--- _id: '32097' author: - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 - first_name: Yannick full_name: Guedes Bonthonneau, Yannick last_name: Guedes Bonthonneau - first_name: Colin full_name: Guillarmou, Colin last_name: Guillarmou citation: ama: Weich T, Guedes Bonthonneau Y, Guillarmou C. SRB Measures of Anosov Actions. Journal of Differential Geometry (to appear) --  arXiv:210312127. Published online 2024. apa: Weich, T., Guedes Bonthonneau, Y., & Guillarmou, C. (2024). SRB Measures of Anosov Actions. Journal of Differential Geometry (to Appear) --  ArXiv:2103.12127. bibtex: '@article{Weich_Guedes Bonthonneau_Guillarmou_2024, title={SRB Measures of Anosov Actions}, journal={Journal of Differential Geometry (to appear) --  arXiv:2103.12127}, author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin}, year={2024} }' chicago: Weich, Tobias, Yannick Guedes Bonthonneau, and Colin Guillarmou. “SRB Measures of Anosov Actions.” Journal of Differential Geometry (to Appear) --  ArXiv:2103.12127, 2024. ieee: T. Weich, Y. Guedes Bonthonneau, and C. Guillarmou, “SRB Measures of Anosov Actions,” Journal of Differential Geometry (to appear) --  arXiv:2103.12127, 2024. mla: Weich, Tobias, et al. “SRB Measures of Anosov Actions.” Journal of Differential Geometry (to Appear) --  ArXiv:2103.12127, 2024. short: T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, Journal of Differential Geometry (to Appear) --  ArXiv:2103.12127 (2024). date_created: 2022-06-22T09:56:23Z date_updated: 2023-12-21T09:47:22Z ddc: - '510' department: - _id: '10' - _id: '623' - _id: '548' external_id: arxiv: - https://arxiv.org/abs/2103.12127 file: - access_level: open_access content_type: application/pdf creator: weich date_created: 2022-06-22T09:56:08Z date_updated: 2022-06-22T09:56:08Z file_id: '32098' file_name: 2103.12127.pdf file_size: 745870 relation: main_file file_date_updated: 2022-06-22T09:56:08Z has_accepted_license: '1' language: - iso: eng oa: '1' publication: Journal of Differential Geometry (to appear) -- arXiv:2103.12127 status: public title: SRB Measures of Anosov Actions type: journal_article user_id: '49178' year: '2024' ... --- _id: '46469' 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. ' article_number: '013104' article_type: original author: - first_name: Christian full_name: Offen, Christian id: '85279' last_name: Offen orcid: 0000-0002-5940-8057 - first_name: Sina full_name: Ober-Blöbaum, Sina id: '16494' last_name: Ober-Blöbaum citation: ama: Offen C, Ober-Blöbaum S. Learning of discrete models of variational PDEs from data. Chaos. 2024;34(1). doi:10.1063/5.0172287 apa: Offen, C., & Ober-Blöbaum, S. (2024). Learning of discrete models of variational PDEs from data. Chaos, 34(1), Article 013104. https://doi.org/10.1063/5.0172287 bibtex: '@article{Offen_Ober-Blöbaum_2024, title={Learning of discrete models of variational PDEs from data}, volume={34}, DOI={10.1063/5.0172287}, number={1013104}, journal={Chaos}, publisher={AIP Publishing}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2024} }' chicago: Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” Chaos 34, no. 1 (2024). https://doi.org/10.1063/5.0172287. ieee: 'C. Offen and S. Ober-Blöbaum, “Learning of discrete models of variational PDEs from data,” Chaos, vol. 34, no. 1, Art. no. 013104, 2024, doi: 10.1063/5.0172287.' mla: Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” Chaos, vol. 34, no. 1, 013104, AIP Publishing, 2024, doi:10.1063/5.0172287. short: C. Offen, S. Ober-Blöbaum, Chaos 34 (2024). date_created: 2023-08-10T08:24:48Z date_updated: 2024-01-09T11:29:06Z ddc: - '510' department: - _id: '636' doi: 10.1063/5.0172287 external_id: arxiv: - '2308.05082 ' file: - access_level: open_access content_type: application/pdf creator: coffen date_created: 2024-01-09T10:48:38Z date_updated: 2024-01-09T10:48:38Z file_id: '50376' file_name: Accepted manuscript with AIP banner CHA23-AR-01370.pdf file_size: 13222105 relation: main_file title: Accepted Manuscript Chaos - access_level: open_access content_type: application/pdf creator: coffen date_created: 2024-01-09T11:19:49Z date_updated: 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 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. file_id: '50390' file_name: LDensityPDE_AIP.pdf file_size: 12960884 relation: main_file title: Learning of discrete models of variational PDEs from data file_date_updated: 2024-01-09T11:19:49Z has_accepted_license: '1' intvolume: ' 34' issue: '1' language: - iso: eng oa: '1' publication: Chaos publication_identifier: issn: - 1054-1500 publication_status: published publisher: AIP Publishing quality_controlled: '1' related_material: link: - description: GitHub relation: software url: https://github.com/Christian-Offen/DLNN_pde status: public title: Learning of discrete models of variational PDEs from data type: journal_article user_id: '85279' volume: 34 year: '2024' ... --- _id: '50554' author: - first_name: Susanne full_name: Prediger, Susanne last_name: Prediger - first_name: Lena full_name: Wessel, Lena id: '85190' last_name: Wessel citation: ama: 'Prediger S, Wessel L. 31 Sprachbildung im berufsbezogenen Mathematikunterricht. In: Efing C, Kalkavan-Aydin Z, eds. Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis. Vol Band 3. DaZ-Handbücher. DE GRUYTER; 2024:363-372.' apa: 'Prediger, S., & Wessel, L. (2024). 31 Sprachbildung im berufsbezogenen Mathematikunterricht. In C. Efing & Z. Kalkavan-Aydin (Eds.), Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis: Vol. Band 3 (pp. 363–372). DE GRUYTER.' bibtex: '@inbook{Prediger_Wessel_2024, place={Berlin}, series={DaZ-Handbücher}, title={31 Sprachbildung im berufsbezogenen Mathematikunterricht.}, volume={Band 3}, booktitle={Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis}, publisher={DE GRUYTER}, author={Prediger, Susanne and Wessel, Lena}, editor={Efing, Christian and Kalkavan-Aydin, Zeynep}, year={2024}, pages={363–372}, collection={DaZ-Handbücher} }' chicago: 'Prediger, Susanne, and Lena Wessel. “31 Sprachbildung im berufsbezogenen Mathematikunterricht.” In Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, edited by Christian Efing and Zeynep Kalkavan-Aydin, Band 3:363–72. DaZ-Handbücher. Berlin: DE GRUYTER, 2024.' ieee: 'S. Prediger and L. Wessel, “31 Sprachbildung im berufsbezogenen Mathematikunterricht.,” in Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, vol. Band 3, C. Efing and Z. Kalkavan-Aydin, Eds. Berlin: DE GRUYTER, 2024, pp. 363–372.' mla: Prediger, Susanne, and Lena Wessel. “31 Sprachbildung im berufsbezogenen Mathematikunterricht.” Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, edited by Christian Efing and Zeynep Kalkavan-Aydin, vol. Band 3, DE GRUYTER, 2024, pp. 363–72. short: 'S. Prediger, L. Wessel, in: C. Efing, Z. Kalkavan-Aydin (Eds.), Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, DE GRUYTER, Berlin, 2024, pp. 363–372.' date_created: 2024-01-17T10:58:04Z date_updated: 2024-01-17T11:07:21Z department: - _id: '34' - _id: '10' - _id: '643' editor: - first_name: Christian full_name: Efing, Christian last_name: Efing - first_name: Zeynep full_name: Kalkavan-Aydin, Zeynep last_name: Kalkavan-Aydin language: - iso: ger main_file_link: - open_access: '1' url: https://www.degruyter.com/document/doi/10.1515/9783110745504/pdf?licenseType=restricted#page=381 oa: '1' page: 363-372 place: Berlin publication: Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis publication_identifier: isbn: - 978-3-11-074544-3 publication_status: published publisher: DE GRUYTER series_title: DaZ-Handbücher status: public title: 31 Sprachbildung im berufsbezogenen Mathematikunterricht. type: book_chapter user_id: '37888' volume: Band 3 year: '2024' ... --- _id: '51208' abstract: - lang: eng text: AbstractApproximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions. author: - first_name: Bennet full_name: Gebken, Bennet id: '32643' last_name: Gebken citation: ama: Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth optimization. Computational Optimization and Applications. Published online 2024. doi:10.1007/s10589-024-00552-0 apa: Gebken, B. (2024). A note on the convergence of deterministic gradient sampling in nonsmooth optimization. Computational Optimization and Applications. https://doi.org/10.1007/s10589-024-00552-0 bibtex: '@article{Gebken_2024, title={A note on the convergence of deterministic gradient sampling in nonsmooth optimization}, DOI={10.1007/s10589-024-00552-0}, journal={Computational Optimization and Applications}, publisher={Springer Science and Business Media LLC}, author={Gebken, Bennet}, year={2024} }' chicago: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling in Nonsmooth Optimization.” Computational Optimization and Applications, 2024. https://doi.org/10.1007/s10589-024-00552-0. ieee: 'B. Gebken, “A note on the convergence of deterministic gradient sampling in nonsmooth optimization,” Computational Optimization and Applications, 2024, doi: 10.1007/s10589-024-00552-0.' mla: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling in Nonsmooth Optimization.” Computational Optimization and Applications, Springer Science and Business Media LLC, 2024, doi:10.1007/s10589-024-00552-0. short: B. Gebken, Computational Optimization and Applications (2024). date_created: 2024-02-07T07:23:23Z date_updated: 2024-02-08T08:05:54Z department: - _id: '101' doi: 10.1007/s10589-024-00552-0 keyword: - Applied Mathematics - Computational Mathematics - Control and Optimization language: - iso: eng publication: Computational Optimization and Applications publication_identifier: issn: - 0926-6003 - 1573-2894 publication_status: published publisher: Springer Science and Business Media LLC status: public title: A note on the convergence of deterministic gradient sampling in nonsmooth optimization type: journal_article user_id: '32643' year: '2024' ... --- _id: '51204' abstract: - lang: eng text: "Given a real semisimple connected Lie group $G$ and a discrete torsion-free\r\nsubgroup $\\Gamma < G$ we prove a precise connection between growth rates of the\r\ngroup $\\Gamma$, polyhedral bounds on the joint spectrum of the ring of\r\ninvariant differential operators, and the decay of matrix coefficients. In\r\nparticular, this allows us to completely characterize temperedness of\r\n$L^2(\\Gamma\\backslash G)$ in this general setting." author: - first_name: Christopher full_name: Lutsko, Christopher last_name: Lutsko - first_name: Tobias full_name: Weich, Tobias last_name: Weich - first_name: Lasse Lennart full_name: Wolf, Lasse Lennart id: '45027' last_name: Wolf citation: ama: Lutsko C, Weich T, Wolf LL. Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces. arXiv:240202530. Published online 2024. apa: Lutsko, C., Weich, T., & Wolf, L. L. (2024). Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces. In arXiv:2402.02530. bibtex: '@article{Lutsko_Weich_Wolf_2024, title={Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces}, journal={arXiv:2402.02530}, author={Lutsko, Christopher and Weich, Tobias and Wolf, Lasse Lennart}, year={2024} }' chicago: Lutsko, Christopher, Tobias Weich, and Lasse Lennart Wolf. “Polyhedral Bounds on the Joint Spectrum and Temperedness of Locally  Symmetric Spaces.” ArXiv:2402.02530, 2024. ieee: C. Lutsko, T. Weich, and L. L. Wolf, “Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces,” arXiv:2402.02530. 2024. mla: Lutsko, Christopher, et al. “Polyhedral Bounds on the Joint Spectrum and Temperedness of Locally  Symmetric Spaces.” ArXiv:2402.02530, 2024. short: C. Lutsko, T. Weich, L.L. Wolf, ArXiv:2402.02530 (2024). date_created: 2024-02-06T20:35:36Z date_updated: 2024-02-11T19:56:35Z department: - _id: '10' - _id: '623' - _id: '548' external_id: arxiv: - '2402.02530' language: - iso: eng publication: arXiv:2402.02530 status: public title: Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces type: preprint user_id: '49178' year: '2024' ... --- _id: '51374' article_number: '110319' author: - first_name: David full_name: Hasler, David last_name: Hasler - first_name: Benjamin full_name: Hinrichs, Benjamin id: '99427' last_name: Hinrichs orcid: 0000-0001-9074-1205 - first_name: Oliver full_name: Siebert, Oliver last_name: Siebert citation: ama: Hasler D, Hinrichs B, Siebert O. Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively. Journal of Functional Analysis. 2024;286(7). doi:10.1016/j.jfa.2024.110319 apa: Hasler, D., Hinrichs, B., & Siebert, O. (2024). Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively. Journal of Functional Analysis, 286(7), Article 110319. https://doi.org/10.1016/j.jfa.2024.110319 bibtex: '@article{Hasler_Hinrichs_Siebert_2024, title={Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively}, volume={286}, DOI={10.1016/j.jfa.2024.110319}, number={7110319}, journal={Journal of Functional Analysis}, publisher={Elsevier BV}, author={Hasler, David and Hinrichs, Benjamin and Siebert, Oliver}, year={2024} }' chicago: Hasler, David, Benjamin Hinrichs, and Oliver Siebert. “Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively.” Journal of Functional Analysis 286, no. 7 (2024). https://doi.org/10.1016/j.jfa.2024.110319. ieee: 'D. Hasler, B. Hinrichs, and O. Siebert, “Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively,” Journal of Functional Analysis, vol. 286, no. 7, Art. no. 110319, 2024, doi: 10.1016/j.jfa.2024.110319.' mla: Hasler, David, et al. “Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively.” Journal of Functional Analysis, vol. 286, no. 7, 110319, Elsevier BV, 2024, doi:10.1016/j.jfa.2024.110319. short: D. Hasler, B. Hinrichs, O. Siebert, Journal of Functional Analysis 286 (2024). date_created: 2024-02-18T12:31:28Z date_updated: 2024-02-18T12:32:23Z department: - _id: '799' doi: 10.1016/j.jfa.2024.110319 extern: '1' external_id: arxiv: - '2302.06998' intvolume: ' 286' issue: '7' keyword: - Analysis language: - iso: eng publication: Journal of Functional Analysis publication_identifier: issn: - 0022-1236 publication_status: published publisher: Elsevier BV status: public title: Non-Fock ground states in the translation-invariant Nelson model revisited non-perturbatively type: journal_article user_id: '99427' volume: 286 year: '2024' ... --- _id: '32101' author: - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 - first_name: Yannick full_name: Guedes Bonthonneau, Yannick last_name: Guedes Bonthonneau - first_name: Colin full_name: Guillarmou, Colin last_name: Guillarmou - first_name: Joachim full_name: Hilgert, Joachim id: '220' last_name: Hilgert citation: ama: Weich T, Guedes Bonthonneau Y, Guillarmou C, Hilgert J. Ruelle-Taylor resonaces of Anosov actions. J Europ Math Soc. Published online 2024:1-36. apa: Weich, T., Guedes Bonthonneau, Y., Guillarmou, C., & Hilgert, J. (2024). Ruelle-Taylor resonaces of Anosov actions. J. Europ. Math. Soc., 1–36. bibtex: '@article{Weich_Guedes Bonthonneau_Guillarmou_Hilgert_2024, title={Ruelle-Taylor resonaces of Anosov actions}, journal={J. Europ. Math. Soc.}, author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin and Hilgert, Joachim}, year={2024}, pages={1–36} }' chicago: Weich, Tobias, Yannick Guedes Bonthonneau, Colin Guillarmou, and Joachim Hilgert. “Ruelle-Taylor Resonaces of Anosov Actions.” J. Europ. Math. Soc., 2024, 1–36. ieee: T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, and J. Hilgert, “Ruelle-Taylor resonaces of Anosov actions,” J. Europ. Math. Soc., pp. 1–36, 2024. mla: Weich, Tobias, et al. “Ruelle-Taylor Resonaces of Anosov Actions.” J. Europ. Math. Soc., 2024, pp. 1–36. short: T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, J. Europ. Math. Soc. (2024) 1–36. date_created: 2022-06-22T09:56:51Z date_updated: 2024-02-19T06:25:13Z ddc: - '510' department: - _id: '10' - _id: '623' - _id: '548' - _id: '91' file: - access_level: open_access content_type: application/pdf creator: weich date_created: 2022-06-22T09:56:47Z date_updated: 2022-06-22T09:56:47Z file_id: '32102' file_name: 2007.14275.pdf file_size: 796410 relation: main_file file_date_updated: 2022-06-22T09:56:47Z has_accepted_license: '1' language: - iso: eng oa: '1' page: 1-36 publication: J. Europ. Math. Soc. publication_status: published status: public title: Ruelle-Taylor resonaces of Anosov actions type: journal_article user_id: '49063' year: '2024' ... --- _id: '51501' author: - first_name: Joachim full_name: Hilgert, Joachim id: '220' last_name: Hilgert citation: ama: Hilgert J. Quantum-Classical Correspondences for Locally Symmetric Spaces. Published online 2024. apa: Hilgert, J. (2024). Quantum-Classical Correspondences for Locally Symmetric Spaces. bibtex: '@article{Hilgert_2024, title={Quantum-Classical Correspondences for Locally Symmetric Spaces}, author={Hilgert, Joachim}, year={2024} }' chicago: Hilgert, Joachim. “Quantum-Classical Correspondences for Locally Symmetric Spaces,” 2024. ieee: J. Hilgert, “Quantum-Classical Correspondences for Locally Symmetric Spaces.” 2024. mla: Hilgert, Joachim. Quantum-Classical Correspondences for Locally Symmetric Spaces. 2024. short: J. Hilgert, (2024). date_created: 2024-02-19T10:31:51Z date_updated: 2024-02-19T10:32:07Z department: - _id: '91' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/pdf/2303.00578.pdf oa: '1' publication_status: published status: public title: Quantum-Classical Correspondences for Locally Symmetric Spaces type: preprint user_id: '49063' year: '2024' ... --- _id: '46019' abstract: - lang: eng text: We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical system in the multiobjective setting, which trajectories converge weakly to Pareto optimal solutions. Discretization of this system yields an inertial multiobjective algorithm which generates sequences that converge weakly to Pareto optimal solutions. We employ Nesterov acceleration to define an algorithm with an improved convergence rate compared to the plain multiobjective steepest descent method (Algorithm 1). A further improvement in terms of efficiency is achieved by avoiding the solution of a quadratic subproblem to compute a common step direction for all objective functions, which is usually required in first-order methods. Using a different discretization of our inertial gradient-like dynamical system, we obtain an accelerated multiobjective gradient method that does not require the solution of a subproblem in each step (Algorithm 2). While this algorithm does not converge in general, it yields good results on test problems while being faster than standard steepest descent. author: - first_name: Konstantin full_name: Sonntag, Konstantin id: '56399' last_name: Sonntag orcid: https://orcid.org/0000-0003-3384-3496 - first_name: Sebastian full_name: Peitz, Sebastian id: '47427' last_name: Peitz orcid: 0000-0002-3389-793X citation: ama: Sonntag K, Peitz S. Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications. Published online 2024. doi:10.1007/s10957-024-02389-3 apa: Sonntag, K., & Peitz, S. (2024). Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications. https://doi.org/10.1007/s10957-024-02389-3 bibtex: '@article{Sonntag_Peitz_2024, title={Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems}, DOI={10.1007/s10957-024-02389-3}, journal={Journal of Optimization Theory and Applications}, publisher={Springer}, author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024} }' chicago: Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal of Optimization Theory and Applications, 2024. https://doi.org/10.1007/s10957-024-02389-3. ieee: 'K. Sonntag and S. Peitz, “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems,” Journal of Optimization Theory and Applications, 2024, doi: 10.1007/s10957-024-02389-3.' mla: Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal of Optimization Theory and Applications, Springer, 2024, doi:10.1007/s10957-024-02389-3. short: K. Sonntag, S. Peitz, Journal of Optimization Theory and Applications (2024). date_created: 2023-07-12T06:35:58Z date_updated: 2024-02-21T10:13:33Z department: - _id: '101' - _id: '655' doi: 10.1007/s10957-024-02389-3 language: - iso: eng main_file_link: - open_access: '1' url: https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf oa: '1' publication: Journal of Optimization Theory and Applications publication_status: published publisher: Springer status: public title: Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems type: journal_article user_id: '56399' year: '2024' ... --- _id: '51334' abstract: - lang: eng text: The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points, where in each iteration, an approximation of the subdifferential is computed in an efficient manner and then used to compute a common descent direction for all objective functions. To prove convergence, we present some new optimality results for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these, we can show that every accumulation point of the sequence generated by our algorithm is Pareto critical under common assumptions. Computational efficiency for finding Pareto critical points is numerically demonstrated for multiobjective optimal control of an obstacle problem. author: - first_name: Konstantin full_name: Sonntag, Konstantin id: '56399' last_name: Sonntag orcid: https://orcid.org/0000-0003-3384-3496 - first_name: Bennet full_name: Gebken, Bennet id: '32643' last_name: Gebken - first_name: Georg full_name: Müller, Georg last_name: Müller - first_name: Sebastian full_name: Peitz, Sebastian id: '47427' last_name: Peitz orcid: 0000-0002-3389-793X - first_name: Stefan full_name: Volkwein, Stefan last_name: Volkwein citation: ama: Sonntag K, Gebken B, Müller G, Peitz S, Volkwein S. A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces. arXiv:240206376. Published online 2024. apa: Sonntag, K., Gebken, B., Müller, G., Peitz, S., & Volkwein, S. (2024). A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces. In arXiv:2402.06376. bibtex: '@article{Sonntag_Gebken_Müller_Peitz_Volkwein_2024, title={A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces}, journal={arXiv:2402.06376}, author={Sonntag, Konstantin and Gebken, Bennet and Müller, Georg and Peitz, Sebastian and Volkwein, Stefan}, year={2024} }' chicago: Sonntag, Konstantin, Bennet Gebken, Georg Müller, Sebastian Peitz, and Stefan Volkwein. “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.” ArXiv:2402.06376, 2024. ieee: K. Sonntag, B. Gebken, G. Müller, S. Peitz, and S. Volkwein, “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces,” arXiv:2402.06376. 2024. mla: Sonntag, Konstantin, et al. “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.” ArXiv:2402.06376, 2024. short: K. Sonntag, B. Gebken, G. Müller, S. Peitz, S. Volkwein, ArXiv:2402.06376 (2024). date_created: 2024-02-13T09:35:26Z date_updated: 2024-02-21T10:21:03Z department: - _id: '101' - _id: '655' external_id: arxiv: - "\t2402.06376" has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2402.06376 oa: '1' publication: arXiv:2402.06376 status: public title: A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces type: preprint user_id: '56399' year: '2024' ... --- _id: '51841' abstract: - lang: ger text: 'athematische Kompetenzen digital zu fördern und digitale Kompetenzen mathematisch zu fördern – dies ist eine Forderung der neuen Bildungsstandards mit Blick auf eine Bildung in der digitalen Welt. Gerade das Potenzial digitaler Medien für das fachliche Lernen wurde in vielen Studien bestätigt. Eine sinnvoll gestaltete Einbettung digitaler Medien bietet die Chance, allen fünf Prinzipien eines guten Unterrichts gerecht zu werden: Verstehensorientierung, Durchgängigkeit, kognitive Aktivierung, Lernendenorientierung & Adaptivität und Kommunikationsförderung. Die flächendeckende Nutzung digitaler Medien etabliert sich bislang nur zögerlich. Aber wie können wir Lehrkräfte stärken, digitale Medien sinnvoll einzusetzen? Wir möchten hier die Bandbreite der Möglichkeiten an Beispielen verdeutlichen, ihren Einsatz motivieren und Wege für einen guten Unterricht aufzeigen.' article_type: original author: - first_name: Bärbel full_name: Barzel, Bärbel last_name: Barzel - first_name: Gilbert full_name: Greefrath, Gilbert last_name: Greefrath - first_name: Mareike full_name: Nagel, Mareike last_name: Nagel - first_name: Max full_name: Hoffmann, Max id: '32202' last_name: Hoffmann orcid: 0000-0002-6964-7123 citation: ama: Barzel B, Greefrath G, Nagel M, Hoffmann M. Digitalisierung als Chance für alle Prinzipien guten Unterrichts. mathematik lehren. 2024;242:42-47. apa: Barzel, B., Greefrath, G., Nagel, M., & Hoffmann, M. (2024). Digitalisierung als Chance für alle Prinzipien guten Unterrichts. mathematik lehren, 242, 42–47. bibtex: '@article{Barzel_Greefrath_Nagel_Hoffmann_2024, title={Digitalisierung als Chance für alle Prinzipien guten Unterrichts}, volume={242}, journal={mathematik lehren}, author={Barzel, Bärbel and Greefrath, Gilbert and Nagel, Mareike and Hoffmann, Max}, year={2024}, pages={42–47} }' chicago: 'Barzel, Bärbel, Gilbert Greefrath, Mareike Nagel, and Max Hoffmann. “Digitalisierung als Chance für alle Prinzipien guten Unterrichts.” mathematik lehren 242 (2024): 42–47.' ieee: B. Barzel, G. Greefrath, M. Nagel, and M. Hoffmann, “Digitalisierung als Chance für alle Prinzipien guten Unterrichts,” mathematik lehren, vol. 242, pp. 42–47, 2024. mla: Barzel, Bärbel, et al. “Digitalisierung als Chance für alle Prinzipien guten Unterrichts.” mathematik lehren, vol. 242, 2024, pp. 42–47. short: B. Barzel, G. Greefrath, M. Nagel, M. Hoffmann, mathematik lehren 242 (2024) 42–47. date_created: 2024-02-25T20:58:51Z date_updated: 2024-02-25T21:01:03Z ddc: - '510' - '370' department: - _id: '97' - _id: '643' file: - access_level: closed content_type: application/pdf creator: maxh date_created: 2024-02-25T20:55:29Z date_updated: 2024-02-25T20:55:29Z file_id: '51842' file_name: Barzel_etal_2024_DigitalisierungalsChancefrallePrinzipiengut.pdf file_size: 1410541 relation: main_file success: 1 file_date_updated: 2024-02-25T20:55:29Z has_accepted_license: '1' intvolume: ' 242' language: - iso: ger main_file_link: - open_access: '1' url: https://www.friedrich-verlag.de/shop/mwdownloads/download/link/id/114555/ oa: '1' page: 42 - 47 publication: mathematik lehren publication_status: published status: public title: Digitalisierung als Chance für alle Prinzipien guten Unterrichts type: journal_article user_id: '32202' volume: 242 year: '2024' ... --- _id: '52342' abstract: - lang: eng text: 'We introduce the concept of a k-token signed graph and study some of its combinatorial and algebraic properties. We prove that two switching isomorphic signed graphs have switching isomorphic token graphs. Moreover, we show that the Laplacian spectrum of a balanced signed graph is contained in the Laplacian spectra of its k-token signed graph. Besides, we introduce and study the unbalance level of a signed graph, which is a new parameter that measures how far a signed graph is from being balanced. Moreover, we study the relation between the frustration index and the unbalance level of signed graphs and their token signed graphs. ' author: - first_name: C. full_name: Dalfó, C. last_name: Dalfó - first_name: M. A. full_name: Fiol, M. A. last_name: Fiol - first_name: Eckhard full_name: Steffen, Eckhard id: '15548' last_name: Steffen orcid: 0000-0002-9808-7401 citation: ama: Dalfó C, Fiol MA, Steffen E. On token signed graphs. arXiv:240302924. Published online 2024. apa: Dalfó, C., Fiol, M. A., & Steffen, E. (2024). On token signed graphs. In arXiv:2403.02924. bibtex: '@article{Dalfó_Fiol_Steffen_2024, title={On token signed graphs}, journal={arXiv:2403.02924}, author={Dalfó, C. and Fiol, M. A. and Steffen, Eckhard}, year={2024} }' chicago: Dalfó, C., M. A. Fiol, and Eckhard Steffen. “On Token Signed Graphs.” ArXiv:2403.02924, 2024. ieee: C. Dalfó, M. A. Fiol, and E. Steffen, “On token signed graphs,” arXiv:2403.02924. 2024. mla: Dalfó, C., et al. “On Token Signed Graphs.” ArXiv:2403.02924, 2024. short: C. Dalfó, M.A. Fiol, E. Steffen, ArXiv:2403.02924 (2024). date_created: 2024-03-07T08:48:39Z date_updated: 2024-03-07T08:50:33Z department: - _id: '542' external_id: arxiv: - '2403.02924' language: - iso: eng publication: arXiv:2403.02924 status: public title: On token signed graphs type: preprint user_id: '15540' year: '2024' ... --- _id: '52691' abstract: - lang: eng text: "We prove Feynman-Kac formulas for the semigroups generated by selfadjoint\r\noperators in a class containing Fr\\\"ohlich Hamiltonians known from solid state\r\nphysics. The latter model multi-polarons, i.e., a fixed number of quantum\r\nmechanical electrons moving in a polarizable crystal and interacting with the\r\nquantized phonon field generated by the crystal's vibrational modes. Both the\r\nelectrons and phonons can be confined to suitable open subsets of Euclidean\r\nspace. We also include possibly very singular magnetic vector potentials and\r\nelectrostatic potentials. Our Feynman-Kac formulas comprise Fock space\r\noperator-valued multiplicative functionals and can be applied to every vector\r\nin the underlying Hilbert space. In comparison to the renormalized Nelson\r\nmodel, for which analogous Feynman-Kac formulas are known, the analysis of the\r\ncreation and annihilation terms in the multiplicative functionals requires\r\nnovel ideas to overcome difficulties caused by the phonon dispersion relation\r\nbeing constant. Getting these terms under control and generalizing other\r\nconstruction steps so as to cover confined systems are the main achievements of\r\nthis article." author: - first_name: Benjamin full_name: Hinrichs, Benjamin id: '99427' last_name: Hinrichs orcid: 0000-0001-9074-1205 - first_name: Oliver full_name: Matte, Oliver last_name: Matte citation: ama: Hinrichs B, Matte O. Feynman-Kac formulas for semigroups generated by multi-polaron  Hamiltonians in magnetic fields and on general domains. arXiv:240312147. Published online 2024. apa: Hinrichs, B., & Matte, O. (2024). Feynman-Kac formulas for semigroups generated by multi-polaron  Hamiltonians in magnetic fields and on general domains. In arXiv:2403.12147. bibtex: '@article{Hinrichs_Matte_2024, title={Feynman-Kac formulas for semigroups generated by multi-polaron  Hamiltonians in magnetic fields and on general domains}, journal={arXiv:2403.12147}, author={Hinrichs, Benjamin and Matte, Oliver}, year={2024} }' chicago: Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formulas for Semigroups Generated by Multi-Polaron  Hamiltonians in Magnetic Fields and on General Domains.” ArXiv:2403.12147, 2024. ieee: B. Hinrichs and O. Matte, “Feynman-Kac formulas for semigroups generated by multi-polaron  Hamiltonians in magnetic fields and on general domains,” arXiv:2403.12147. 2024. mla: Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formulas for Semigroups Generated by Multi-Polaron  Hamiltonians in Magnetic Fields and on General Domains.” ArXiv:2403.12147, 2024. short: B. Hinrichs, O. Matte, ArXiv:2403.12147 (2024). date_created: 2024-03-20T14:56:05Z date_updated: 2024-03-20T14:56:50Z department: - _id: '799' external_id: arxiv: - '2403.12147' language: - iso: eng publication: arXiv:2403.12147 status: public title: Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians in magnetic fields and on general domains type: preprint user_id: '99427' year: '2024' ... --- _id: '52726' abstract: - lang: eng text: Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures. article_type: original author: - first_name: Christian full_name: Bick, Christian last_name: Bick - first_name: Sören full_name: von der Gracht, Sören id: '97359' last_name: von der Gracht orcid: 0000-0002-8054-2058 citation: ama: Bick C, von der Gracht S. Heteroclinic dynamics in network dynamical systems with higher-order interactions. Journal of Complex Networks. 2024;12(2). doi:10.1093/comnet/cnae009 apa: Bick, C., & von der Gracht, S. (2024). Heteroclinic dynamics in network dynamical systems with higher-order interactions. Journal of Complex Networks, 12(2). https://doi.org/10.1093/comnet/cnae009 bibtex: '@article{Bick_von der Gracht_2024, title={Heteroclinic dynamics in network dynamical systems with higher-order interactions}, volume={12}, DOI={10.1093/comnet/cnae009}, number={2}, journal={Journal of Complex Networks}, publisher={Oxford University Press (OUP)}, author={Bick, Christian and von der Gracht, Sören}, year={2024} }' chicago: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks 12, no. 2 (2024). https://doi.org/10.1093/comnet/cnae009. ieee: 'C. Bick and S. von der Gracht, “Heteroclinic dynamics in network dynamical systems with higher-order interactions,” Journal of Complex Networks, vol. 12, no. 2, 2024, doi: 10.1093/comnet/cnae009.' mla: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks, vol. 12, no. 2, Oxford University Press (OUP), 2024, doi:10.1093/comnet/cnae009. short: C. Bick, S. von der Gracht, Journal of Complex Networks 12 (2024). date_created: 2024-03-22T09:04:57Z date_updated: 2024-03-22T09:11:53Z ddc: - '510' department: - _id: '101' doi: 10.1093/comnet/cnae009 external_id: arxiv: - '2309.02006' file: - access_level: closed content_type: application/pdf creator: svdg date_created: 2024-03-22T09:06:07Z date_updated: 2024-03-22T09:06:07Z file_id: '52728' file_name: heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf file_size: 649155 relation: main_file success: 1 file_date_updated: 2024-03-22T09:06:07Z has_accepted_license: '1' intvolume: ' 12' issue: '2' keyword: - Applied Mathematics - Computational Mathematics - Control and Optimization - Management Science and Operations Research - Computer Networks and Communications language: - iso: eng main_file_link: - open_access: '1' url: https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf oa: '1' publication: Journal of Complex Networks publication_identifier: issn: - 2051-1329 publication_status: published publisher: Oxford University Press (OUP) status: public title: Heteroclinic dynamics in network dynamical systems with higher-order interactions type: journal_article user_id: '97359' volume: 12 year: '2024' ... --- _id: '49905' abstract: - lang: eng text: "For 0 ≤ t ≤ r let m(t, r) be the maximum number s such that every t-edge-connected r-graph has s pairwise disjoint perfect matchings. There are only a few values of m(t, r) known, for instance m(3, 3) = m(4, r) = 1, and m(t, r) ≤ r − 2 for all t \x03 = 5,\r\nand m(t, r) ≤ r − 3 if r is even. We prove that m(2l, r) ≤ 3l − 6 for every l ≥ 3 and r ≥ 2l." author: - first_name: Yulai full_name: Ma, Yulai id: '92748' last_name: Ma - first_name: Davide full_name: Mattiolo, Davide last_name: Mattiolo - first_name: Eckhard full_name: Steffen, Eckhard id: '15548' last_name: Steffen orcid: 0000-0002-9808-7401 - first_name: Isaak Hieronymus full_name: Wolf, Isaak Hieronymus id: '88145' last_name: Wolf citation: ama: Ma Y, Mattiolo D, Steffen E, Wolf IH. Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs. Combinatorica. 2024;44:429-440. doi:10.1007/s00493-023-00078-9 apa: Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2024). Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs. Combinatorica, 44, 429–440. https://doi.org/10.1007/s00493-023-00078-9 bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2024, title={Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs}, volume={44}, DOI={10.1007/s00493-023-00078-9}, journal={Combinatorica}, publisher={Springer Science and Business Media LLC}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2024}, pages={429–440} }' chicago: 'Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.” Combinatorica 44 (2024): 429–40. https://doi.org/10.1007/s00493-023-00078-9.' ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs,” Combinatorica, vol. 44, pp. 429–440, 2024, doi: 10.1007/s00493-023-00078-9.' mla: Ma, Yulai, et al. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.” Combinatorica, vol. 44, Springer Science and Business Media LLC, 2024, pp. 429–40, doi:10.1007/s00493-023-00078-9. short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 44 (2024) 429–440. date_created: 2023-12-20T10:31:27Z date_updated: 2024-03-22T12:11:35Z department: - _id: '542' doi: 10.1007/s00493-023-00078-9 intvolume: ' 44' keyword: - Computational Mathematics - Discrete Mathematics and Combinatorics language: - iso: eng page: 429-440 publication: Combinatorica publication_identifier: issn: - 0209-9683 - 1439-6912 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs type: journal_article user_id: '15540' volume: 44 year: '2024' ... --- _id: '53101' abstract: - lang: eng text: In this work, we consider optimal control problems for mechanical systems with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an affine control term. Classically, Pontryagin's maximum principle gives necessary optimality conditions for the optimal control problem. For smooth problems, alternatively, a variational approach based on an augmented objective can be followed. Here, we propose a new Lagrangian approach leading to equivalent necessary optimality conditions in the form of Euler-Lagrange equations. Thus, the differential geometric structure (similar to classical Lagrangian dynamics) can be exploited in the framework of optimal control problems. In particular, the formulation enables the symplectic discretisation of the optimal control problem via variational integrators in a straightforward way. article_type: original author: - first_name: Sigrid full_name: Leyendecker, Sigrid last_name: Leyendecker - first_name: Sofya full_name: Maslovskaya, Sofya id: '87909' last_name: Maslovskaya - first_name: Sina full_name: Ober-Blöbaum, Sina id: '16494' last_name: Ober-Blöbaum - first_name: Rodrigo T. Sato Martín de full_name: Almagro, Rodrigo T. Sato Martín de last_name: Almagro - first_name: Flóra Orsolya full_name: Szemenyei, Flóra Orsolya last_name: Szemenyei citation: ama: Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Almagro RTSM de, Szemenyei FO. A new Lagrangian approach to control affine systems with a quadratic Lagrange term. Journal of Computational Dynamics. 2024;0(0):0-0. doi:10.3934/jcd.2024017 apa: Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., Almagro, R. T. S. M. de, & Szemenyei, F. O. (2024). A new Lagrangian approach to control affine systems with a quadratic Lagrange term. Journal of Computational Dynamics, 0(0), 0–0. https://doi.org/10.3934/jcd.2024017 bibtex: '@article{Leyendecker_Maslovskaya_Ober-Blöbaum_Almagro_Szemenyei_2024, title={A new Lagrangian approach to control affine systems with a quadratic Lagrange term}, volume={0}, DOI={10.3934/jcd.2024017}, number={0}, journal={Journal of Computational Dynamics}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Leyendecker, Sigrid and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Almagro, Rodrigo T. Sato Martín de and Szemenyei, Flóra Orsolya}, year={2024}, pages={0–0} }' chicago: 'Leyendecker, Sigrid, Sofya Maslovskaya, Sina Ober-Blöbaum, Rodrigo T. Sato Martín de Almagro, and Flóra Orsolya Szemenyei. “A New Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term.” Journal of Computational Dynamics 0, no. 0 (2024): 0–0. https://doi.org/10.3934/jcd.2024017.' ieee: 'S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. S. M. de Almagro, and F. O. Szemenyei, “A new Lagrangian approach to control affine systems with a quadratic Lagrange term,” Journal of Computational Dynamics, vol. 0, no. 0, pp. 0–0, 2024, doi: 10.3934/jcd.2024017.' mla: Leyendecker, Sigrid, et al. “A New Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term.” Journal of Computational Dynamics, vol. 0, no. 0, American Institute of Mathematical Sciences (AIMS), 2024, pp. 0–0, doi:10.3934/jcd.2024017. short: S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T.S.M. de Almagro, F.O. Szemenyei, Journal of Computational Dynamics 0 (2024) 0–0. date_created: 2024-03-28T15:58:02Z date_updated: 2024-03-28T16:07:34Z ddc: - '510' department: - _id: '636' doi: 10.3934/jcd.2024017 has_accepted_license: '1' issue: '0' keyword: - Optimal control problem - Lagrangian system - Hamiltonian system - Variations - Pontryagin's maximum principle. language: - iso: eng main_file_link: - open_access: '1' url: https://www.aimsciences.org/article/doi/10.3934/jcd.2024017 oa: '1' page: 0-0 publication: Journal of Computational Dynamics publication_identifier: issn: - 2158-2491 - 2158-2505 publication_status: published publisher: American Institute of Mathematical Sciences (AIMS) status: public title: A new Lagrangian approach to control affine systems with a quadratic Lagrange term type: journal_article user_id: '87909' volume: '0' year: '2024' ... --- _id: '21199' abstract: - lang: eng 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." article_number: '110840' author: - first_name: Sebastian full_name: Peitz, Sebastian id: '47427' last_name: Peitz orcid: 0000-0002-3389-793X - first_name: Katharina full_name: Bieker, Katharina id: '32829' last_name: Bieker citation: ama: Peitz S, Bieker K. On the Universal Transformation of Data-Driven Models to Control Systems. Automatica. 2023;149. doi:10.1016/j.automatica.2022.110840 apa: Peitz, S., & Bieker, K. (2023). On the Universal Transformation of Data-Driven Models to Control Systems. Automatica, 149, Article 110840. https://doi.org/10.1016/j.automatica.2022.110840 bibtex: '@article{Peitz_Bieker_2023, title={On the Universal Transformation of Data-Driven Models to Control Systems}, volume={149}, DOI={10.1016/j.automatica.2022.110840}, number={110840}, journal={Automatica}, publisher={Elsevier}, author={Peitz, Sebastian and Bieker, Katharina}, year={2023} }' chicago: Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of Data-Driven Models to Control Systems.” Automatica 149 (2023). https://doi.org/10.1016/j.automatica.2022.110840. ieee: 'S. Peitz and K. Bieker, “On the Universal Transformation of Data-Driven Models to Control Systems,” Automatica, vol. 149, Art. no. 110840, 2023, doi: 10.1016/j.automatica.2022.110840.' mla: Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of Data-Driven Models to Control Systems.” Automatica, vol. 149, 110840, Elsevier, 2023, doi:10.1016/j.automatica.2022.110840. short: S. Peitz, K. Bieker, Automatica 149 (2023). date_created: 2021-02-10T07:04:15Z date_updated: 2023-01-07T12:01:58Z department: - _id: '101' - _id: '655' doi: 10.1016/j.automatica.2022.110840 intvolume: ' 149' language: - iso: eng main_file_link: - open_access: '1' url: https://www.sciencedirect.com/science/article/pii/S0005109822007075/pdfft?isDTMRedir=true&download=true oa: '1' project: - _id: '52' name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing' publication: Automatica publication_status: published publisher: Elsevier status: public title: On the Universal Transformation of Data-Driven Models to Control Systems type: journal_article user_id: '47427' volume: 149 year: '2023' ... --- _id: '35697' author: - first_name: Laura full_name: Ostsieker, Laura last_name: Ostsieker - first_name: Rolf full_name: Biehler, Rolf id: '16274' last_name: Biehler citation: ama: 'Ostsieker L, Biehler R. Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences. In: Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing; 2023:181-201. doi:10.1007/978-3-031-14175-1_9' apa: 'Ostsieker, L., & Biehler, R. (2023). Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences. In Practice-Oriented Research in Tertiary Mathematics Education (pp. 181–201). Springer International Publishing. https://doi.org/10.1007/978-3-031-14175-1_9' bibtex: '@inbook{Ostsieker_Biehler_2023, place={Cham}, title={Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences}, DOI={10.1007/978-3-031-14175-1_9}, booktitle={Practice-Oriented Research in Tertiary Mathematics Education}, publisher={Springer International Publishing}, author={Ostsieker, Laura and Biehler, Rolf}, year={2023}, pages={181–201} }' chicago: 'Ostsieker, Laura, and Rolf Biehler. “Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences.” In Practice-Oriented Research in Tertiary Mathematics Education, 181–201. Cham: Springer International Publishing, 2023. https://doi.org/10.1007/978-3-031-14175-1_9.' ieee: 'L. Ostsieker and R. Biehler, “Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences,” in Practice-Oriented Research in Tertiary Mathematics Education, Cham: Springer International Publishing, 2023, pp. 181–201.' mla: 'Ostsieker, Laura, and Rolf Biehler. “Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences.” Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, 2023, pp. 181–201, doi:10.1007/978-3-031-14175-1_9.' short: 'L. Ostsieker, R. Biehler, in: Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2023, pp. 181–201.' date_created: 2023-01-10T09:03:11Z date_updated: 2023-01-11T08:19:24Z department: - _id: '34' - _id: '10' - _id: '97' - _id: '363' doi: 10.1007/978-3-031-14175-1_9 language: - iso: eng page: 181-201 place: Cham publication: Practice-Oriented Research in Tertiary Mathematics Education publication_identifier: isbn: - '9783031141744' - '9783031141751' issn: - 1869-4918 - 1869-4926 publication_status: published publisher: Springer International Publishing status: public title: 'Supporting Students in Developing Adequate Concept Images and Definitions at University: The Case of the Convergence of Sequences' type: book_chapter user_id: '37888' year: '2023' ... --- _id: '35678' author: - first_name: Jörg full_name: Kortemeyer, Jörg last_name: Kortemeyer - first_name: Rolf full_name: Biehler, Rolf id: '16274' last_name: Biehler citation: ama: 'Kortemeyer J, Biehler R. Analyzing the Interface Between Mathematics and Engineering in Basic Engineering Courses. In: Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing; 2023:669-692. doi:10.1007/978-3-031-14175-1_32' apa: Kortemeyer, J., & Biehler, R. (2023). Analyzing the Interface Between Mathematics and Engineering in Basic Engineering Courses. In Practice-Oriented Research in Tertiary Mathematics Education (pp. 669–692). Springer International Publishing. https://doi.org/10.1007/978-3-031-14175-1_32 bibtex: '@inbook{Kortemeyer_Biehler_2023, place={Cham}, title={Analyzing the Interface Between Mathematics and Engineering in Basic Engineering Courses}, DOI={10.1007/978-3-031-14175-1_32}, booktitle={Practice-Oriented Research in Tertiary Mathematics Education}, publisher={Springer International Publishing}, author={Kortemeyer, Jörg and Biehler, Rolf}, year={2023}, pages={669–692} }' chicago: 'Kortemeyer, Jörg, and Rolf Biehler. “Analyzing the Interface Between Mathematics and Engineering in Basic Engineering Courses.” In Practice-Oriented Research in Tertiary Mathematics Education, 669–92. Cham: Springer International Publishing, 2023. https://doi.org/10.1007/978-3-031-14175-1_32.' ieee: 'J. Kortemeyer and R. Biehler, “Analyzing the Interface Between Mathematics and Engineering in Basic Engineering Courses,” in Practice-Oriented Research in Tertiary Mathematics Education, Cham: Springer International Publishing, 2023, pp. 669–692.' mla: Kortemeyer, Jörg, and Rolf Biehler. “Analyzing the Interface Between Mathematics and Engineering in Basic Engineering Courses.” Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, 2023, pp. 669–92, doi:10.1007/978-3-031-14175-1_32. short: 'J. Kortemeyer, R. Biehler, in: Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2023, pp. 669–692.' date_created: 2023-01-10T08:53:44Z date_updated: 2023-01-11T08:20:40Z department: - _id: '34' - _id: '10' - _id: '97' - _id: '363' doi: 10.1007/978-3-031-14175-1_32 language: - iso: eng page: 669-692 place: Cham publication: Practice-Oriented Research in Tertiary Mathematics Education publication_identifier: isbn: - '9783031141744' - '9783031141751' issn: - 1869-4918 - 1869-4926 publication_status: published publisher: Springer International Publishing status: public title: Analyzing the Interface Between Mathematics and Engineering in Basic Engineering Courses type: book_chapter user_id: '37888' year: '2023' ... --- _id: '35669' author: - first_name: Rolf full_name: Biehler, Rolf id: '16274' last_name: Biehler - first_name: Michael full_name: Liebendörfer, Michael last_name: Liebendörfer - first_name: Ghislaine full_name: Gueudet, Ghislaine last_name: Gueudet - first_name: Chris full_name: Rasmussen, Chris last_name: Rasmussen - first_name: Carl full_name: Winsløw, Carl last_name: Winsløw citation: ama: 'Biehler R, Liebendörfer M, Gueudet G, Rasmussen C, Winsløw C. Practice-Oriented Research in Tertiary Mathematics Education – An Introduction. In: Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing; 2023. doi:10.1007/978-3-031-14175-1_1' apa: Biehler, R., Liebendörfer, M., Gueudet, G., Rasmussen, C., & Winsløw, C. (2023). Practice-Oriented Research in Tertiary Mathematics Education – An Introduction. In Practice-Oriented Research in Tertiary Mathematics Education. Springer International Publishing. https://doi.org/10.1007/978-3-031-14175-1_1 bibtex: '@inbook{Biehler_Liebendörfer_Gueudet_Rasmussen_Winsløw_2023, place={Cham}, title={Practice-Oriented Research in Tertiary Mathematics Education – An Introduction}, DOI={10.1007/978-3-031-14175-1_1}, booktitle={Practice-Oriented Research in Tertiary Mathematics Education}, publisher={Springer International Publishing}, author={Biehler, Rolf and Liebendörfer, Michael and Gueudet, Ghislaine and Rasmussen, Chris and Winsløw, Carl}, year={2023} }' chicago: 'Biehler, Rolf, Michael Liebendörfer, Ghislaine Gueudet, Chris Rasmussen, and Carl Winsløw. “Practice-Oriented Research in Tertiary Mathematics Education – An Introduction.” In Practice-Oriented Research in Tertiary Mathematics Education. Cham: Springer International Publishing, 2023. https://doi.org/10.1007/978-3-031-14175-1_1.' ieee: 'R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, and C. Winsløw, “Practice-Oriented Research in Tertiary Mathematics Education – An Introduction,” in Practice-Oriented Research in Tertiary Mathematics Education, Cham: Springer International Publishing, 2023.' mla: Biehler, Rolf, et al. “Practice-Oriented Research in Tertiary Mathematics Education – An Introduction.” Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, 2023, doi:10.1007/978-3-031-14175-1_1. short: 'R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, C. Winsløw, in: Practice-Oriented Research in Tertiary Mathematics Education, Springer International Publishing, Cham, 2023.' date_created: 2023-01-10T08:46:17Z date_updated: 2023-01-11T08:38:52Z department: - _id: '34' - _id: '10' - _id: '97' - _id: '363' doi: 10.1007/978-3-031-14175-1_1 language: - iso: eng place: Cham publication: Practice-Oriented Research in Tertiary Mathematics Education publication_identifier: isbn: - '9783031141744' - '9783031141751' issn: - 1869-4918 - 1869-4926 publication_status: published publisher: Springer International Publishing status: public title: Practice-Oriented Research in Tertiary Mathematics Education – An Introduction type: book_chapter user_id: '37888' year: '2023' ...