--- _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: '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: '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: '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: '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: '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: '27426' abstract: - lang: eng text: "Regularization is used in many different areas of optimization when solutions\r\nare sought which not only minimize a given function, but also possess a certain\r\ndegree of regularity. Popular applications are image denoising, sparse\r\nregression and machine learning. Since the choice of the regularization\r\nparameter is crucial but often difficult, path-following methods are used to\r\napproximate the entire regularization path, i.e., the set of all possible\r\nsolutions for all regularization parameters. Due to their nature, the\r\ndevelopment of these methods requires structural results about the\r\nregularization path. The goal of this article is to derive these results for\r\nthe case of a smooth objective function which is penalized by a piecewise\r\ndifferentiable regularization term. We do this by treating regularization as a\r\nmultiobjective optimization problem. Our results suggest that even in this\r\ngeneral case, the regularization path is piecewise smooth. Moreover, our theory\r\nallows for a classification of the nonsmooth features that occur in between\r\nsmooth parts. This is demonstrated in two applications, namely support-vector\r\nmachines and exact penalty methods." author: - first_name: Bennet full_name: Gebken, Bennet id: '32643' last_name: Gebken - first_name: Katharina full_name: Bieker, Katharina id: '32829' last_name: Bieker - first_name: Sebastian full_name: Peitz, Sebastian id: '47427' last_name: Peitz orcid: 0000-0002-3389-793X citation: ama: Gebken B, Bieker K, Peitz S. On the structure of regularization paths for piecewise differentiable regularization terms. Journal of Global Optimization. 2023;85(3):709-741. doi:10.1007/s10898-022-01223-2 apa: Gebken, B., Bieker, K., & Peitz, S. (2023). On the structure of regularization paths for piecewise differentiable regularization terms. Journal of Global Optimization, 85(3), 709–741. https://doi.org/10.1007/s10898-022-01223-2 bibtex: '@article{Gebken_Bieker_Peitz_2023, title={On the structure of regularization paths for piecewise differentiable regularization terms}, volume={85}, DOI={10.1007/s10898-022-01223-2}, number={3}, journal={Journal of Global Optimization}, author={Gebken, Bennet and Bieker, Katharina and Peitz, Sebastian}, year={2023}, pages={709–741} }' chicago: 'Gebken, Bennet, Katharina Bieker, and Sebastian Peitz. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal of Global Optimization 85, no. 3 (2023): 709–41. https://doi.org/10.1007/s10898-022-01223-2.' ieee: 'B. Gebken, K. Bieker, and S. Peitz, “On the structure of regularization paths for piecewise differentiable regularization terms,” Journal of Global Optimization, vol. 85, no. 3, pp. 709–741, 2023, doi: 10.1007/s10898-022-01223-2.' mla: Gebken, Bennet, et al. “On the Structure of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal of Global Optimization, vol. 85, no. 3, 2023, pp. 709–41, doi:10.1007/s10898-022-01223-2. short: B. Gebken, K. Bieker, S. Peitz, Journal of Global Optimization 85 (2023) 709–741. date_created: 2021-11-15T09:24:59Z date_updated: 2023-03-11T17:16:33Z department: - _id: '101' - _id: '655' doi: 10.1007/s10898-022-01223-2 intvolume: ' 85' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf oa: '1' page: 709-741 publication: Journal of Global Optimization status: public title: On the structure of regularization paths for piecewise differentiable regularization terms type: journal_article user_id: '47427' volume: 85 year: '2023' ... --- _id: '44501' abstract: - lang: eng text: "Extending the notion of maxcut, the study of the frustration index of signed graphs is one of the basic questions in the theory of signed graphs. Recently two of the authors initiated the study of critically frustrated signed graphs. That is a signed graph whose frustration index decreases with the removal of any edge. The main focus of this study is on critical signed graphs which are not edge-disjoint unions of critically frustrated signed graphs (namely non-decomposable signed graphs) and which are not built from other critically frustrated signed graphs by subdivision. We conjecture that for any given k there are only finitely many critically k-frustrated signed graphs of this kind.\r\nProviding support for this conjecture we show that there are only two of such critically 3-frustrated signed graphs where there is no pair of edge-disjoint negative cycles. Similarly, we show that there are exactly ten critically 3-frustrated signed planar graphs that are neither decomposable nor subdivisions of other critically frustrated signed graphs. We present a method for building non-decomposable critically frustrated signed graphs based on two given such signed graphs. We also show that the condition of being non-decomposable is necessary for our conjecture. " author: - first_name: Chiara full_name: Cappello, Chiara id: '72874' last_name: Cappello - first_name: Reza full_name: Naserasr, Reza last_name: Naserasr - first_name: Eckhard full_name: Steffen, Eckhard id: '15548' last_name: Steffen orcid: 0000-0002-9808-7401 - first_name: Zhouningxin full_name: Wang, Zhouningxin last_name: Wang citation: ama: Cappello C, Naserasr R, Steffen E, Wang Z. Critically 3-frustrated signed graphs. arXiv:230410243. Published online 2023. apa: Cappello, C., Naserasr, R., Steffen, E., & Wang, Z. (2023). Critically 3-frustrated signed graphs. In arXiv:2304.10243. bibtex: '@article{Cappello_Naserasr_Steffen_Wang_2023, title={Critically 3-frustrated signed graphs}, journal={arXiv:2304.10243}, author={Cappello, Chiara and Naserasr, Reza and Steffen, Eckhard and Wang, Zhouningxin}, year={2023} }' chicago: Cappello, Chiara, Reza Naserasr, Eckhard Steffen, and Zhouningxin Wang. “Critically 3-Frustrated Signed Graphs.” ArXiv:2304.10243, 2023. ieee: C. Cappello, R. Naserasr, E. Steffen, and Z. Wang, “Critically 3-frustrated signed graphs,” arXiv:2304.10243. 2023. mla: Cappello, Chiara, et al. “Critically 3-Frustrated Signed Graphs.” ArXiv:2304.10243, 2023. short: C. Cappello, R. Naserasr, E. Steffen, Z. Wang, ArXiv:2304.10243 (2023). date_created: 2023-05-05T06:52:39Z date_updated: 2023-05-05T06:53:47Z department: - _id: '542' external_id: arxiv: - '2304.10243' language: - iso: eng publication: arXiv:2304.10243 status: public title: Critically 3-frustrated signed graphs type: preprint user_id: '15540' year: '2023' ... --- _id: '44857' abstract: - lang: eng text: Ancestral reconstruction is a classic task in comparative genomics. Here, we study the genome median problem, a related computational problem which, given a set of three or more genomes, asks to find a new genome that minimizes the sum of pairwise distances between it and the given genomes. The distance stands for the amount of evolution observed at the genome level, for which we determine the minimum number of rearrangement operations necessary to transform one genome into the other. For almost all rearrangement operations the median problem is NP-hard, with the exception of the breakpoint median that can be constructed efficiently for multichromosomal circular and mixed genomes. In this work, we study the median problem under a restricted rearrangement measure called c4-distance, which is closely related to the breakpoint and the DCJ distance. We identify tight bounds and decomposers of the c4-median and develop algorithms for its construction, one exact ILP-based and three combinatorial heuristics. Subsequently, we perform experiments on simulated data sets. Our results suggest that the c4-distance is useful for the study the genome median problem, from theoretical and practical perspectives. author: - first_name: Helmuth O.M. full_name: Silva, Helmuth O.M. last_name: Silva - first_name: Diego P. full_name: Rubert, Diego P. last_name: Rubert - first_name: Eloi full_name: Araujo, Eloi last_name: Araujo - first_name: Eckhard full_name: Steffen, Eckhard id: '15548' last_name: Steffen orcid: 0000-0002-9808-7401 - first_name: Daniel full_name: Doerr, Daniel last_name: Doerr - first_name: Fábio V. full_name: Martinez, Fábio V. last_name: Martinez citation: ama: Silva HOM, Rubert DP, Araujo E, Steffen E, Doerr D, Martinez FV. Algorithms for the genome median under a restricted measure of rearrangement. RAIRO - Operations Research. 2023;57(3):1045-1058. doi:10.1051/ro/2023052 apa: Silva, H. O. M., Rubert, D. P., Araujo, E., Steffen, E., Doerr, D., & Martinez, F. V. (2023). Algorithms for the genome median under a restricted measure of rearrangement. RAIRO - Operations Research, 57(3), 1045–1058. https://doi.org/10.1051/ro/2023052 bibtex: '@article{Silva_Rubert_Araujo_Steffen_Doerr_Martinez_2023, title={Algorithms for the genome median under a restricted measure of rearrangement}, volume={57}, DOI={10.1051/ro/2023052}, number={3}, journal={RAIRO - Operations Research}, publisher={EDP Sciences}, author={Silva, Helmuth O.M. and Rubert, Diego P. and Araujo, Eloi and Steffen, Eckhard and Doerr, Daniel and Martinez, Fábio V.}, year={2023}, pages={1045–1058} }' chicago: 'Silva, Helmuth O.M., Diego P. Rubert, Eloi Araujo, Eckhard Steffen, Daniel Doerr, and Fábio V. Martinez. “Algorithms for the Genome Median under a Restricted Measure of Rearrangement.” RAIRO - Operations Research 57, no. 3 (2023): 1045–58. https://doi.org/10.1051/ro/2023052.' ieee: 'H. O. M. Silva, D. P. Rubert, E. Araujo, E. Steffen, D. Doerr, and F. V. Martinez, “Algorithms for the genome median under a restricted measure of rearrangement,” RAIRO - Operations Research, vol. 57, no. 3, pp. 1045–1058, 2023, doi: 10.1051/ro/2023052.' mla: Silva, Helmuth O. M., et al. “Algorithms for the Genome Median under a Restricted Measure of Rearrangement.” RAIRO - Operations Research, vol. 57, no. 3, EDP Sciences, 2023, pp. 1045–58, doi:10.1051/ro/2023052. short: H.O.M. Silva, D.P. Rubert, E. Araujo, E. Steffen, D. Doerr, F.V. Martinez, RAIRO - Operations Research 57 (2023) 1045–1058. date_created: 2023-05-16T08:48:22Z date_updated: 2023-05-16T08:49:30Z department: - _id: '542' doi: 10.1051/ro/2023052 intvolume: ' 57' issue: '3' keyword: - Management Science and Operations Research - Computer Science Applications - Theoretical Computer Science language: - iso: eng page: 1045-1058 publication: RAIRO - Operations Research publication_identifier: issn: - 0399-0559 - 2804-7303 publication_status: published publisher: EDP Sciences status: public title: Algorithms for the genome median under a restricted measure of rearrangement type: journal_article user_id: '15540' volume: 57 year: '2023' ... --- _id: '44859' 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. Sets of r-graphs that color all r-graphs. arXiv:230508619. Published online 2023. apa: Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Sets of r-graphs that color all r-graphs. In arXiv:2305.08619. bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Sets of r-graphs that color all r-graphs}, journal={arXiv:2305.08619}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023} }' chicago: Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Sets of R-Graphs That Color All r-Graphs.” ArXiv:2305.08619, 2023. ieee: Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-graphs that color all r-graphs,” arXiv:2305.08619. 2023. mla: Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” ArXiv:2305.08619, 2023. short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, ArXiv:2305.08619 (2023). date_created: 2023-05-16T10:07:47Z date_updated: 2023-05-16T11:17:26Z department: - _id: '542' external_id: arxiv: - '2305.08619' language: - iso: eng publication: arXiv:2305.08619 status: public title: Sets of r-graphs that color all r-graphs type: preprint user_id: '15540' year: '2023' ... --- _id: '45498' abstract: - lang: eng text: "We present a novel method for high-order phase reduction in networks of\r\nweakly coupled oscillators and, more generally, perturbations of reducible\r\nnormally hyperbolic (quasi-)periodic tori. Our method works by computing an\r\nasymptotic expansion for an embedding of the perturbed invariant torus, as well\r\nas for the reduced phase dynamics in local coordinates. Both can be determined\r\nto arbitrary degrees of accuracy, and we show that the phase dynamics may\r\ndirectly be obtained in normal form. We apply the method to predict remote\r\nsynchronisation in a chain of coupled Stuart-Landau oscillators." author: - first_name: Sören full_name: von der Gracht, Sören id: '97359' last_name: von der Gracht orcid: 0000-0002-8054-2058 - first_name: Eddie full_name: Nijholt, Eddie last_name: Nijholt - first_name: Bob full_name: Rink, Bob last_name: Rink citation: ama: von der Gracht S, Nijholt E, Rink B. A parametrisation method for high-order phase reduction in coupled  oscillator networks. arXiv:230603320. apa: von der Gracht, S., Nijholt, E., & Rink, B. (n.d.). A parametrisation method for high-order phase reduction in coupled  oscillator networks. In arXiv:2306.03320. bibtex: '@article{von der Gracht_Nijholt_Rink, title={A parametrisation method for high-order phase reduction in coupled  oscillator networks}, journal={arXiv:2306.03320}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob} }' chicago: Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “A Parametrisation Method for High-Order Phase Reduction in Coupled  Oscillator Networks.” ArXiv:2306.03320, n.d. ieee: S. von der Gracht, E. Nijholt, and B. Rink, “A parametrisation method for high-order phase reduction in coupled  oscillator networks,” arXiv:2306.03320. . mla: von der Gracht, Sören, et al. “A Parametrisation Method for High-Order Phase Reduction in Coupled  Oscillator Networks.” ArXiv:2306.03320. short: S. von der Gracht, E. Nijholt, B. Rink, ArXiv:2306.03320 (n.d.). date_created: 2023-06-07T07:57:28Z date_updated: 2023-06-07T07:59:06Z department: - _id: '101' external_id: arxiv: - '2306.03320' language: - iso: eng main_file_link: - url: https://arxiv.org/pdf/2306.03320 page: '29' publication: arXiv:2306.03320 publication_status: submitted status: public title: A parametrisation method for high-order phase reduction in coupled oscillator networks type: preprint user_id: '97359' year: '2023' ... --- _id: '46256' 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. Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete Mathematics. 2023;37(3):1548-1565. doi:10.1137/22m1500654 apa: Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete Mathematics, 37(3), 1548–1565. https://doi.org/10.1137/22m1500654 bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs}, volume={37}, DOI={10.1137/22m1500654}, number={3}, journal={SIAM Journal on Discrete Mathematics}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={1548–1565} }' chicago: 'Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” SIAM Journal on Discrete Mathematics 37, no. 3 (2023): 1548–65. https://doi.org/10.1137/22m1500654.' ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs,” SIAM Journal on Discrete Mathematics, vol. 37, no. 3, pp. 1548–1565, 2023, doi: 10.1137/22m1500654.' mla: Ma, Yulai, et al. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” SIAM Journal on Discrete Mathematics, vol. 37, no. 3, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 1548–65, doi:10.1137/22m1500654. short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, SIAM Journal on Discrete Mathematics 37 (2023) 1548–1565. date_created: 2023-08-01T10:08:32Z date_updated: 2023-08-01T10:09:35Z department: - _id: '542' doi: 10.1137/22m1500654 intvolume: ' 37' issue: '3' keyword: - General Mathematics language: - iso: eng page: 1548-1565 publication: SIAM Journal on Discrete Mathematics publication_identifier: issn: - 0895-4801 - 1095-7146 publication_status: published publisher: Society for Industrial & Applied Mathematics (SIAM) status: public title: Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs type: journal_article user_id: '15540' volume: 37 year: '2023' ... --- _id: '42163' abstract: - lang: eng text: 'The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that is modelled as a neural network. Careful regularisation of the loss function for training $L_d$ is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler--Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE.' 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 discrete Lagrangians for variational PDEs from data and detection of travelling waves. In: Nielsen F, Barbaresco F, eds. Geometric Science of Information. Vol 14071. Lecture Notes in Computer Science (LNCS). Springer, Cham.; 2023:569-579. doi:10.1007/978-3-031-38271-0_57' apa: Offen, C., & Ober-Blöbaum, S. (2023). Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In F. Nielsen & F. Barbaresco (Eds.), Geometric Science of Information (Vol. 14071, pp. 569–579). Springer, Cham. https://doi.org/10.1007/978-3-031-38271-0_57 bibtex: '@inproceedings{Offen_Ober-Blöbaum_2023, series={Lecture Notes in Computer Science (LNCS)}, title={Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves}, volume={14071}, DOI={10.1007/978-3-031-38271-0_57}, booktitle={Geometric Science of Information}, publisher={Springer, Cham.}, author={Offen, Christian and Ober-Blöbaum, Sina}, editor={Nielsen, F and Barbaresco, F}, year={2023}, pages={569–579}, collection={Lecture Notes in Computer Science (LNCS)} }' chicago: Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” In Geometric Science of Information, edited by F Nielsen and F Barbaresco, 14071:569–79. Lecture Notes in Computer Science (LNCS). Springer, Cham., 2023. https://doi.org/10.1007/978-3-031-38271-0_57. ieee: 'C. Offen and S. Ober-Blöbaum, “Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves,” in Geometric Science of Information, Saint-Malo, Palais du Grand Large, France, 2023, vol. 14071, pp. 569–579, doi: 10.1007/978-3-031-38271-0_57.' mla: Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” Geometric Science of Information, edited by F Nielsen and F Barbaresco, vol. 14071, Springer, Cham., 2023, pp. 569–79, doi:10.1007/978-3-031-38271-0_57. short: 'C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric Science of Information, Springer, Cham., 2023, pp. 569–579.' conference: end_date: 2023-09-01 location: Saint-Malo, Palais du Grand Large, France name: ' GSI''23 6th International Conference on Geometric Science of Information' start_date: 2023-08-30 date_created: 2023-02-16T11:32:48Z date_updated: 2023-08-10T08:34:04Z ddc: - '510' department: - _id: '636' doi: 10.1007/978-3-031-38271-0_57 editor: - first_name: F full_name: Nielsen, F last_name: Nielsen - first_name: F full_name: Barbaresco, F last_name: Barbaresco external_id: arxiv: - '2302.08232 ' file: - access_level: open_access content_type: application/pdf creator: coffen date_created: 2023-08-02T12:04:17Z date_updated: 2023-08-02T12:04:17Z description: |- The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density Ld that is modelled as a neural network. Careful regularisation of the loss function for training Ld is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler–Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE. file_id: '46273' file_name: LDensityLearning.pdf file_size: 1938962 relation: main_file title: Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves file_date_updated: 2023-08-02T12:04:17Z has_accepted_license: '1' intvolume: ' 14071' keyword: - System identification - discrete Lagrangians - travelling waves language: - iso: eng oa: '1' page: 569-579 publication: Geometric Science of Information publication_identifier: eisbn: - 978-3-031-38271-0 publication_status: published publisher: Springer, Cham. quality_controlled: '1' related_material: link: - description: GitHub relation: software url: https://github.com/Christian-Offen/LagrangianDensityML series_title: Lecture Notes in Computer Science (LNCS) status: public title: Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves type: conference user_id: '85279' volume: 14071 year: '2023' ... --- _id: '29240' abstract: - lang: eng text: "The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exhibit those motions which extremise an action functional. Many qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equations, are related to the existence of an action functional. Incorporating variational structure into learning algorithms for dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features with the exact physical system. In this paper we show how to incorporate variational principles into trajectory predictions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position data of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no prior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward error analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the learned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,\r\nwe introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of variational backward error analysis. (3) Finally, we introduce a method to perform system identification from position observations only, based on variational backward error analysis." article_type: original author: - first_name: Sina full_name: Ober-Blöbaum, Sina id: '16494' last_name: Ober-Blöbaum - first_name: Christian full_name: Offen, Christian id: '85279' last_name: Offen orcid: 0000-0002-5940-8057 citation: ama: Ober-Blöbaum S, Offen C. Variational Learning of Euler–Lagrange Dynamics from Data. Journal of Computational and Applied Mathematics. 2023;421:114780. doi:10.1016/j.cam.2022.114780 apa: Ober-Blöbaum, S., & Offen, C. (2023). Variational Learning of Euler–Lagrange Dynamics from Data. Journal of Computational and Applied Mathematics, 421, 114780. https://doi.org/10.1016/j.cam.2022.114780 bibtex: '@article{Ober-Blöbaum_Offen_2023, title={Variational Learning of Euler–Lagrange Dynamics from Data}, volume={421}, DOI={10.1016/j.cam.2022.114780}, journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier}, author={Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={114780} }' chicago: 'Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” Journal of Computational and Applied Mathematics 421 (2023): 114780. https://doi.org/10.1016/j.cam.2022.114780.' ieee: 'S. Ober-Blöbaum and C. Offen, “Variational Learning of Euler–Lagrange Dynamics from Data,” Journal of Computational and Applied Mathematics, vol. 421, p. 114780, 2023, doi: 10.1016/j.cam.2022.114780.' mla: Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” Journal of Computational and Applied Mathematics, vol. 421, Elsevier, 2023, p. 114780, doi:10.1016/j.cam.2022.114780. short: S. Ober-Blöbaum, C. Offen, Journal of Computational and Applied Mathematics 421 (2023) 114780. date_created: 2022-01-11T13:24:00Z date_updated: 2023-08-10T08:42:39Z ddc: - '510' department: - _id: '636' doi: 10.1016/j.cam.2022.114780 external_id: arxiv: - '2112.12619' file: - access_level: open_access content_type: application/pdf creator: coffen date_created: 2022-06-28T15:25:50Z date_updated: 2022-06-28T15:25:50Z description: |- The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exhibit those motions which extremise an action functional. Many qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equa- tions, are related to the existence of an action functional. Incorporating variational structure into learning algorithms for dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features with the exact physical system. In this paper we show how to incorporate variational principles into trajectory predic- tions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position data of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no prior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward error analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the learned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this, we introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of variational backward error analysis. (3) Finally, we introduce a method to perform system identification from position observations only, based on variational backward error analysis. file_id: '32274' file_name: ShadowLagrangian_revision1_journal_style_arxiv.pdf file_size: 3640770 relation: main_file title: Variational Learning of Euler–Lagrange Dynamics from Data file_date_updated: 2022-06-28T15:25:50Z has_accepted_license: '1' intvolume: ' 421' keyword: - Lagrangian learning - variational backward error analysis - modified Lagrangian - variational integrators - physics informed learning language: - iso: eng oa: '1' page: '114780' publication: Journal of Computational and Applied Mathematics publication_identifier: issn: - 0377-0427 publication_status: epub_ahead publisher: Elsevier quality_controlled: '1' related_material: link: - relation: software url: https://github.com/Christian-Offen/LagrangianShadowIntegration status: public title: Variational Learning of Euler–Lagrange Dynamics from Data type: journal_article user_id: '85279' volume: 421 year: '2023' ... --- _id: '29236' abstract: - lang: eng text: The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analysis. If the original and modified equation share structural properties, then the exact and approximate solution share geometric features such as the existence of conserved quantities. Conjugate symplectic methods preserve a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian system. We show how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures. In contrast to other approaches, our backward error analysis method does not rely on an ansatz but computes the structures systematically, provided that a variational formulation of the method is known. The technique is illustrated on the example of symmetric linear multistep methods with matrix coefficients. article_type: original author: - first_name: Robert full_name: McLachlan, Robert last_name: McLachlan - first_name: Christian full_name: Offen, Christian id: '85279' last_name: Offen orcid: 0000-0002-5940-8057 citation: ama: McLachlan R, Offen C. Backward error analysis for conjugate symplectic methods. Journal of Geometric Mechanics. 2023;15(1):98-115. doi:10.3934/jgm.2023005 apa: McLachlan, R., & Offen, C. (2023). Backward error analysis for conjugate symplectic methods. Journal of Geometric Mechanics, 15(1), 98–115. https://doi.org/10.3934/jgm.2023005 bibtex: '@article{McLachlan_Offen_2023, title={Backward error analysis for conjugate symplectic methods}, volume={15}, DOI={10.3934/jgm.2023005}, number={1}, journal={Journal of Geometric Mechanics}, publisher={AIMS Press}, author={McLachlan, Robert and Offen, Christian}, year={2023}, pages={98–115} }' chicago: 'McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate Symplectic Methods.” Journal of Geometric Mechanics 15, no. 1 (2023): 98–115. https://doi.org/10.3934/jgm.2023005.' ieee: 'R. McLachlan and C. Offen, “Backward error analysis for conjugate symplectic methods,” Journal of Geometric Mechanics, vol. 15, no. 1, pp. 98–115, 2023, doi: 10.3934/jgm.2023005.' mla: McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate Symplectic Methods.” Journal of Geometric Mechanics, vol. 15, no. 1, AIMS Press, 2023, pp. 98–115, doi:10.3934/jgm.2023005. short: R. McLachlan, C. Offen, Journal of Geometric Mechanics 15 (2023) 98–115. date_created: 2022-01-11T12:48:39Z date_updated: 2023-08-10T08:40:30Z ddc: - '510' department: - _id: '636' doi: 10.3934/jgm.2023005 external_id: arxiv: - '2201.03911' file: - access_level: open_access content_type: application/pdf creator: coffen date_created: 2022-08-12T16:48:59Z date_updated: 2022-08-12T16:48:59Z description: The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analysis. If the original and modified equation share structural properties, then the exact and approximate solution share geometric features such as the existence of conserved quantities. Conjugate symplectic methods preserve a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian system. We show how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures. In contrast to other approaches, our backward error analysis method does not rely on an ansatz but computes the structures systematically, provided that a variational formulation of the method is known. The technique is illustrated on the example of symmetric linear multistep methods with matrix coefficients. file_id: '32801' file_name: BEA_MultiStep_Matrix.pdf file_size: 827030 relation: main_file title: Backward error analysis for conjugate symplectic methods file_date_updated: 2022-08-12T16:48:59Z has_accepted_license: '1' intvolume: ' 15' issue: '1' keyword: - variational integrators - backward error analysis - Euler--Lagrange equations - multistep methods - conjugate symplectic methods language: - iso: eng oa: '1' page: 98-115 publication: Journal of Geometric Mechanics publication_status: published publisher: AIMS Press quality_controlled: '1' related_material: link: - relation: software url: https://github.com/Christian-Offen/BEAConjugateSymplectic status: public title: Backward error analysis for conjugate symplectic methods type: journal_article user_id: '85279' volume: 15 year: '2023' ... --- _id: '37654' abstract: - lang: eng text: "Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when\r\nlearning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite\r\nthe data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we\r\nenhance the HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach\r\nallows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples,\r\na pendulum on a cart and a two-body problem from astrodynamics are considered." article_number: '063115' article_type: original author: - first_name: Eva full_name: Dierkes, Eva last_name: Dierkes - 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 - first_name: Kathrin full_name: Flaßkamp, Kathrin last_name: Flaßkamp citation: ama: Dierkes E, Offen C, Ober-Blöbaum S, Flaßkamp K. Hamiltonian Neural Networks with Automatic Symmetry Detection. Chaos. 2023;33(6). doi:10.1063/5.0142969 apa: Dierkes, E., Offen, C., Ober-Blöbaum, S., & Flaßkamp, K. (2023). Hamiltonian Neural Networks with Automatic Symmetry Detection. Chaos, 33(6), Article 063115. https://doi.org/10.1063/5.0142969 bibtex: '@article{Dierkes_Offen_Ober-Blöbaum_Flaßkamp_2023, title={Hamiltonian Neural Networks with Automatic Symmetry Detection}, volume={33}, DOI={10.1063/5.0142969}, number={6063115}, journal={Chaos}, publisher={AIP Publishing}, author={Dierkes, Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}, year={2023} }' chicago: Dierkes, Eva, Christian Offen, Sina Ober-Blöbaum, and Kathrin Flaßkamp. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” Chaos 33, no. 6 (2023). https://doi.org/10.1063/5.0142969. ieee: 'E. Dierkes, C. Offen, S. Ober-Blöbaum, and K. Flaßkamp, “Hamiltonian Neural Networks with Automatic Symmetry Detection,” Chaos, vol. 33, no. 6, Art. no. 063115, 2023, doi: 10.1063/5.0142969.' mla: Dierkes, Eva, et al. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” Chaos, vol. 33, no. 6, 063115, AIP Publishing, 2023, doi:10.1063/5.0142969. short: E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023). date_created: 2023-01-20T09:10:06Z date_updated: 2023-08-10T08:37:01Z ddc: - '510' department: - _id: '636' doi: 10.1063/5.0142969 external_id: arxiv: - '2301.07928' file: - access_level: open_access content_type: application/pdf creator: coffen date_created: 2023-04-26T16:20:56Z date_updated: 2023-04-26T16:20:56Z description: |- Incorporating physical system knowledge into data-driven system identification has been shown to be beneficial. The approach presented in this article combines learning of an energy-conserving model from data with detecting a Lie group representation of the unknown system symmetry. The proposed approach can improve the learned model and reveal underlying symmetry simultaneously. file_id: '44205' file_name: JournalPaper_main.pdf file_size: 5200111 relation: main_file title: Hamiltonian Neural Networks with Automatic Symmetry Detection file_date_updated: 2023-04-26T16:20:56Z has_accepted_license: '1' intvolume: ' 33' issue: '6' language: - iso: eng oa: '1' publication: Chaos publication_identifier: issn: - 1054-1500 publication_status: published publisher: AIP Publishing related_material: link: - description: GitHub relation: software url: https://github.com/eva-dierkes/HNN_withSymmetries status: public title: Hamiltonian Neural Networks with Automatic Symmetry Detection type: journal_article user_id: '85279' volume: 33 year: '2023' ... --- _id: '23428' abstract: - lang: eng text: "The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems in recent years, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are still quite scarce. In this paper, we derive probabilistic bounds for the approximation error and the prediction error depending on the number of training data points; for both ordinary and stochastic differential equations. Moreover, we extend our analysis to nonlinear control-affine systems using either ergodic trajectories or i.i.d.\r\nsamples. Here, we exploit the linearity of the Koopman generator to obtain a bilinear system and, thus, circumvent the curse of dimensionality since we do not autonomize the system by augmenting the state by the control inputs. To the\r\nbest of our knowledge, this is the first finite-data error analysis in the stochastic and/or control setting. Finally, we demonstrate the effectiveness of the proposed approach by comparing it with state-of-the-art techniques showing its superiority whenever state and control are coupled." article_number: '14' author: - first_name: Feliks full_name: Nüske, Feliks id: '81513' last_name: Nüske orcid: 0000-0003-2444-7889 - first_name: Sebastian full_name: Peitz, Sebastian id: '47427' last_name: Peitz orcid: 0000-0002-3389-793X - first_name: Friedrich full_name: Philipp, Friedrich last_name: Philipp - first_name: Manuel full_name: Schaller, Manuel last_name: Schaller - first_name: Karl full_name: Worthmann, Karl last_name: Worthmann citation: ama: Nüske F, Peitz S, Philipp F, Schaller M, Worthmann K. Finite-data error bounds for Koopman-based prediction and control. Journal of Nonlinear Science. 2023;33. doi:10.1007/s00332-022-09862-1 apa: Nüske, F., Peitz, S., Philipp, F., Schaller, M., & Worthmann, K. (2023). Finite-data error bounds for Koopman-based prediction and control. Journal of Nonlinear Science, 33, Article 14. https://doi.org/10.1007/s00332-022-09862-1 bibtex: '@article{Nüske_Peitz_Philipp_Schaller_Worthmann_2023, title={Finite-data error bounds for Koopman-based prediction and control}, volume={33}, DOI={10.1007/s00332-022-09862-1}, number={14}, journal={Journal of Nonlinear Science}, author={Nüske, Feliks and Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl}, year={2023} }' chicago: Nüske, Feliks, Sebastian Peitz, Friedrich Philipp, Manuel Schaller, and Karl Worthmann. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.” Journal of Nonlinear Science 33 (2023). https://doi.org/10.1007/s00332-022-09862-1. ieee: 'F. Nüske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann, “Finite-data error bounds for Koopman-based prediction and control,” Journal of Nonlinear Science, vol. 33, Art. no. 14, 2023, doi: 10.1007/s00332-022-09862-1.' mla: Nüske, Feliks, et al. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.” Journal of Nonlinear Science, vol. 33, 14, 2023, doi:10.1007/s00332-022-09862-1. short: F. Nüske, S. Peitz, F. Philipp, M. Schaller, K. Worthmann, Journal of Nonlinear Science 33 (2023). date_created: 2021-08-17T12:25:09Z date_updated: 2023-08-24T07:50:12Z department: - _id: '101' - _id: '655' doi: 10.1007/s00332-022-09862-1 intvolume: ' 33' language: - iso: eng main_file_link: - open_access: '1' url: https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf oa: '1' publication: Journal of Nonlinear Science publication_status: published status: public title: Finite-data error bounds for Koopman-based prediction and control type: journal_article user_id: '47427' volume: 33 year: '2023' ... --- _id: '21600' abstract: - lang: eng text: Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it results in prohibitively large errors or computational effort. To this end, adaptive schemes, such as solvers based on Runge–Kutta pairs, have been developed which adapt the step size based on local error estimations at each step. While the classical schemes apply very generally and are highly efficient on regular systems, they can behave suboptimally when an inefficient step rejection mechanism is triggered by structurally complex systems such as chaotic systems. To overcome these issues, we propose a method to tailor numerical schemes to the problem class at hand. This is achieved by combining simple, classical quadrature rules or ODE solvers with data-driven time-stepping controllers. Compared with learning solution operators to ODEs directly, it generalizes better to unseen initial data as our approach employs classical numerical schemes as base methods. At the same time it can make use of identified structures of a problem class and, therefore, outperforms state-of-the-art adaptive schemes. Several examples demonstrate superior efficiency. Source code is available at https://github.com/lueckem/quadrature-ML. author: - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Eyke full_name: Hüllermeier, Eyke id: '48129' last_name: Hüllermeier - first_name: Marvin full_name: Lücke, Marvin last_name: Lücke - first_name: Sina full_name: Ober-Blöbaum, Sina id: '16494' last_name: Ober-Blöbaum - first_name: Christian full_name: Offen, Christian id: '85279' last_name: Offen orcid: 0000-0002-5940-8057 - first_name: Sebastian full_name: Peitz, Sebastian id: '47427' last_name: Peitz orcid: 0000-0002-3389-793X - first_name: Karlson full_name: Pfannschmidt, Karlson id: '13472' last_name: Pfannschmidt orcid: 0000-0001-9407-7903 citation: ama: Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical integration using reinforcement  learning. SIAM Journal on Scientific Computing. 2023;45(2):A579-A595. doi:10.1137/21M1412682 apa: Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz, S., & Pfannschmidt, K. (2023). Efficient time stepping for numerical integration using reinforcement  learning. SIAM Journal on Scientific Computing, 45(2), A579–A595. https://doi.org/10.1137/21M1412682 bibtex: '@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023, title={Efficient time stepping for numerical integration using reinforcement  learning}, volume={45}, DOI={10.1137/21M1412682}, number={2}, journal={SIAM Journal on Scientific Computing}, author={Dellnitz, Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen, Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, year={2023}, pages={A579–A595} }' chicago: 'Dellnitz, Michael, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum, Christian Offen, Sebastian Peitz, and Karlson Pfannschmidt. “Efficient Time Stepping for Numerical Integration Using Reinforcement  Learning.” SIAM Journal on Scientific Computing 45, no. 2 (2023): A579–95. https://doi.org/10.1137/21M1412682.' ieee: 'M. Dellnitz et al., “Efficient time stepping for numerical integration using reinforcement  learning,” SIAM Journal on Scientific Computing, vol. 45, no. 2, pp. A579–A595, 2023, doi: 10.1137/21M1412682.' mla: Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration Using Reinforcement  Learning.” SIAM Journal on Scientific Computing, vol. 45, no. 2, 2023, pp. A579–95, doi:10.1137/21M1412682. short: M. Dellnitz, E. Hüllermeier, M. Lücke, S. Ober-Blöbaum, C. Offen, S. Peitz, K. Pfannschmidt, SIAM Journal on Scientific Computing 45 (2023) A579–A595. date_created: 2021-04-09T07:59:19Z date_updated: 2023-08-25T09:24:50Z ddc: - '510' department: - _id: '101' - _id: '636' - _id: '355' - _id: '655' doi: 10.1137/21M1412682 external_id: arxiv: - arXiv:2104.03562 has_accepted_license: '1' intvolume: ' 45' issue: '2' language: - iso: eng main_file_link: - url: https://epubs.siam.org/doi/reader/10.1137/21M1412682 page: A579-A595 publication: SIAM Journal on Scientific Computing publication_status: published related_material: link: - description: GitHub relation: software url: https://github.com/lueckem/quadrature-ML status: public title: Efficient time stepping for numerical integration using reinforcement learning type: journal_article user_id: '47427' volume: 45 year: '2023' ...