[{"external_id":{"arxiv":["2308.05082 "]},"oa":"1","file_date_updated":"2024-01-09T11:19:49Z","citation":{"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>.","short":"C. Offen, S. Ober-Blöbaum, Chaos 34 (2024).","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>."},"quality_controlled":"1","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"publisher":"AIP Publishing","_id":"46469","user_id":"85279","ddc":["510"],"volume":34,"status":"public","has_accepted_license":"1","file":[{"relation":"main_file","date_updated":"2024-01-09T10:48:38Z","file_name":"Accepted manuscript with AIP banner CHA23-AR-01370.pdf","access_level":"open_access","file_size":13222105,"title":"Accepted Manuscript Chaos","file_id":"50376","content_type":"application/pdf","creator":"coffen","date_created":"2024-01-09T10:48:38Z"},{"title":"Learning of discrete models of variational PDEs from data","file_id":"50390","content_type":"application/pdf","relation":"main_file","date_updated":"2024-01-09T11:19:49Z","file_name":"LDensityPDE_AIP.pdf","file_size":12960884,"access_level":"open_access","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.","date_created":"2024-01-09T11:19:49Z","creator":"coffen"}],"date_created":"2023-08-10T08:24:48Z","type":"journal_article","department":[{"_id":"636"}],"issue":"1","publication":"Chaos","abstract":[{"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. ","lang":"eng"}],"related_material":{"link":[{"description":"GitHub","url":"https://github.com/Christian-Offen/DLNN_pde","relation":"software"}]},"article_number":"013104","language":[{"iso":"eng"}],"doi":"10.1063/5.0172287","year":"2024","title":"Learning of discrete models of variational PDEs from data","publication_identifier":{"issn":["1054-1500"]},"author":[{"id":"85279","full_name":"Offen, Christian","first_name":"Christian","last_name":"Offen","orcid":"0000-0002-5940-8057"},{"id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"}],"publication_status":"published","date_updated":"2024-08-12T13:45:43Z","article_type":"original","intvolume":"        34"},{"status":"public","has_accepted_license":"1","_id":"55159","page":"28","user_id":"85279","ddc":["510"],"citation":{"mla":"Offen, Christian. <i>Machine Learning of Discrete Field Theories with Guaranteed Convergence and Uncertainty Quantification</i>.","ama":"Offen C. Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification.","bibtex":"@article{Offen, title={Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification}, author={Offen, Christian} }","apa":"Offen, C. (n.d.). <i>Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification</i>.","ieee":"C. Offen, “Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification.” .","short":"C. Offen, (n.d.).","chicago":"Offen, Christian. “Machine Learning of Discrete Field Theories with Guaranteed Convergence and Uncertainty Quantification,” n.d."},"file_date_updated":"2024-07-10T13:39:32Z","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"external_id":{"arxiv":["2407.07642"]},"oa":"1","author":[{"id":"85279","full_name":"Offen, Christian","first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen"}],"year":"2024","title":"Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification","publication_status":"submitted","date_updated":"2024-08-12T13:43:32Z","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","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."}],"related_material":{"link":[{"description":"GitHub","url":"https://github.com/Christian-Offen/Lagrangian_GP_PDE","relation":"software"}]},"date_created":"2024-07-10T13:43:50Z","file":[{"creator":"coffen","date_created":"2024-07-10T13:39:32Z","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.","file_name":"L_Collocation.pdf","access_level":"open_access","file_size":4569314,"relation":"main_file","date_updated":"2024-07-10T13:39:32Z","file_id":"55160","content_type":"application/pdf","title":"Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification"}],"department":[{"_id":"636"}],"type":"preprint","keyword":["System identification","inverse problem of variational calculus","Gaussian process","Lagrangian learning","physics informed machine learning","geometry aware learning"]},{"citation":{"chicago":"Kovács, Balázs. “Numerical Surgery for Mean Curvature Flow of Surfaces.” <i>SIAM Journal on Scientific Computing</i> 46, no. 2 (2024): A645--A669. <a href=\"https://doi.org/10.1137/22M1531919\">https://doi.org/10.1137/22M1531919</a>.","short":"B. Kovács, SIAM Journal on Scientific Computing 46 (2024) A645--A669.","ieee":"B. Kovács, “Numerical surgery for mean curvature flow of surfaces,” <i>SIAM Journal on Scientific Computing</i>, vol. 46, no. 2, pp. A645--A669, 2024, doi: <a href=\"https://doi.org/10.1137/22M1531919\">10.1137/22M1531919</a>.","apa":"Kovács, B. (2024). Numerical surgery for mean curvature flow of surfaces. <i>SIAM Journal on Scientific Computing</i>, <i>46</i>(2), A645--A669. <a href=\"https://doi.org/10.1137/22M1531919\">https://doi.org/10.1137/22M1531919</a>","bibtex":"@article{Kovács_2024, title={Numerical surgery for mean curvature flow of surfaces}, volume={46}, DOI={<a href=\"https://doi.org/10.1137/22M1531919\">10.1137/22M1531919</a>}, number={2}, journal={SIAM Journal on Scientific Computing}, author={Kovács, Balázs}, year={2024}, pages={A645--A669} }","ama":"Kovács B. Numerical surgery for mean curvature flow of surfaces. <i>SIAM Journal on Scientific Computing</i>. 2024;46(2):A645--A669. doi:<a href=\"https://doi.org/10.1137/22M1531919\">10.1137/22M1531919</a>","mla":"Kovács, Balázs. “Numerical Surgery for Mean Curvature Flow of Surfaces.” <i>SIAM Journal on Scientific Computing</i>, vol. 46, no. 2, 2024, pp. A645--A669, doi:<a href=\"https://doi.org/10.1137/22M1531919\">10.1137/22M1531919</a>."},"publication":"SIAM Journal on Scientific Computing","issue":"2","extern":"1","date_created":"2023-07-10T12:32:34Z","department":[{"_id":"841"}],"type":"journal_article","author":[{"id":"100441","orcid":"0000-0001-9872-3474","first_name":"Balázs","last_name":"Kovács","full_name":"Kovács, Balázs"}],"title":"Numerical surgery for mean curvature flow of surfaces","year":"2024","status":"public","intvolume":"        46","date_updated":"2024-08-27T07:42:56Z","_id":"45972","language":[{"iso":"eng"}],"page":"A645--A669","volume":46,"doi":"10.1137/22M1531919","user_id":"100441"},{"doi":"10.1016/j.disc.2024.114258","article_number":"114258","language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2024-10-10T12:28:13Z","intvolume":"       348","year":"2024","title":"Critically 3-frustrated signed graphs","author":[{"first_name":"Chiara","last_name":"Cappello","full_name":"Cappello, Chiara"},{"last_name":"Naserasr","first_name":"Reza","full_name":"Naserasr, Reza"},{"full_name":"Steffen, Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401","first_name":"Eckhard","id":"15548"},{"full_name":"Wang, Zhouningxin","last_name":"Wang","first_name":"Zhouningxin"}],"publication_identifier":{"issn":["0012-365X"]},"type":"journal_article","department":[{"_id":"542"}],"date_created":"2024-10-10T12:27:11Z","publication":"Discrete Mathematics","issue":"1","user_id":"15540","volume":348,"publisher":"Elsevier BV","_id":"56497","status":"public","citation":{"chicago":"Cappello, Chiara, Reza Naserasr, Eckhard Steffen, and Zhouningxin Wang. “Critically 3-Frustrated Signed Graphs.” <i>Discrete Mathematics</i> 348, no. 1 (2024). <a href=\"https://doi.org/10.1016/j.disc.2024.114258\">https://doi.org/10.1016/j.disc.2024.114258</a>.","short":"C. Cappello, R. Naserasr, E. Steffen, Z. Wang, Discrete Mathematics 348 (2024).","apa":"Cappello, C., Naserasr, R., Steffen, E., &#38; Wang, Z. (2024). Critically 3-frustrated signed graphs. <i>Discrete Mathematics</i>, <i>348</i>(1), Article 114258. <a href=\"https://doi.org/10.1016/j.disc.2024.114258\">https://doi.org/10.1016/j.disc.2024.114258</a>","ieee":"C. Cappello, R. Naserasr, E. Steffen, and Z. Wang, “Critically 3-frustrated signed graphs,” <i>Discrete Mathematics</i>, vol. 348, no. 1, Art. no. 114258, 2024, doi: <a href=\"https://doi.org/10.1016/j.disc.2024.114258\">10.1016/j.disc.2024.114258</a>.","ama":"Cappello C, Naserasr R, Steffen E, Wang Z. Critically 3-frustrated signed graphs. <i>Discrete Mathematics</i>. 2024;348(1). doi:<a href=\"https://doi.org/10.1016/j.disc.2024.114258\">10.1016/j.disc.2024.114258</a>","bibtex":"@article{Cappello_Naserasr_Steffen_Wang_2024, title={Critically 3-frustrated signed graphs}, volume={348}, DOI={<a href=\"https://doi.org/10.1016/j.disc.2024.114258\">10.1016/j.disc.2024.114258</a>}, number={1114258}, journal={Discrete Mathematics}, publisher={Elsevier BV}, author={Cappello, Chiara and Naserasr, Reza and Steffen, Eckhard and Wang, Zhouningxin}, year={2024} }","mla":"Cappello, Chiara, et al. “Critically 3-Frustrated Signed Graphs.” <i>Discrete Mathematics</i>, vol. 348, no. 1, 114258, Elsevier BV, 2024, doi:<a href=\"https://doi.org/10.1016/j.disc.2024.114258\">10.1016/j.disc.2024.114258</a>."}},{"language":[{"iso":"eng"}],"doi":"10.1016/j.ifacol.2024.10.118","author":[{"id":"87909","first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina","id":"16494"}],"publication_identifier":{"issn":["2405-8963"]},"year":"2024","title":"Symplectic Methods in Deep Learning","intvolume":"        58","publication_status":"published","date_updated":"2025-05-05T09:22:27Z","date_created":"2025-05-05T09:21:13Z","department":[{"_id":"636"}],"type":"conference","issue":"17","publication":"IFAC-PapersOnLine","_id":"59791","publisher":"Elsevier BV","page":"85-90","volume":58,"user_id":"87909","status":"public","citation":{"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>","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>.","short":"S. Maslovskaya, S. Ober-Blöbaum, in: IFAC-PapersOnLine, Elsevier BV, 2024, pp. 85–90.","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>.","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>.","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>","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} }"}},{"date_created":"2025-05-05T09:42:19Z","department":[{"_id":"636"}],"type":"preprint","citation":{"short":"F. Jean, S. Maslovskaya, (2024).","chicago":"Jean, Frédéric, and Sofya Maslovskaya. “Inverse Optimal Control Problem in the Non Autonomous Linear-Quadratic Case,” 2024.","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>.","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.","mla":"Jean, Frédéric, and Sofya Maslovskaya. <i>Inverse Optimal Control Problem in the Non Autonomous Linear-Quadratic Case</i>. 2024."},"_id":"59801","language":[{"iso":"eng"}],"user_id":"87909","author":[{"full_name":"Jean, Frédéric","first_name":"Frédéric","last_name":"Jean"},{"first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","id":"87909"}],"title":"Inverse optimal control problem in the non autonomous linear-quadratic case","year":"2024","status":"public","date_updated":"2025-05-05T09:43:05Z"},{"type":"preprint","department":[{"_id":"841"}],"external_id":{"arxiv":["2407.02101"]},"date_created":"2024-07-04T12:53:47Z","abstract":[{"text":"This paper develops and discusses a residual-based a posteriori error\r\nestimate and a space--time adaptive algorithm for solving parabolic surface\r\npartial differential equations on closed stationary surfaces. The full\r\ndiscretization uses the surface finite element method in space and the backward\r\nEuler method in time. The proposed error indicator bounds the error quantities\r\nglobally in space from above and below, and globally in time from above and\r\nlocally from below. A space--time adaptive algorithm is proposed using the\r\nderived error indicator. Numerical experiments illustrate and complement the\r\ntheory.","lang":"eng"}],"publication":"arXiv:2407.02101","citation":{"chicago":"Kovács, Balázs, and Michael Frederik Raúl Lantelme. “A Posteriori Error Estimates for Parabolic Partial Differential Equations on Stationary Surfaces.” <i>ArXiv:2407.02101</i>, 2024.","short":"B. Kovács, M.F.R. Lantelme, ArXiv:2407.02101 (2024).","apa":"Kovács, B., &#38; Lantelme, M. F. R. (2024). A posteriori error estimates for parabolic partial differential equations on stationary surfaces. In <i>arXiv:2407.02101</i>.","ieee":"B. Kovács and M. F. R. Lantelme, “A posteriori error estimates for parabolic partial differential equations on stationary surfaces,” <i>arXiv:2407.02101</i>. 2024.","ama":"Kovács B, Lantelme MFR. A posteriori error estimates for parabolic partial differential equations on stationary surfaces. <i>arXiv:240702101</i>. Published online 2024.","bibtex":"@article{Kovács_Lantelme_2024, title={A posteriori error estimates for parabolic partial differential equations on stationary surfaces}, journal={arXiv:2407.02101}, author={Kovács, Balázs and Lantelme, Michael Frederik Raúl}, year={2024} }","mla":"Kovács, Balázs, and Michael Frederik Raúl Lantelme. “A Posteriori Error Estimates for Parabolic Partial Differential Equations on Stationary Surfaces.” <i>ArXiv:2407.02101</i>, 2024."},"user_id":"100441","_id":"55078","language":[{"iso":"eng"}],"date_updated":"2026-02-18T14:45:36Z","year":"2024","status":"public","title":"A posteriori error estimates for parabolic partial differential equations on stationary surfaces","author":[{"first_name":"Balázs","orcid":"0000-0001-9872-3474","last_name":"Kovács","full_name":"Kovács, Balázs","id":"100441"},{"id":"102867","first_name":"Michael Frederik Raúl","last_name":"Lantelme","full_name":"Lantelme, Michael Frederik Raúl"}]},{"date_updated":"2024-11-15T12:34:03Z","title":"Transitivity in wreath products with symmetric groups","status":"public","year":"2024","author":[{"full_name":"Klawuhn, Lukas-André Dominik","orcid":"0009-0009-7736-4885","last_name":"Klawuhn","first_name":"Lukas-André Dominik","id":"91965"},{"full_name":"Schmidt, Kai-Uwe","last_name":"Schmidt","first_name":"Kai-Uwe"}],"user_id":"91965","page":"38","_id":"56429","language":[{"iso":"eng"}],"abstract":[{"text":"It is known that the notion of a transitive subgroup of a permutation group\r\n$P$ extends naturally to the subsets of $P$. We study transitive subsets of the\r\nwreath product $G \\wr S_n$, where $G$ is a finite abelian group. This includes\r\nthe hyperoctahedral group for $G=C_2$. We give structural characterisations of\r\ntransitive subsets using the character theory of $G \\wr S_n$ and interpret such\r\nsubsets as designs in the conjugacy class association scheme of $G \\wr S_n$. In\r\nparticular, we prove a generalisation of the Livingstone-Wagner theorem and\r\ngive explicit constructions of transitive sets. Moreover, we establish\r\nconnections to orthogonal polynomials, namely the Charlier polynomials, and use\r\nthem to study codes and designs in $C_r \\wr S_n$. Many of our results extend\r\nresults about the symmetric group $S_n$.","lang":"eng"}],"publication":"arXiv:2409.20495","citation":{"short":"L.-A.D. Klawuhn, K.-U. Schmidt, ArXiv:2409.20495 (2024).","chicago":"Klawuhn, Lukas-André Dominik, and Kai-Uwe Schmidt. “Transitivity in Wreath Products with Symmetric Groups.” <i>ArXiv:2409.20495</i>, 2024.","apa":"Klawuhn, L.-A. D., &#38; Schmidt, K.-U. (2024). Transitivity in wreath products with symmetric groups. In <i>arXiv:2409.20495</i>.","ieee":"L.-A. D. Klawuhn and K.-U. Schmidt, “Transitivity in wreath products with symmetric groups,” <i>arXiv:2409.20495</i>. 2024.","ama":"Klawuhn L-AD, Schmidt K-U. Transitivity in wreath products with symmetric groups. <i>arXiv:240920495</i>. Published online 2024.","bibtex":"@article{Klawuhn_Schmidt_2024, title={Transitivity in wreath products with symmetric groups}, journal={arXiv:2409.20495}, author={Klawuhn, Lukas-André Dominik and Schmidt, Kai-Uwe}, year={2024} }","mla":"Klawuhn, Lukas-André Dominik, and Kai-Uwe Schmidt. “Transitivity in Wreath Products with Symmetric Groups.” <i>ArXiv:2409.20495</i>, 2024."},"type":"preprint","department":[{"_id":"100"}],"external_id":{"arxiv":["2409.20495"]},"date_created":"2024-10-08T13:14:45Z"},{"has_accepted_license":"1","status":"public","user_id":"97359","ddc":["510"],"volume":480,"publisher":"The Royal Society","_id":"59171","file_date_updated":"2025-03-27T10:19:48Z","citation":{"ama":"von der Gracht S, Nijholt E, Rink B. Higher-order interactions lead to ‘reluctant’ synchrony breaking. <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. 2024;480(2301). doi:<a href=\"https://doi.org/10.1098/rspa.2023.0945\">10.1098/rspa.2023.0945</a>","bibtex":"@article{von der Gracht_Nijholt_Rink_2024, title={Higher-order interactions lead to ‘reluctant’ synchrony breaking}, volume={480}, DOI={<a href=\"https://doi.org/10.1098/rspa.2023.0945\">10.1098/rspa.2023.0945</a>}, number={2301}, journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, publisher={The Royal Society}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2024} }","mla":"von der Gracht, Sören, et al. “Higher-Order Interactions Lead to ‘Reluctant’ Synchrony Breaking.” <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 480, no. 2301, The Royal Society, 2024, doi:<a href=\"https://doi.org/10.1098/rspa.2023.0945\">10.1098/rspa.2023.0945</a>.","chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Higher-Order Interactions Lead to ‘Reluctant’ Synchrony Breaking.” <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i> 480, no. 2301 (2024). <a href=\"https://doi.org/10.1098/rspa.2023.0945\">https://doi.org/10.1098/rspa.2023.0945</a>.","short":"S. von der Gracht, E. Nijholt, B. Rink, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 480 (2024).","apa":"von der Gracht, S., Nijholt, E., &#38; Rink, B. (2024). Higher-order interactions lead to ‘reluctant’ synchrony breaking. <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, <i>480</i>(2301). <a href=\"https://doi.org/10.1098/rspa.2023.0945\">https://doi.org/10.1098/rspa.2023.0945</a>","ieee":"S. von der Gracht, E. Nijholt, and B. Rink, “Higher-order interactions lead to ‘reluctant’ synchrony breaking,” <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 480, no. 2301, 2024, doi: <a href=\"https://doi.org/10.1098/rspa.2023.0945\">10.1098/rspa.2023.0945</a>."},"oa":"1","publication_status":"published","date_updated":"2025-03-27T10:19:56Z","intvolume":"       480","year":"2024","title":"Higher-order interactions lead to ‘reluctant’ synchrony breaking","author":[{"id":"97359","full_name":"von der Gracht, Sören","first_name":"Sören","orcid":"0000-0002-8054-2058","last_name":"von der Gracht"},{"full_name":"Nijholt, Eddie","first_name":"Eddie","last_name":"Nijholt"},{"full_name":"Rink, Bob","first_name":"Bob","last_name":"Rink"}],"publication_identifier":{"issn":["1364-5021","1471-2946"]},"doi":"10.1098/rspa.2023.0945","language":[{"iso":"eng"}],"abstract":[{"text":"To model dynamical systems on networks with higher-order (non-pairwise) interactions, we recently introduced a new class of ordinary differential equations (ODEs) on hypernetworks. Here, we consider one-parameter synchrony breaking bifurcations in such ODEs. We call a synchrony breaking steady-state branch ‘reluctant’ if it is tangent to a synchrony space, but does not lie inside it. We prove that reluctant synchrony breaking is ubiquitous in hypernetwork systems, by constructing a large class of examples that support it. We also give an explicit formula for the order of tangency to the synchrony space of a reluctant steady-state branch.","lang":"eng"}],"publication":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","issue":"2301","type":"journal_article","keyword":["higher-order interactions","synchrony breaking","network dynamics","coupled cell systems"],"department":[{"_id":"101"}],"file":[{"file_id":"59172","content_type":"application/pdf","file_name":"higher-order-interactions-lead-to-reluctant-synchrony-breaking.pdf","access_level":"open_access","file_size":820435,"relation":"main_file","date_updated":"2025-03-27T10:19:48Z","date_created":"2025-03-27T10:16:20Z","creator":"svdg"}],"date_created":"2025-03-27T10:15:06Z"},{"doi":"10.1016/j.automatica.2022.110840","article_number":"110840","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0005109822007075/pdfft?isDTMRedir=true&download=true","open_access":"1"}],"language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-01-07T12:01:58Z","intvolume":"       149","year":"2023","title":"On the Universal Transformation of Data-Driven Models to Control Systems","author":[{"id":"47427","first_name":"Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","full_name":"Peitz, Sebastian"},{"full_name":"Bieker, Katharina","last_name":"Bieker","first_name":"Katharina","id":"32829"}],"type":"journal_article","department":[{"_id":"101"},{"_id":"655"}],"date_created":"2021-02-10T07:04:15Z","abstract":[{"text":"As in almost every other branch of science, the major advances in data\r\nscience and machine learning have also resulted in significant improvements\r\nregarding the modeling and simulation of nonlinear dynamical systems. It is\r\nnowadays possible to make accurate medium to long-term predictions of highly\r\ncomplex systems such as the weather, the dynamics within a nuclear fusion\r\nreactor, of disease models or the stock market in a very efficient manner. In\r\nmany cases, predictive methods are advertised to ultimately be useful for\r\ncontrol, as the control of high-dimensional nonlinear systems is an engineering\r\ngrand challenge with huge potential in areas such as clean and efficient energy\r\nproduction, or the development of advanced medical devices. However, the\r\nquestion of how to use a predictive model for control is often left unanswered\r\ndue to the associated challenges, namely a significantly higher system\r\ncomplexity, the requirement of much larger data sets and an increased and often\r\nproblem-specific modeling effort. To solve these issues, we present a universal\r\nframework (which we call QuaSiModO:\r\nQuantization-Simulation-Modeling-Optimization) to transform arbitrary\r\npredictive models into control systems and use them for feedback control. The\r\nadvantages of our approach are a linear increase in data requirements with\r\nrespect to the control dimension, performance guarantees that rely exclusively\r\non the accuracy of the predictive model, and only little prior knowledge\r\nrequirements in control theory to solve complex control problems. In particular\r\nthe latter point is of key importance to enable a large number of researchers\r\nand practitioners to exploit the ever increasing capabilities of predictive\r\nmodels for control in a straight-forward and systematic fashion.","lang":"eng"}],"publication":"Automatica","user_id":"47427","volume":149,"publisher":"Elsevier","_id":"21199","status":"public","oa":"1","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"citation":{"mla":"Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of Data-Driven Models to Control Systems.” <i>Automatica</i>, vol. 149, 110840, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">10.1016/j.automatica.2022.110840</a>.","bibtex":"@article{Peitz_Bieker_2023, title={On the Universal Transformation of Data-Driven Models to Control Systems}, volume={149}, DOI={<a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">10.1016/j.automatica.2022.110840</a>}, number={110840}, journal={Automatica}, publisher={Elsevier}, author={Peitz, Sebastian and Bieker, Katharina}, year={2023} }","ama":"Peitz S, Bieker K. On the Universal Transformation of Data-Driven Models to Control Systems. <i>Automatica</i>. 2023;149. doi:<a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">10.1016/j.automatica.2022.110840</a>","ieee":"S. Peitz and K. Bieker, “On the Universal Transformation of Data-Driven Models to Control Systems,” <i>Automatica</i>, vol. 149, Art. no. 110840, 2023, doi: <a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">10.1016/j.automatica.2022.110840</a>.","apa":"Peitz, S., &#38; Bieker, K. (2023). On the Universal Transformation of Data-Driven Models to Control Systems. <i>Automatica</i>, <i>149</i>, Article 110840. <a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">https://doi.org/10.1016/j.automatica.2022.110840</a>","chicago":"Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of Data-Driven Models to Control Systems.” <i>Automatica</i> 149 (2023). <a href=\"https://doi.org/10.1016/j.automatica.2022.110840\">https://doi.org/10.1016/j.automatica.2022.110840</a>.","short":"S. Peitz, K. Bieker, Automatica 149 (2023)."}},{"citation":{"ieee":"S. von der Gracht, E. Nijholt, and B. Rink, “Hypernetworks: Cluster Synchronization Is a Higher-Order Effect,” <i>SIAM Journal on Applied Mathematics</i>, vol. 83, no. 6, pp. 2329–2353, 2023, doi: <a href=\"https://doi.org/10.1137/23m1561075\">10.1137/23m1561075</a>.","apa":"von der Gracht, S., Nijholt, E., &#38; Rink, B. (2023). Hypernetworks: Cluster Synchronization Is a Higher-Order Effect. <i>SIAM Journal on Applied Mathematics</i>, <i>83</i>(6), 2329–2353. <a href=\"https://doi.org/10.1137/23m1561075\">https://doi.org/10.1137/23m1561075</a>","chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Hypernetworks: Cluster Synchronization Is a Higher-Order Effect.” <i>SIAM Journal on Applied Mathematics</i> 83, no. 6 (2023): 2329–53. <a href=\"https://doi.org/10.1137/23m1561075\">https://doi.org/10.1137/23m1561075</a>.","short":"S. von der Gracht, E. Nijholt, B. Rink, SIAM Journal on Applied Mathematics 83 (2023) 2329–2353.","mla":"von der Gracht, Sören, et al. “Hypernetworks: Cluster Synchronization Is a Higher-Order Effect.” <i>SIAM Journal on Applied Mathematics</i>, vol. 83, no. 6, Society for Industrial &#38; Applied Mathematics (SIAM), 2023, pp. 2329–53, doi:<a href=\"https://doi.org/10.1137/23m1561075\">10.1137/23m1561075</a>.","bibtex":"@article{von der Gracht_Nijholt_Rink_2023, title={Hypernetworks: Cluster Synchronization Is a Higher-Order Effect}, volume={83}, DOI={<a href=\"https://doi.org/10.1137/23m1561075\">10.1137/23m1561075</a>}, number={6}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2023}, pages={2329–2353} }","ama":"von der Gracht S, Nijholt E, Rink B. Hypernetworks: Cluster Synchronization Is a Higher-Order Effect. <i>SIAM Journal on Applied Mathematics</i>. 2023;83(6):2329-2353. doi:<a href=\"https://doi.org/10.1137/23m1561075\">10.1137/23m1561075</a>"},"external_id":{"arxiv":["2302.08974"]},"status":"public","publisher":"Society for Industrial & Applied Mathematics (SIAM)","_id":"49326","page":"2329-2353","volume":83,"user_id":"97359","issue":"6","publication":"SIAM Journal on Applied Mathematics","abstract":[{"lang":"eng","text":"Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by defining a class of admissible maps for every such hypernetwork. We explain how to classify robust cluster synchronization patterns on hypernetworks by finding balanced partitions, and we generalize the concept of a graph fibration to the hypernetwork context. We also show that robust synchronization patterns are only fully determined by polynomial admissible maps of high order. This means that, unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order, i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork, for the degree of the polynomial admissible maps that determine robust synchronization patterns. We also demonstrate that this degree is optimal by investigating a class of examples. We conclude by demonstrating how this effect may cause remarkable synchrony breaking bifurcations that occur at high polynomial degree."}],"date_created":"2023-11-29T10:50:05Z","department":[{"_id":"101"}],"type":"journal_article","keyword":["Applied Mathematics"],"author":[{"full_name":"von der Gracht, Sören","orcid":"0000-0002-8054-2058","last_name":"von der Gracht","first_name":"Sören","id":"97359"},{"last_name":"Nijholt","first_name":"Eddie","full_name":"Nijholt, Eddie"},{"full_name":"Rink, Bob","last_name":"Rink","first_name":"Bob"}],"publication_identifier":{"issn":["0036-1399","1095-712X"]},"title":"Hypernetworks: Cluster Synchronization Is a Higher-Order Effect","year":"2023","intvolume":"        83","publication_status":"published","date_updated":"2023-11-29T10:52:23Z","language":[{"iso":"eng"}],"doi":"10.1137/23m1561075"},{"status":"public","title":"Idélic Approach in Enumerating Heisenberg Extensions","year":"2023","author":[{"id":"21202","last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen"},{"full_name":"Wang, Jiuya","first_name":"Jiuya","last_name":"Wang"}],"publication_identifier":{"issn":["2730-9657"]},"date_updated":"2023-12-06T09:50:43Z","publication_status":"published","language":[{"iso":"eng"}],"_id":"49372","publisher":"Springer Science and Business Media LLC","doi":"10.1007/s44007-023-00067-w","user_id":"21202","publication":"La Matematica","citation":{"ieee":"J. Klüners and J. Wang, “Idélic Approach in Enumerating Heisenberg Extensions,” <i>La Matematica</i>, 2023, doi: <a href=\"https://doi.org/10.1007/s44007-023-00067-w\">10.1007/s44007-023-00067-w</a>.","apa":"Klüners, J., &#38; Wang, J. (2023). Idélic Approach in Enumerating Heisenberg Extensions. <i>La Matematica</i>. <a href=\"https://doi.org/10.1007/s44007-023-00067-w\">https://doi.org/10.1007/s44007-023-00067-w</a>","mla":"Klüners, Jürgen, and Jiuya Wang. “Idélic Approach in Enumerating Heisenberg Extensions.” <i>La Matematica</i>, Springer Science and Business Media LLC, 2023, doi:<a href=\"https://doi.org/10.1007/s44007-023-00067-w\">10.1007/s44007-023-00067-w</a>.","bibtex":"@article{Klüners_Wang_2023, title={Idélic Approach in Enumerating Heisenberg Extensions}, DOI={<a href=\"https://doi.org/10.1007/s44007-023-00067-w\">10.1007/s44007-023-00067-w</a>}, journal={La Matematica}, publisher={Springer Science and Business Media LLC}, author={Klüners, Jürgen and Wang, Jiuya}, year={2023} }","chicago":"Klüners, Jürgen, and Jiuya Wang. “Idélic Approach in Enumerating Heisenberg Extensions.” <i>La Matematica</i>, 2023. <a href=\"https://doi.org/10.1007/s44007-023-00067-w\">https://doi.org/10.1007/s44007-023-00067-w</a>.","short":"J. Klüners, J. Wang, La Matematica (2023).","ama":"Klüners J, Wang J. Idélic Approach in Enumerating Heisenberg Extensions. <i>La Matematica</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1007/s44007-023-00067-w\">10.1007/s44007-023-00067-w</a>"},"date_created":"2023-12-01T09:23:59Z","type":"journal_article","department":[{"_id":"102"}]},{"user_id":"85279","ddc":["510"],"volume":56,"page":"3203-3210","_id":"34135","publisher":"Elsevier","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"},"oa":"1","external_id":{"arxiv":["2211.10830"]},"quality_controlled":"1","file_date_updated":"2023-04-17T08:05:55Z","citation":{"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>","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} }","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>.","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.","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>","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>."},"doi":"10.1016/j.ifacol.2023.10.1457","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S2405896323018657"}],"language":[{"iso":"eng"}],"publication_status":"published","date_updated":"2023-12-29T14:26:00Z","intvolume":"        56","year":"2023","title":"Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery","author":[{"full_name":"Lishkova, Yana","last_name":"Lishkova","first_name":"Yana"},{"full_name":"Scherer, Paul","last_name":"Scherer","first_name":"Paul"},{"last_name":"Ridderbusch","first_name":"Steffen","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","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"},{"full_name":"Offen, Christian","first_name":"Christian","last_name":"Offen","orcid":"0000-0002-5940-8057","id":"85279"}],"type":"conference","department":[{"_id":"636"}],"file":[{"relation":"main_file","date_updated":"2023-04-17T08:05:55Z","file_name":"LNN_project.pdf","access_level":"open_access","file_size":576115,"title":"Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery","file_id":"44037","content_type":"application/pdf","creator":"coffen","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"}],"date_created":"2022-11-23T08:17:10Z","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":[{"description":"GitHub","url":"https://github.com/yanalish/SymDLNN","relation":"software"}]},"issue":"2","publication":"IFAC-PapersOnLine"},{"volume":3,"doi":"10.5070/c63160424","user_id":"70420","_id":"50298","language":[{"iso":"eng"}],"intvolume":"         3","date_updated":"2024-01-08T14:39:20Z","publication_status":"published","author":[{"full_name":"Schmidt, Kai-Uwe","last_name":"Schmidt","first_name":"Kai-Uwe"},{"first_name":"Charlene","last_name":"Weiß","full_name":"Weiß, Charlene","id":"70420"}],"status":"public","title":"Packings and Steiner systems in polar spaces","year":"2023","department":[{"_id":"100"}],"type":"journal_article","date_created":"2024-01-08T14:33:54Z","abstract":[{"text":"A finite classical polar space of rank $n$ consists of the totally isotropic subspaces of a finite vector space equipped with a nondegenerate form such that $n$ is the maximal dimension of such a subspace. A $t$-Steiner system in a finite classical polar space of rank $n$ is a collection $Y$ of totally isotropic $n$-spaces such that each totally isotropic $t$-space is contained in exactly one member of $Y$. Nontrivial examples are known only for $t=1$ and $t=n-1$. We give an almost complete classification of such $t$-Steiner systems, showing that such objects can only exist in some corner cases. This classification result arises from a more general result on packings in polar spaces.","lang":"eng"}],"citation":{"ama":"Schmidt K-U, Weiß C. Packings and Steiner systems in polar spaces. <i>Combinatorial Theory</i>. 2023;3(1). doi:<a href=\"https://doi.org/10.5070/c63160424\">10.5070/c63160424</a>","bibtex":"@article{Schmidt_Weiß_2023, title={Packings and Steiner systems in polar spaces}, volume={3}, DOI={<a href=\"https://doi.org/10.5070/c63160424\">10.5070/c63160424</a>}, number={1}, journal={Combinatorial Theory}, author={Schmidt, Kai-Uwe and Weiß, Charlene}, year={2023} }","mla":"Schmidt, Kai-Uwe, and Charlene Weiß. “Packings and Steiner Systems in Polar Spaces.” <i>Combinatorial Theory</i>, vol. 3, no. 1, 2023, doi:<a href=\"https://doi.org/10.5070/c63160424\">10.5070/c63160424</a>.","chicago":"Schmidt, Kai-Uwe, and Charlene Weiß. “Packings and Steiner Systems in Polar Spaces.” <i>Combinatorial Theory</i> 3, no. 1 (2023). <a href=\"https://doi.org/10.5070/c63160424\">https://doi.org/10.5070/c63160424</a>.","short":"K.-U. Schmidt, C. Weiß, Combinatorial Theory 3 (2023).","apa":"Schmidt, K.-U., &#38; Weiß, C. (2023). Packings and Steiner systems in polar spaces. <i>Combinatorial Theory</i>, <i>3</i>(1). <a href=\"https://doi.org/10.5070/c63160424\">https://doi.org/10.5070/c63160424</a>","ieee":"K.-U. Schmidt and C. Weiß, “Packings and Steiner systems in polar spaces,” <i>Combinatorial Theory</i>, vol. 3, no. 1, 2023, doi: <a href=\"https://doi.org/10.5070/c63160424\">10.5070/c63160424</a>."},"issue":"1","publication":"Combinatorial Theory"},{"user_id":"70420","volume":31,"page":"422-431","_id":"50297","publisher":"Wiley","status":"public","citation":{"apa":"Schmidt, K., &#38; Weiß, C. (2023). Existence of small ordered orthogonal arrays. <i>Journal of Combinatorial Designs</i>, <i>31</i>(9), 422–431. <a href=\"https://doi.org/10.1002/jcd.21903\">https://doi.org/10.1002/jcd.21903</a>","ieee":"K. Schmidt and C. Weiß, “Existence of small ordered orthogonal arrays,” <i>Journal of Combinatorial Designs</i>, vol. 31, no. 9, pp. 422–431, 2023, doi: <a href=\"https://doi.org/10.1002/jcd.21903\">10.1002/jcd.21903</a>.","chicago":"Schmidt, Kai‐Uwe, and Charlene Weiß. “Existence of Small Ordered Orthogonal Arrays.” <i>Journal of Combinatorial Designs</i> 31, no. 9 (2023): 422–31. <a href=\"https://doi.org/10.1002/jcd.21903\">https://doi.org/10.1002/jcd.21903</a>.","short":"K. Schmidt, C. Weiß, Journal of Combinatorial Designs 31 (2023) 422–431.","mla":"Schmidt, Kai‐Uwe, and Charlene Weiß. “Existence of Small Ordered Orthogonal Arrays.” <i>Journal of Combinatorial Designs</i>, vol. 31, no. 9, Wiley, 2023, pp. 422–31, doi:<a href=\"https://doi.org/10.1002/jcd.21903\">10.1002/jcd.21903</a>.","ama":"Schmidt K, Weiß C. Existence of small ordered orthogonal arrays. <i>Journal of Combinatorial Designs</i>. 2023;31(9):422-431. doi:<a href=\"https://doi.org/10.1002/jcd.21903\">10.1002/jcd.21903</a>","bibtex":"@article{Schmidt_Weiß_2023, title={Existence of small ordered orthogonal arrays}, volume={31}, DOI={<a href=\"https://doi.org/10.1002/jcd.21903\">10.1002/jcd.21903</a>}, number={9}, journal={Journal of Combinatorial Designs}, publisher={Wiley}, author={Schmidt, Kai‐Uwe and Weiß, Charlene}, year={2023}, pages={422–431} }"},"doi":"10.1002/jcd.21903","language":[{"iso":"eng"}],"date_updated":"2024-01-08T14:38:53Z","publication_status":"published","intvolume":"        31","year":"2023","title":"Existence of small ordered orthogonal arrays","author":[{"last_name":"Schmidt","first_name":"Kai‐Uwe","full_name":"Schmidt, Kai‐Uwe"},{"last_name":"Weiß","first_name":"Charlene","full_name":"Weiß, Charlene","id":"70420"}],"type":"journal_article","department":[{"_id":"100"}],"date_created":"2024-01-08T14:25:28Z","abstract":[{"text":"We show that there exist ordered orthogonal arrays, whose sizes deviate from the Rao bound by a factor that is polynomial in the parameters of the ordered orthogonal array. The proof is nonconstructive and based on a probabilistic method due to Kuperberg, Lovett and Peled.","lang":"eng"}],"publication":"Journal of Combinatorial Designs","issue":"9"},{"author":[{"id":"70420","last_name":"Weiß","first_name":"Charlene","full_name":"Weiß, Charlene"}],"title":"Linear programming bounds in classical association schemes","status":"public","year":"2023","date_updated":"2024-01-08T14:46:14Z","language":[{"iso":"eng"}],"_id":"50300","user_id":"70420","doi":"10.17619/UNIPB/1-1672","citation":{"apa":"Weiß, C. (2023). <i>Linear programming bounds in classical association schemes</i>. <a href=\"https://doi.org/10.17619/UNIPB/1-1672\">https://doi.org/10.17619/UNIPB/1-1672</a>","ieee":"C. Weiß, <i>Linear programming bounds in classical association schemes</i>. 2023.","short":"C. Weiß, Linear Programming Bounds in Classical Association Schemes, 2023.","chicago":"Weiß, Charlene. <i>Linear Programming Bounds in Classical Association Schemes</i>, 2023. <a href=\"https://doi.org/10.17619/UNIPB/1-1672\">https://doi.org/10.17619/UNIPB/1-1672</a>.","mla":"Weiß, Charlene. <i>Linear Programming Bounds in Classical Association Schemes</i>. 2023, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1672\">10.17619/UNIPB/1-1672</a>.","ama":"Weiß C. <i>Linear Programming Bounds in Classical Association Schemes</i>.; 2023. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-1672\">10.17619/UNIPB/1-1672</a>","bibtex":"@book{Weiß_2023, title={Linear programming bounds in classical association schemes}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-1672\">10.17619/UNIPB/1-1672</a>}, author={Weiß, Charlene}, year={2023} }"},"abstract":[{"text":"Digital communications relies heavily on the usage of different types of codes. Prominent codes nowadays are rank-metric codes and subspace codes - the q-analogs of binary codes and binary codes with constant weight. All these codes can be viewed as subsets of classical association schemes. A central coding-theoretic problem is to derive upper bounds for the size of codes. This thesis investigates Delsartes powerful linear program whose optimum is precisely such a bound for codes in association schemes. The linear programs for binary codes and binary constant-weight codes have been extensively studied since the 1970s, but their optimum is still unknown. We determine in a unified way the optimum of the linear program in several ordinary q-analogs as well as in their affine counterparts. In particular, bounds and constructions for codes in polar spaces are established, where the bounds are sharp up to a constant factor in many cases. Moreover, based on these results, an almost complete classification of Steiner systems in polar spaces is provided by showing that they could only exist in some corner cases.","lang":"eng"}],"date_created":"2024-01-08T14:42:12Z","department":[{"_id":"100"}],"type":"dissertation"},{"publication":"Discrete Applied Mathematics","department":[{"_id":"542"}],"keyword":["Applied Mathematics","Discrete Mathematics and Combinatorics"],"type":"journal_article","date_created":"2024-02-14T17:33:29Z","intvolume":"       337","date_updated":"2024-02-14T17:33:59Z","publication_status":"published","publication_identifier":{"issn":["0166-218X"]},"author":[{"id":"15548","last_name":"Steffen","first_name":"Eckhard","orcid":"0000-0002-9808-7401","full_name":"Steffen, Eckhard"},{"last_name":"Wolf","first_name":"Isaak Hieronymus","full_name":"Wolf, Isaak Hieronymus","id":"88145"}],"year":"2023","title":"Bounds for the chromatic index of signed multigraphs","doi":"10.1016/j.dam.2023.05.008","language":[{"iso":"eng"}],"citation":{"apa":"Steffen, E., &#38; Wolf, I. H. (2023). Bounds for the chromatic index of signed multigraphs. <i>Discrete Applied Mathematics</i>, <i>337</i>, 185–189. <a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">https://doi.org/10.1016/j.dam.2023.05.008</a>","ieee":"E. Steffen and I. H. Wolf, “Bounds for the chromatic index of signed multigraphs,” <i>Discrete Applied Mathematics</i>, vol. 337, pp. 185–189, 2023, doi: <a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">10.1016/j.dam.2023.05.008</a>.","chicago":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic Index of Signed Multigraphs.” <i>Discrete Applied Mathematics</i> 337 (2023): 185–89. <a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">https://doi.org/10.1016/j.dam.2023.05.008</a>.","short":"E. Steffen, I.H. Wolf, Discrete Applied Mathematics 337 (2023) 185–189.","mla":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic Index of Signed Multigraphs.” <i>Discrete Applied Mathematics</i>, vol. 337, Elsevier BV, 2023, pp. 185–89, doi:<a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">10.1016/j.dam.2023.05.008</a>.","ama":"Steffen E, Wolf IH. Bounds for the chromatic index of signed multigraphs. <i>Discrete Applied Mathematics</i>. 2023;337:185-189. doi:<a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">10.1016/j.dam.2023.05.008</a>","bibtex":"@article{Steffen_Wolf_2023, title={Bounds for the chromatic index of signed multigraphs}, volume={337}, DOI={<a href=\"https://doi.org/10.1016/j.dam.2023.05.008\">10.1016/j.dam.2023.05.008</a>}, journal={Discrete Applied Mathematics}, publisher={Elsevier BV}, author={Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={185–189} }"},"status":"public","volume":337,"user_id":"15540","_id":"51351","publisher":"Elsevier BV","page":"185-189"},{"status":"public","year":"2023","title":"Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks","publication_identifier":{"isbn":["9783031261039","9783031261046"]},"author":[{"first_name":"Chiara","last_name":"Cappello","full_name":"Cappello, Chiara","id":"72874"},{"id":"15548","full_name":"Steffen, Eckhard","orcid":"0000-0002-9808-7401","last_name":"Steffen","first_name":"Eckhard"}],"publication_status":"published","date_updated":"2024-02-16T07:42:38Z","page":"93--110","_id":"45190","language":[{"iso":"eng"}],"publisher":"Springer International Publishing","user_id":"15540","doi":"10.1007/978-3-031-26104-6_5","publication":"The Digital Twin of Humans","citation":{"short":"C. Cappello, E. Steffen, in: The Digital Twin of Humans, Springer International Publishing, Cham, 2023, pp. 93--110.","chicago":"Cappello, Chiara, and Eckhard Steffen. “Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks.” In <i>The Digital Twin of Humans</i>, 93--110. Cham: Springer International Publishing, 2023. <a href=\"https://doi.org/10.1007/978-3-031-26104-6_5\">https://doi.org/10.1007/978-3-031-26104-6_5</a>.","apa":"Cappello, C., &#38; Steffen, E. (2023). Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks. In <i>The Digital Twin of Humans</i> (pp. 93--110). Springer International Publishing. <a href=\"https://doi.org/10.1007/978-3-031-26104-6_5\">https://doi.org/10.1007/978-3-031-26104-6_5</a>","ieee":"C. Cappello and E. Steffen, “Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks,” in <i>The Digital Twin of Humans</i>, Cham: Springer International Publishing, 2023, pp. 93--110.","ama":"Cappello C, Steffen E. Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks. In: <i>The Digital Twin of Humans</i>. Springer International Publishing; 2023:93--110. doi:<a href=\"https://doi.org/10.1007/978-3-031-26104-6_5\">10.1007/978-3-031-26104-6_5</a>","bibtex":"@inbook{Cappello_Steffen_2023, place={Cham}, title={Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks}, DOI={<a href=\"https://doi.org/10.1007/978-3-031-26104-6_5\">10.1007/978-3-031-26104-6_5</a>}, booktitle={The Digital Twin of Humans}, publisher={Springer International Publishing}, author={Cappello, Chiara and Steffen, Eckhard}, year={2023}, pages={93--110} }","mla":"Cappello, Chiara, and Eckhard Steffen. “Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks.” <i>The Digital Twin of Humans</i>, Springer International Publishing, 2023, pp. 93--110, doi:<a href=\"https://doi.org/10.1007/978-3-031-26104-6_5\">10.1007/978-3-031-26104-6_5</a>."},"date_created":"2023-05-22T10:22:21Z","place":"Cham","type":"book_chapter","department":[{"_id":"542"}]},{"department":[{"_id":"542"}],"keyword":["Discrete Mathematics and Combinatorics","Theoretical Computer Science"],"type":"journal_article","date_created":"2024-02-16T08:44:50Z","citation":{"chicago":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” <i>Discrete Mathematics</i>, 2023. <a href=\"https://doi.org/10.1016/j.disc.2023.113457\">https://doi.org/10.1016/j.disc.2023.113457</a>.","short":"E. Steffen, I.H. Wolf, Discrete Mathematics (2023).","ieee":"E. Steffen and I. H. Wolf, “Rotation r-graphs,” <i>Discrete Mathematics</i>, Art. no. 113457, 2023, doi: <a href=\"https://doi.org/10.1016/j.disc.2023.113457\">10.1016/j.disc.2023.113457</a>.","apa":"Steffen, E., &#38; Wolf, I. H. (2023). Rotation r-graphs. <i>Discrete Mathematics</i>, Article 113457. <a href=\"https://doi.org/10.1016/j.disc.2023.113457\">https://doi.org/10.1016/j.disc.2023.113457</a>","bibtex":"@article{Steffen_Wolf_2023, title={Rotation r-graphs}, DOI={<a href=\"https://doi.org/10.1016/j.disc.2023.113457\">10.1016/j.disc.2023.113457</a>}, number={113457}, journal={Discrete Mathematics}, publisher={Elsevier BV}, author={Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023} }","ama":"Steffen E, Wolf IH. Rotation r-graphs. <i>Discrete Mathematics</i>. Published online 2023. doi:<a href=\"https://doi.org/10.1016/j.disc.2023.113457\">10.1016/j.disc.2023.113457</a>","mla":"Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” <i>Discrete Mathematics</i>, 113457, Elsevier BV, 2023, doi:<a href=\"https://doi.org/10.1016/j.disc.2023.113457\">10.1016/j.disc.2023.113457</a>."},"publication":"Discrete Mathematics","doi":"10.1016/j.disc.2023.113457","user_id":"15540","language":[{"iso":"eng"}],"_id":"51357","publisher":"Elsevier BV","article_number":"113457","date_updated":"2024-02-16T08:45:10Z","publication_status":"published","publication_identifier":{"issn":["0012-365X"]},"author":[{"id":"15548","full_name":"Steffen, Eckhard","first_name":"Eckhard","last_name":"Steffen","orcid":"0000-0002-9808-7401"},{"full_name":"Wolf, Isaak Hieronymus","first_name":"Isaak Hieronymus","last_name":"Wolf","id":"88145"}],"year":"2023","title":"Rotation r-graphs","status":"public"},{"language":[{"iso":"eng"}],"_id":"46578","main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2308.01113"}],"user_id":"47427","author":[{"last_name":"Bernreuther","first_name":"Marco","full_name":"Bernreuther, Marco"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"id":"32643","first_name":"Bennet","last_name":"Gebken","full_name":"Gebken, Bennet"},{"full_name":"Müller, Georg","last_name":"Müller","first_name":"Georg"},{"full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian","id":"47427"},{"full_name":"Sonntag, Konstantin","first_name":"Konstantin","last_name":"Sonntag","orcid":"https://orcid.org/0000-0003-3384-3496","id":"56399"},{"last_name":"Volkwein","first_name":"Stefan","full_name":"Volkwein, Stefan"}],"year":"2023","title":"Multiobjective Optimization of Non-Smooth PDE-Constrained Problems","status":"public","date_updated":"2024-02-21T12:22:20Z","date_created":"2023-08-21T05:50:12Z","external_id":{"arxiv":["2308.01113"]},"oa":"1","department":[{"_id":"655"},{"_id":"101"}],"type":"preprint","citation":{"ieee":"M. Bernreuther <i>et al.</i>, “Multiobjective Optimization of Non-Smooth PDE-Constrained Problems,” <i>arXiv:2308.01113</i>. 2023.","apa":"Bernreuther, M., Dellnitz, M., Gebken, B., Müller, G., Peitz, S., Sonntag, K., &#38; Volkwein, S. (2023). Multiobjective Optimization of Non-Smooth PDE-Constrained Problems. In <i>arXiv:2308.01113</i>.","short":"M. Bernreuther, M. Dellnitz, B. Gebken, G. Müller, S. Peitz, K. Sonntag, S. Volkwein, ArXiv:2308.01113 (2023).","chicago":"Bernreuther, Marco, Michael Dellnitz, Bennet Gebken, Georg Müller, Sebastian Peitz, Konstantin Sonntag, and Stefan Volkwein. “Multiobjective Optimization of Non-Smooth PDE-Constrained Problems.” <i>ArXiv:2308.01113</i>, 2023.","mla":"Bernreuther, Marco, et al. “Multiobjective Optimization of Non-Smooth PDE-Constrained Problems.” <i>ArXiv:2308.01113</i>, 2023.","bibtex":"@article{Bernreuther_Dellnitz_Gebken_Müller_Peitz_Sonntag_Volkwein_2023, title={Multiobjective Optimization of Non-Smooth PDE-Constrained Problems}, journal={arXiv:2308.01113}, author={Bernreuther, Marco and Dellnitz, Michael and Gebken, Bennet and Müller, Georg and Peitz, Sebastian and Sonntag, Konstantin and Volkwein, Stefan}, year={2023} }","ama":"Bernreuther M, Dellnitz M, Gebken B, et al. Multiobjective Optimization of Non-Smooth PDE-Constrained Problems. <i>arXiv:230801113</i>. Published online 2023."},"publication":"arXiv:2308.01113","abstract":[{"lang":"eng","text":"Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 \"Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction\" of the DFG Priority Programm 1962 \"Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization\"."}]}]