Robert"},{"id":"85279","orcid":"0000-0002-5940-8057","last_name":"Offen","first_name":"Christian","full_name":"Offen, Christian"}],"doi":"10.3934/jgm.2023005","language":[{"iso":"eng"}]},{"related_material":{"link":[{"description":"GitHub","url":"https://github.com/eva-dierkes/HNN_withSymmetries","relation":"software"}]},"abstract":[{"text":"Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when\r\nlearning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite\r\nthe data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we\r\nenhance the HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach\r\nallows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples,\r\na pendulum on a cart and a two-body problem from astrodynamics are considered.","lang":"eng"}],"publication":"Chaos","issue":"6","type":"journal_article","department":[{"_id":"636"}],"file":[{"file_name":"JournalPaper_main.pdf","file_size":5200111,"access_level":"open_access","relation":"main_file","date_updated":"2023-04-26T16:20:56Z","file_id":"44205","content_type":"application/pdf","title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","creator":"coffen","date_created":"2023-04-26T16:20:56Z","description":"Incorporating physical system knowledge into data-driven\nsystem identification has been shown to be beneficial. The\napproach presented in this article combines learning of an\nenergy-conserving model from data with detecting a Lie\ngroup representation of the unknown system symmetry.\nThe proposed approach can improve the learned model\nand reveal underlying symmetry simultaneously."}],"date_created":"2023-01-20T09:10:06Z","publication_status":"published","date_updated":"2023-08-10T08:37:01Z","article_type":"original","intvolume":"        33","title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","year":"2023","author":[{"full_name":"Dierkes, Eva","last_name":"Dierkes","first_name":"Eva"},{"id":"85279","full_name":"Offen, Christian","first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen"},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"},{"full_name":"Flaßkamp, Kathrin","last_name":"Flaßkamp","first_name":"Kathrin"}],"publication_identifier":{"issn":["1054-1500"]},"doi":"10.1063/5.0142969","article_number":"063115","language":[{"iso":"eng"}],"file_date_updated":"2023-04-26T16:20:56Z","citation":{"apa":"Dierkes, E., Offen, C., Ober-Blöbaum, S., &#38; Flaßkamp, K. (2023). Hamiltonian Neural Networks with Automatic Symmetry Detection. <i>Chaos</i>, <i>33</i>(6), Article 063115. <a href=\"https://doi.org/10.1063/5.0142969\">https://doi.org/10.1063/5.0142969</a>","ieee":"E. Dierkes, C. Offen, S. Ober-Blöbaum, and K. Flaßkamp, “Hamiltonian Neural Networks with Automatic Symmetry Detection,” <i>Chaos</i>, vol. 33, no. 6, Art. no. 063115, 2023, doi: <a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>.","short":"E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023).","chicago":"Dierkes, Eva, Christian Offen, Sina Ober-Blöbaum, and Kathrin Flaßkamp. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” <i>Chaos</i> 33, no. 6 (2023). <a href=\"https://doi.org/10.1063/5.0142969\">https://doi.org/10.1063/5.0142969</a>.","mla":"Dierkes, Eva, et al. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” <i>Chaos</i>, vol. 33, no. 6, 063115, AIP Publishing, 2023, doi:<a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>.","ama":"Dierkes E, Offen C, Ober-Blöbaum S, Flaßkamp K. Hamiltonian Neural Networks with Automatic Symmetry Detection. <i>Chaos</i>. 2023;33(6). doi:<a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>","bibtex":"@article{Dierkes_Offen_Ober-Blöbaum_Flaßkamp_2023, title={Hamiltonian Neural Networks with Automatic Symmetry Detection}, volume={33}, DOI={<a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>}, number={6063115}, journal={Chaos}, publisher={AIP Publishing}, author={Dierkes, Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}, year={2023} }"},"oa":"1","external_id":{"arxiv":["2301.07928"]},"has_accepted_license":"1","status":"public","user_id":"85279","ddc":["510"],"volume":33,"publisher":"AIP Publishing","_id":"37654"},{"year":"2023","title":"Efficient time stepping for numerical integration using reinforcement  learning","author":[{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"full_name":"Hüllermeier, Eyke","first_name":"Eyke","last_name":"Hüllermeier","id":"48129"},{"last_name":"Lücke","first_name":"Marvin","full_name":"Lücke, Marvin"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"first_name":"Christian","last_name":"Offen","orcid":"0000-0002-5940-8057","full_name":"Offen, Christian","id":"85279"},{"full_name":"Peitz, Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X","first_name":"Sebastian","id":"47427"},{"id":"13472","full_name":"Pfannschmidt, Karlson","first_name":"Karlson","orcid":"0000-0001-9407-7903","last_name":"Pfannschmidt"}],"date_updated":"2023-08-25T09:24:50Z","publication_status":"published","intvolume":"        45","main_file_link":[{"url":"https://epubs.siam.org/doi/reader/10.1137/21M1412682"}],"language":[{"iso":"eng"}],"doi":"10.1137/21M1412682","issue":"2","publication":"SIAM Journal on Scientific Computing","abstract":[{"lang":"eng","text":"Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it results in prohibitively large errors or computational effort. To this end, adaptive schemes, such as solvers based on Runge–Kutta pairs, have been developed which adapt the step size based on local error estimations at each step. While the classical schemes apply very generally and are highly efficient on regular systems, they can behave suboptimally when an inefficient step rejection mechanism is triggered by structurally complex systems such as chaotic systems. To overcome these issues, we propose a method to tailor numerical schemes to the problem class at hand. This is achieved by combining simple, classical quadrature rules or ODE solvers with data-driven time-stepping controllers. Compared with learning solution operators to ODEs directly, it generalizes better to unseen initial data as our approach employs classical numerical schemes as base methods. At the same time it can make use of identified structures of a problem class and, therefore, outperforms state-of-the-art adaptive schemes. Several examples demonstrate superior efficiency. Source code is available at https://github.com/lueckem/quadrature-ML."}],"related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/lueckem/quadrature-ML"}]},"date_created":"2021-04-09T07:59:19Z","type":"journal_article","department":[{"_id":"101"},{"_id":"636"},{"_id":"355"},{"_id":"655"}],"status":"public","has_accepted_license":"1","page":"A579-A595","_id":"21600","ddc":["510"],"user_id":"47427","volume":45,"citation":{"mla":"Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration Using Reinforcement  Learning.” <i>SIAM Journal on Scientific Computing</i>, vol. 45, no. 2, 2023, pp. A579–95, doi:<a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>.","ama":"Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical integration using reinforcement  learning. <i>SIAM Journal on Scientific Computing</i>. 2023;45(2):A579-A595. doi:<a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>","bibtex":"@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023, title={Efficient time stepping for numerical integration using reinforcement  learning}, volume={45}, DOI={<a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>}, number={2}, journal={SIAM Journal on Scientific Computing}, author={Dellnitz, Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen, Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, year={2023}, pages={A579–A595} }","apa":"Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz, S., &#38; Pfannschmidt, K. (2023). Efficient time stepping for numerical integration using reinforcement  learning. <i>SIAM Journal on Scientific Computing</i>, <i>45</i>(2), A579–A595. <a href=\"https://doi.org/10.1137/21M1412682\">https://doi.org/10.1137/21M1412682</a>","ieee":"M. Dellnitz <i>et al.</i>, “Efficient time stepping for numerical integration using reinforcement  learning,” <i>SIAM Journal on Scientific Computing</i>, vol. 45, no. 2, pp. A579–A595, 2023, doi: <a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>.","short":"M. Dellnitz, E. Hüllermeier, M. Lücke, S. Ober-Blöbaum, C. Offen, S. Peitz, K. Pfannschmidt, SIAM Journal on Scientific Computing 45 (2023) A579–A595.","chicago":"Dellnitz, Michael, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum, Christian Offen, Sebastian Peitz, and Karlson Pfannschmidt. “Efficient Time Stepping for Numerical Integration Using Reinforcement  Learning.” <i>SIAM Journal on Scientific Computing</i> 45, no. 2 (2023): A579–95. <a href=\"https://doi.org/10.1137/21M1412682\">https://doi.org/10.1137/21M1412682</a>."},"external_id":{"arxiv":["arXiv:2104.03562"]}},{"date_created":"2022-03-24T12:26:10Z","type":"journal_article","department":[{"_id":"636"}],"publication":"AIMS","citation":{"mla":"Cresson, Jacky, et al. “Continuous and Discrete Noether’s Fractional Conserved Quantities for Restricted Calculus of Variations.” <i>AIMS</i>, vol. 14(1), 2022, pp. 57–89.","apa":"Cresson, J., Jiménez, F., &#38; Ober-Blöbaum, S. (2022). Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations. <i>AIMS</i>, <i>14(1)</i>, 57–89.","ieee":"J. Cresson, F. Jiménez, and S. Ober-Blöbaum, “Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations,” <i>AIMS</i>, vol. 14(1), pp. 57–89, 2022.","chicago":"Cresson, Jacky, Fernando Jiménez, and Sina Ober-Blöbaum. “Continuous and Discrete Noether’s Fractional Conserved Quantities for Restricted Calculus of Variations.” <i>AIMS</i> 14(1) (2022): 57–89.","ama":"Cresson J, Jiménez F, Ober-Blöbaum S. Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations. <i>AIMS</i>. 2022;14(1):57-89.","short":"J. Cresson, F. Jiménez, S. Ober-Blöbaum, AIMS 14(1) (2022) 57–89.","bibtex":"@article{Cresson_Jiménez_Ober-Blöbaum_2022, title={Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations}, volume={14(1)}, journal={AIMS}, author={Cresson, Jacky and Jiménez, Fernando and Ober-Blöbaum, Sina}, year={2022}, pages={57–89} }"},"page":"57-89","_id":"30490","language":[{"iso":"eng"}],"user_id":"15694","volume":"14(1)","status":"public","title":"Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations","year":"2022","author":[{"last_name":"Cresson","first_name":"Jacky","full_name":"Cresson, Jacky"},{"full_name":"Jiménez, Fernando","first_name":"Fernando","last_name":"Jiménez"},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494"}],"date_updated":"2022-03-24T12:26:32Z"},{"abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>We consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions are concatenations of singular and bang arcs and exhibit the chattering or <jats:italic>Fuller</jats:italic> phenomenon, which is problematic for applications. To avoid chattering, we introduce a reduced model which is still biologically relevant and retains the important structural features of the original problem. Using a combination of analytical and numerical methods, we show that the singular arc is dominant in the studied DOCPs and exhibits the <jats:italic>turnpike</jats:italic> property. This property is further used in order to design simple and realistic suboptimal control strategies.</jats:p>"}],"publication":"Journal of Optimization Theory and Applications","citation":{"ieee":"J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, and J.-B. Pomet, “Turnpike Property in Optimal Microbial Metabolite Production,” <i>Journal of Optimization Theory and Applications</i>, 2022, doi: <a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>.","apa":"Caillau, J.-B., Djema, W., Gouzé, J.-L., Maslovskaya, S., &#38; Pomet, J.-B. (2022). Turnpike Property in Optimal Microbial Metabolite Production. <i>Journal of Optimization Theory and Applications</i>. <a href=\"https://doi.org/10.1007/s10957-022-02023-0\">https://doi.org/10.1007/s10957-022-02023-0</a>","short":"J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, J.-B. Pomet, Journal of Optimization Theory and Applications (2022).","chicago":"Caillau, Jean-Baptiste, Walid Djema, Jean-Luc Gouzé, Sofya Maslovskaya, and Jean-Baptiste Pomet. “Turnpike Property in Optimal Microbial Metabolite Production.” <i>Journal of Optimization Theory and Applications</i>, 2022. <a href=\"https://doi.org/10.1007/s10957-022-02023-0\">https://doi.org/10.1007/s10957-022-02023-0</a>.","mla":"Caillau, Jean-Baptiste, et al. “Turnpike Property in Optimal Microbial Metabolite Production.” <i>Journal of Optimization Theory and Applications</i>, Springer Science and Business Media LLC, 2022, doi:<a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>.","bibtex":"@article{Caillau_Djema_Gouzé_Maslovskaya_Pomet_2022, title={Turnpike Property in Optimal Microbial Metabolite Production}, DOI={<a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>}, journal={Journal of Optimization Theory and Applications}, publisher={Springer Science and Business Media LLC}, author={Caillau, Jean-Baptiste and Djema, Walid and Gouzé, Jean-Luc and Maslovskaya, Sofya and Pomet, Jean-Baptiste}, year={2022} }","ama":"Caillau J-B, Djema W, Gouzé J-L, Maslovskaya S, Pomet J-B. Turnpike Property in Optimal Microbial Metabolite Production. <i>Journal of Optimization Theory and Applications</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1007/s10957-022-02023-0\">10.1007/s10957-022-02023-0</a>"},"type":"journal_article","keyword":["Applied Mathematics","Management Science and Operations Research","Control and Optimization"],"department":[{"_id":"636"}],"date_created":"2022-04-08T17:23:13Z","publication_status":"published","date_updated":"2022-04-08T18:23:02Z","title":"Turnpike Property in Optimal Microbial Metabolite Production","status":"public","year":"2022","publication_identifier":{"issn":["0022-3239","1573-2878"]},"author":[{"last_name":"Caillau","first_name":"Jean-Baptiste","full_name":"Caillau, Jean-Baptiste"},{"full_name":"Djema, Walid","last_name":"Djema","first_name":"Walid"},{"first_name":"Jean-Luc","last_name":"Gouzé","full_name":"Gouzé, Jean-Luc"},{"id":"87909","last_name":"Maslovskaya","first_name":"Sofya","full_name":"Maslovskaya, Sofya"},{"first_name":"Jean-Baptiste","last_name":"Pomet","full_name":"Pomet, Jean-Baptiste"}],"user_id":"87909","doi":"10.1007/s10957-022-02023-0","_id":"30861","language":[{"iso":"eng"}],"publisher":"Springer Science and Business Media LLC"},{"citation":{"bibtex":"@inproceedings{Vertovec_Ober-Blöbaum_Margellos_2022, title={Verification of safety critical control policies using kernel methods}, author={Vertovec, Nikolaus and Ober-Blöbaum, Sina and Margellos, Kostas}, year={2022}, pages={1870–1875} }","chicago":"Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Verification of Safety Critical Control Policies Using Kernel Methods,” 1870–75, 2022.","short":"N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: 2022, pp. 1870–1875.","ama":"Vertovec N, Ober-Blöbaum S, Margellos K. Verification of safety critical control policies using kernel methods. In: ; 2022:1870-1875.","ieee":"N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Verification of safety critical control policies using kernel methods,” London, 2022, pp. 1870–1875.","apa":"Vertovec, N., Ober-Blöbaum, S., &#38; Margellos, K. (2022). <i>Verification of safety critical control policies using kernel methods</i>. 1870–1875.","mla":"Vertovec, Nikolaus, et al. <i>Verification of Safety Critical Control Policies Using Kernel Methods</i>. 2022, pp. 1870–75."},"abstract":[{"lang":"eng","text":"Hamilton-Jacobi reachability methods for safety-critical control have been well studied, but the safety guarantees derived rely on the accuracy of the numerical computation. Thus, it is crucial to understand and account for any inaccuracies that occur due to uncertainty in the underlying dynamics and environment as well as the induced numerical errors. To this end, we propose a framework for modeling the error of the value function inherent in Hamilton-Jacobi reachability using a Gaussian process. The derived safety controller can be used in conjuncture with arbitrary controllers to provide a safe hybrid control law. The marginal likelihood of the Gaussian process then provides a confidence metric used to determine switches between a least restrictive controller and a safety controller. We test both the prediction as well as the correction capabilities of the presented method in a classical pursuit-evasion example."}],"date_created":"2022-03-31T11:14:13Z","type":"conference","department":[{"_id":"636"}],"status":"public","year":"2022","title":"Verification of safety critical control policies using kernel methods","conference":{"end_date":"2022-07-15","location":"London","start_date":"2022-07-12","name":"2022 European Control Conference (ECC)"},"author":[{"full_name":"Vertovec, Nikolaus","first_name":"Nikolaus","last_name":"Vertovec","id":"93930"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494"},{"full_name":"Margellos, Kostas","last_name":"Margellos","first_name":"Kostas"}],"date_updated":"2023-11-29T10:00:18Z","has_accepted_license":"1","page":"1870-1875","_id":"30733","language":[{"iso":"eng"}],"ddc":["510"],"user_id":"15694"},{"user_id":"15694","volume":34,"page":"759-788","language":[{"iso":"eng"}],"_id":"44624","publisher":"Springer","date_updated":"2023-05-08T09:04:26Z","intvolume":"        34","year":"2022","status":"public","title":"Manifold turnpikes, trims, and symmetries","author":[{"last_name":"Faulwasser","first_name":"Timm","full_name":"Faulwasser, Timm"},{"last_name":"Flaßkamp","first_name":"Kathrin","full_name":"Flaßkamp, Kathrin"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Manuel","last_name":"Schaller","full_name":"Schaller, Manuel"},{"first_name":"Karl","last_name":"Worthmann","full_name":"Worthmann, Karl"}],"type":"journal_article","department":[{"_id":"636"}],"date_created":"2023-05-08T09:04:06Z","publication":"Mathematics of Control, Signals, and Systems","citation":{"ieee":"T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, M. Schaller, and K. Worthmann, “Manifold turnpikes, trims, and symmetries,” <i>Mathematics of Control, Signals, and Systems</i>, vol. 34, pp. 759–788, 2022.","apa":"Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., Schaller, M., &#38; Worthmann, K. (2022). Manifold turnpikes, trims, and symmetries. <i>Mathematics of Control, Signals, and Systems</i>, <i>34</i>, 759–788.","chicago":"Faulwasser, Timm, Kathrin Flaßkamp, Sina Ober-Blöbaum, Manuel Schaller, and Karl Worthmann. “Manifold Turnpikes, Trims, and Symmetries.” <i>Mathematics of Control, Signals, and Systems</i> 34 (2022): 759–88.","short":"T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, M. Schaller, K. Worthmann, Mathematics of Control, Signals, and Systems 34 (2022) 759–788.","mla":"Faulwasser, Timm, et al. “Manifold Turnpikes, Trims, and Symmetries.” <i>Mathematics of Control, Signals, and Systems</i>, vol. 34, Springer, 2022, pp. 759–88.","bibtex":"@article{Faulwasser_Flaßkamp_Ober-Blöbaum_Schaller_Worthmann_2022, title={Manifold turnpikes, trims, and symmetries}, volume={34}, journal={Mathematics of Control, Signals, and Systems}, publisher={Springer}, author={Faulwasser, Timm and Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Schaller, Manuel and Worthmann, Karl}, year={2022}, pages={759–788} }","ama":"Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Schaller M, Worthmann K. Manifold turnpikes, trims, and symmetries. <i>Mathematics of Control, Signals, and Systems</i>. 2022;34:759-788."}},{"type":"journal_article","department":[{"_id":"636"}],"file":[{"date_created":"2022-06-13T09:11:38Z","description":"In backward error analysis, an approximate solution to an equa-\ntion is compared to the exact solution to a nearby ‘modified’ equation. In\nnumerical ordinary differential equations, the two agree up to any power of\nthe step size. If the differential equation has a geometric property then the\nmodified equation may share it. In this way, known properties of differential\nequations can be applied to the approximation. But for partial differential\nequations, the known modified equations are of higher order, limiting appli-\ncability of the theory. Therefore, we study symmetric solutions of discretized\npartial differential equations that arise from a discrete variational principle.\nThese symmetric solutions obey infinite-dimensional functional equations. We\nshow that these equations admit second-order modified equations which are\nHamiltonian and also possess first-order Lagrangians in modified coordinates.\nThe modified equation and its associated structures are computed explicitly\nfor the case of rotating travelling waves in the nonlinear wave equation.","creator":"coffen","file_id":"31859","content_type":"application/pdf","title":"Backward error analysis for variational discretisations of PDEs","file_name":"2_BlendedBEASymmPDE.pdf","access_level":"open_access","file_size":1507248,"relation":"main_file","date_updated":"2022-06-13T09:11:38Z"}],"date_created":"2020-10-06T16:33:19Z","abstract":[{"text":"In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby ‘modified’ equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the differential equation has a geometric property then the modified equation may share it. In this way, known properties of differential equations can be applied to the approximation. But for partial differential equations, the known modified equations are of higher order, limiting applicability of the theory. Therefore, we study symmetric solutions of discretized\r\npartial differential equations that arise from a discrete variational principle. These symmetric solutions obey infinite-dimensional functional equations. We show that these equations admit second-order modified equations which are Hamiltonian and also possess first-order Lagrangians in modified coordinates. The modified equation and its associated structures are computed explicitly for the case of rotating travelling waves in the nonlinear wave equation.","lang":"eng"}],"related_material":{"link":[{"url":"https://github.com/Christian-Offen/multisymplectic","relation":"software"}]},"issue":"3","publication":"Journal of Geometric Mechanics","doi":"10.3934/jgm.2022014","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-08-10T08:44:55Z","article_type":"original","intvolume":"        14","title":"Backward error analysis for variational discretisations of partial  differential equations","year":"2022","author":[{"first_name":"Robert I","last_name":"McLachlan","full_name":"McLachlan, Robert I"},{"id":"85279","full_name":"Offen, Christian","orcid":"https://orcid.org/0000-0002-5940-8057","last_name":"Offen","first_name":"Christian"}],"oa":"1","external_id":{"arxiv":["2006.14172"]},"file_date_updated":"2022-06-13T09:11:38Z","citation":{"ieee":"R. I. McLachlan and C. Offen, “Backward error analysis for variational discretisations of partial  differential equations,” <i>Journal of Geometric Mechanics</i>, vol. 14, no. 3, pp. 447–471, 2022, doi: <a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>.","apa":"McLachlan, R. I., &#38; Offen, C. (2022). Backward error analysis for variational discretisations of partial  differential equations. <i>Journal of Geometric Mechanics</i>, <i>14</i>(3), 447–471. <a href=\"https://doi.org/10.3934/jgm.2022014\">https://doi.org/10.3934/jgm.2022014</a>","short":"R.I. McLachlan, C. Offen, Journal of Geometric Mechanics 14 (2022) 447–471.","chicago":"McLachlan, Robert I, and Christian Offen. “Backward Error Analysis for Variational Discretisations of Partial  Differential Equations.” <i>Journal of Geometric Mechanics</i> 14, no. 3 (2022): 447–71. <a href=\"https://doi.org/10.3934/jgm.2022014\">https://doi.org/10.3934/jgm.2022014</a>.","mla":"McLachlan, Robert I., and Christian Offen. “Backward Error Analysis for Variational Discretisations of Partial  Differential Equations.” <i>Journal of Geometric Mechanics</i>, vol. 14, no. 3, AIMS, 2022, pp. 447–71, doi:<a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>.","bibtex":"@article{McLachlan_Offen_2022, title={Backward error analysis for variational discretisations of partial  differential equations}, volume={14}, DOI={<a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>}, number={3}, journal={Journal of Geometric Mechanics}, publisher={AIMS}, author={McLachlan, Robert I and Offen, Christian}, year={2022}, pages={447–471} }","ama":"McLachlan RI, Offen C. Backward error analysis for variational discretisations of partial  differential equations. <i>Journal of Geometric Mechanics</i>. 2022;14(3):447-471. doi:<a href=\"https://doi.org/10.3934/jgm.2022014\">10.3934/jgm.2022014</a>"},"user_id":"85279","ddc":["510"],"volume":14,"page":"447 - 471","publisher":"AIMS","_id":"19941","has_accepted_license":"1","status":"public"},{"publication":"Chaos: An Interdisciplinary Journal of Nonlinear Science","abstract":[{"text":"Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation laws. To predict Hamiltonian dynamics based on discrete trajectory observations, incorporation of prior knowledge about Hamiltonian structure greatly improves predictions. This is typically done by learning the system's Hamiltonian and then integrating the Hamiltonian vector field with a symplectic integrator. For this, however, Hamiltonian data needs to be approximated based on the trajectory observations. Moreover, the numerical integrator introduces an additional discretisation error. In this paper, we show that an inverse modified Hamiltonian structure adapted to the geometric integrator can be learned directly from observations. A separate approximation step for the Hamiltonian data avoided. The inverse modified data compensates for the discretisation error such that the discretisation error is eliminated. The technique is developed for Gaussian Processes.","lang":"eng"}],"related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/symplectic-shadow-integration","description":"GitHub"}]},"file":[{"date_created":"2021-12-13T14:56:15Z","creator":"coffen","file_id":"28734","content_type":"application/pdf","relation":"main_file","date_updated":"2021-12-13T14:56:15Z","file_name":"SymplecticShadowIntegration_AIP.pdf","file_size":2285059,"access_level":"open_access"}],"date_created":"2021-08-11T08:24:02Z","type":"journal_article","department":[{"_id":"636"}],"year":"2022","title":"Symplectic integration of learned Hamiltonian systems","author":[{"full_name":"Offen, Christian","first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","id":"85279"},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"}],"publication_status":"published","date_updated":"2023-08-10T08:48:14Z","article_type":"original","main_file_link":[{"open_access":"1","url":"https://aip.scitation.org/doi/abs/10.1063/5.0065913"}],"language":[{"iso":"eng"}],"doi":"10.1063/5.0065913","file_date_updated":"2021-12-13T14:56:15Z","citation":{"bibtex":"@article{Offen_Ober-Blöbaum_2022, title={Symplectic integration of learned Hamiltonian systems}, volume={32(1)}, DOI={<a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2022} }","ama":"Offen C, Ober-Blöbaum S. Symplectic integration of learned Hamiltonian systems. <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>. 2022;32(1). doi:<a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>","short":"C. Offen, S. Ober-Blöbaum, Chaos: An Interdisciplinary Journal of Nonlinear Science 32(1) (2022).","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned Hamiltonian Systems.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i> 32(1) (2022). <a href=\"https://doi.org/10.1063/5.0065913\">https://doi.org/10.1063/5.0065913</a>.","ieee":"C. Offen and S. Ober-Blöbaum, “Symplectic integration of learned Hamiltonian systems,” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, vol. 32(1), 2022, doi: <a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>.","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned Hamiltonian Systems.” <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, vol. 32(1), AIP, 2022, doi:<a href=\"https://doi.org/10.1063/5.0065913\">10.1063/5.0065913</a>.","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2022). Symplectic integration of learned Hamiltonian systems. <i>Chaos: An Interdisciplinary Journal of Nonlinear Science</i>, <i>32(1)</i>. <a href=\"https://doi.org/10.1063/5.0065913\">https://doi.org/10.1063/5.0065913</a>"},"quality_controlled":"1","external_id":{"arxiv":["2108.02492"]},"oa":"1","status":"public","has_accepted_license":"1","_id":"23382","publisher":"AIP","user_id":"85279","ddc":["510"],"volume":"32(1)"},{"publication":"7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC","citation":{"apa":"Ober-Blöbaum, S., &#38; Vermeeren, M. (2021). Superconvergence of galerkin variational integrators. In IFAC-PapersOnLine (Ed.), <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC: Vol. 54(19)</i> (pp. 327–333).","ieee":"S. Ober-Blöbaum and M. Vermeeren, “Superconvergence of galerkin variational integrators,” in <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>, 2021, vol. 54(19), pp. 327–333.","short":"S. Ober-Blöbaum, M. Vermeeren, in: IFAC-PapersOnLine (Ed.), 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC, 2021, pp. 327–333.","chicago":"Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational Integrators.” In <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>, edited by IFAC-PapersOnLine, 54(19):327–33, 2021.","mla":"Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational Integrators.” <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>, edited by IFAC-PapersOnLine, vol. 54(19), 2021, pp. 327–33.","ama":"Ober-Blöbaum S, Vermeeren M. Superconvergence of galerkin variational integrators. In: IFAC-PapersOnLine, ed. <i>7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC</i>. Vol 54(19). ; 2021:327-333.","bibtex":"@inproceedings{Ober-Blöbaum_Vermeeren_2021, title={Superconvergence of galerkin variational integrators}, volume={54(19)}, booktitle={7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC}, author={Ober-Blöbaum, Sina and Vermeeren, M.}, editor={IFAC-PapersOnLine}, year={2021}, pages={327–333} }"},"date_created":"2022-01-18T14:27:56Z","type":"conference","department":[{"_id":"636"}],"title":"Superconvergence of galerkin variational integrators","status":"public","year":"2021","author":[{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina","id":"16494"},{"full_name":"Vermeeren, M.","last_name":"Vermeeren","first_name":"M."}],"corporate_editor":["IFAC-PapersOnLine"],"date_updated":"2022-01-21T13:36:53Z","page":"327-333","_id":"29421","language":[{"iso":"eng"}],"user_id":"15694","volume":"54(19)"},{"status":"public","user_id":"87909","volume":132,"_id":"29543","publisher":"Elsevier BV","citation":{"short":"W. Djema, L. Giraldi, S. Maslovskaya, O. Bernard, Automatica 132 (2021).","ama":"Djema W, Giraldi L, Maslovskaya S, Bernard O. Turnpike features in optimal selection of species represented by quota models. <i>Automatica</i>. 2021;132. doi:<a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>","chicago":"Djema, Walid, Laetitia Giraldi, Sofya Maslovskaya, and Olivier Bernard. “Turnpike Features in Optimal Selection of Species Represented by Quota Models.” <i>Automatica</i> 132 (2021). <a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">https://doi.org/10.1016/j.automatica.2021.109804</a>.","bibtex":"@article{Djema_Giraldi_Maslovskaya_Bernard_2021, title={Turnpike features in optimal selection of species represented by quota models}, volume={132}, DOI={<a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>}, number={109804}, journal={Automatica}, publisher={Elsevier BV}, author={Djema, Walid and Giraldi, Laetitia and Maslovskaya, Sofya and Bernard, Olivier}, year={2021} }","mla":"Djema, Walid, et al. “Turnpike Features in Optimal Selection of Species Represented by Quota Models.” <i>Automatica</i>, vol. 132, 109804, Elsevier BV, 2021, doi:<a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>.","apa":"Djema, W., Giraldi, L., Maslovskaya, S., &#38; Bernard, O. (2021). Turnpike features in optimal selection of species represented by quota models. <i>Automatica</i>, <i>132</i>, Article 109804. <a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">https://doi.org/10.1016/j.automatica.2021.109804</a>","ieee":"W. Djema, L. Giraldi, S. Maslovskaya, and O. Bernard, “Turnpike features in optimal selection of species represented by quota models,” <i>Automatica</i>, vol. 132, Art. no. 109804, 2021, doi: <a href=\"https://doi.org/10.1016/j.automatica.2021.109804\">10.1016/j.automatica.2021.109804</a>."},"date_updated":"2022-01-26T13:15:33Z","publication_status":"published","intvolume":"       132","title":"Turnpike features in optimal selection of species represented by quota models","year":"2021","author":[{"last_name":"Djema","first_name":"Walid","full_name":"Djema, Walid"},{"full_name":"Giraldi, Laetitia","last_name":"Giraldi","first_name":"Laetitia"},{"first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","id":"87909"},{"full_name":"Bernard, Olivier","first_name":"Olivier","last_name":"Bernard"}],"publication_identifier":{"issn":["0005-1098"]},"doi":"10.1016/j.automatica.2021.109804","article_number":"109804","language":[{"iso":"eng"}],"publication":"Automatica","type":"journal_article","keyword":["Electrical and Electronic Engineering","Control and Systems Engineering"],"department":[{"_id":"636"}],"date_created":"2022-01-26T13:13:06Z"},{"file":[{"date_updated":"2021-07-29T09:37:49Z","relation":"main_file","access_level":"open_access","file_size":3125220,"file_name":"ifacconf.pdf","content_type":"application/pdf","file_id":"22895","creator":"coffen","date_created":"2021-07-29T09:37:49Z"}],"date_created":"2021-07-29T09:38:32Z","type":"conference","keyword":["optimal control","catastrophe theory","bifurcations","variational methods","symplectic integrators"],"department":[{"_id":"636"}],"abstract":[{"text":"The first order optimality conditions of optimal control problems (OCPs) can\r\nbe regarded as boundary value problems for Hamiltonian systems. Variational or\r\nsymplectic discretisation methods are classically known for their excellent\r\nlong term behaviour. As boundary value problems are posed on intervals of\r\nfixed, moderate length, it is not immediately clear whether methods can profit\r\nfrom structure preservation in this context. When parameters are present,\r\nsolutions can undergo bifurcations, for instance, two solutions can merge and\r\nannihilate one another as parameters are varied. We will show that generic\r\nbifurcations of an OCP are preserved under discretisation when the OCP is\r\neither directly discretised to a discrete OCP (direct method) or translated\r\ninto a Hamiltonian boundary value problem using first order necessary\r\nconditions of optimality which is then solved using a symplectic integrator\r\n(indirect method). Moreover, certain bifurcations break when a non-symplectic\r\nscheme is used. The general phenomenon is illustrated on the example of a cut\r\nlocus of an ellipsoid.","lang":"eng"}],"related_material":{"link":[{"description":"GitHub/Zenodo","url":"https://doi.org/10.5281/zenodo.4562664","relation":"software"}]},"main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/S2405896321021236"}],"language":[{"iso":"eng"}],"series_title":"IFAC-PapersOnLine","doi":"https://doi.org/10.1016/j.ifacol.2021.11.099","title":"Bifurcation preserving discretisations of optimal control problems","year":"2021","author":[{"id":"85279","full_name":"Offen, Christian","last_name":"Offen","orcid":"0000-0002-5940-8057","first_name":"Christian"},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"}],"publication_identifier":{"issn":["2405-8963"]},"publication_status":"published","date_updated":"2023-11-29T10:19:41Z","external_id":{"arxiv":["2107.13853"]},"oa":"1","file_date_updated":"2021-07-29T09:37:49Z","citation":{"bibtex":"@article{Offen_Ober-Blöbaum_2021, series={IFAC-PapersOnLine}, title={Bifurcation preserving discretisations of optimal control problems}, volume={54(19)}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2021}, pages={334–339}, collection={IFAC-PapersOnLine} }","ama":"Offen C, Ober-Blöbaum S. Bifurcation preserving discretisations of optimal control problems. 2021;54(19):334-339. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>","mla":"Offen, Christian, and Sina Ober-Blöbaum. <i>Bifurcation Preserving Discretisations of Optimal Control Problems</i>. 2021, pp. 334–39, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>.","short":"C. Offen, S. Ober-Blöbaum, 54(19) (2021) 334–339.","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Bifurcation Preserving Discretisations of Optimal Control Problems.” IFAC-PapersOnLine, 2021. <a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>.","ieee":"C. Offen and S. Ober-Blöbaum, “Bifurcation preserving discretisations of optimal control problems,” vol. 54(19). pp. 334–339, 2021, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>.","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2021). <i>Bifurcation preserving discretisations of optimal control problems: Vol. 54(19)</i> (pp. 334–339). <a href=\"https://doi.org/10.1016/j.ifacol.2021.11.099\">https://doi.org/10.1016/j.ifacol.2021.11.099</a>"},"quality_controlled":"1","page":"334-339","_id":"22894","user_id":"15694","ddc":["510"],"volume":"54(19)","status":"public","conference":{"end_date":"2021-10-13","start_date":"2021-10-11","name":"7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, LHMNC 2021","location":"Berlin, Germany"},"has_accepted_license":"1"},{"date_created":"2021-03-30T10:27:44Z","type":"conference","department":[{"_id":"636"}],"publication":"2021 60th IEEE Conference on Decision and Control (CDC)","related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/Crown421/StructureGPs-paper"}]},"language":[{"iso":"eng"}],"doi":"10.1109/CDC45484.2021.9683426","title":"Learning ODE Models with Qualitative Structure Using Gaussian Processes ","year":"2021","author":[{"last_name":"Ridderbusch","first_name":"Steffen","full_name":"Ridderbusch, Steffen"},{"last_name":"Offen","orcid":"0000-0002-5940-8057","first_name":"Christian","full_name":"Offen, Christian","id":"85279"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"full_name":"Goulart, Paul","last_name":"Goulart","first_name":"Paul"}],"publication_identifier":{"eisbn":["978-1-6654-3659-5"]},"date_updated":"2023-11-29T10:24:55Z","publication_status":"published","external_id":{"arxiv":["2011.05364"]},"citation":{"apa":"Ridderbusch, S., Offen, C., Ober-Blöbaum, S., &#38; Goulart, P. (2021). Learning ODE Models with Qualitative Structure Using Gaussian Processes . <i>2021 60th IEEE Conference on Decision and Control (CDC)</i>, 2896. <a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">https://doi.org/10.1109/CDC45484.2021.9683426</a>","ieee":"S. Ridderbusch, C. Offen, S. Ober-Blöbaum, and P. Goulart, “Learning ODE Models with Qualitative Structure Using Gaussian Processes ,” in <i>2021 60th IEEE Conference on Decision and Control (CDC)</i>, Austin, TX, USA, 2021, p. 2896, doi: <a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">10.1109/CDC45484.2021.9683426</a>.","chicago":"Ridderbusch, Steffen, Christian Offen, Sina Ober-Blöbaum, and Paul Goulart. “Learning ODE Models with Qualitative Structure Using Gaussian Processes .” In <i>2021 60th IEEE Conference on Decision and Control (CDC)</i>, 2896. IEEE, 2021. <a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">https://doi.org/10.1109/CDC45484.2021.9683426</a>.","short":"S. Ridderbusch, C. Offen, S. Ober-Blöbaum, P. Goulart, in: 2021 60th IEEE Conference on Decision and Control (CDC), IEEE, 2021, p. 2896.","mla":"Ridderbusch, Steffen, et al. “Learning ODE Models with Qualitative Structure Using Gaussian Processes .” <i>2021 60th IEEE Conference on Decision and Control (CDC)</i>, IEEE, 2021, p. 2896, doi:<a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">10.1109/CDC45484.2021.9683426</a>.","ama":"Ridderbusch S, Offen C, Ober-Blöbaum S, Goulart P. Learning ODE Models with Qualitative Structure Using Gaussian Processes . In: <i>2021 60th IEEE Conference on Decision and Control (CDC)</i>. IEEE; 2021:2896. doi:<a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">10.1109/CDC45484.2021.9683426</a>","bibtex":"@inproceedings{Ridderbusch_Offen_Ober-Blöbaum_Goulart_2021, title={Learning ODE Models with Qualitative Structure Using Gaussian Processes }, DOI={<a href=\"https://doi.org/10.1109/CDC45484.2021.9683426\">10.1109/CDC45484.2021.9683426</a>}, booktitle={2021 60th IEEE Conference on Decision and Control (CDC)}, publisher={IEEE}, author={Ridderbusch, Steffen and Offen, Christian and Ober-Blöbaum, Sina and Goulart, Paul}, year={2021}, pages={2896} }"},"page":"2896","_id":"21572","publisher":"IEEE","user_id":"15694","status":"public","conference":{"location":"Austin, TX, USA","start_date":"2021-12-14","name":"60th IEEE Conference on Decision and Control (CDC)","end_date":"2021-12-17"}}]