[{"_id":"63557","department":[{"_id":"636"}],"user_id":"87909","language":[{"iso":"eng"}],"publication":"Multibody System Dynamics","type":"journal_article","abstract":[{"lang":"eng","text":"We discretise a recently proposed new Lagrangian approach to optimal control problems with dynamics described by force-controlled Euler-Lagrange equations (Konopik et al., in Nonlinearity 38:11, 2025). The resulting discretisations are in the form of discrete Lagrangians. We show that the discrete necessary conditions for optimality obtained provide variational integrators for the continuous problem, akin to Karush-Kuhn-Tucker (KKT) conditions for standard direct approaches. This approach paves the way for the use of variational error analysis to derive the order of convergence of the resulting numerical schemes for both state and costate variables and to apply discrete Noether’s theorem to compute conserved quantities, distinguishing itself from existing geometric approaches. We show for a family of low-order discretisations that the resulting numerical schemes are ‘doubly-symplectic’, meaning they yield forced symplectic integrators for the underlying controlled mechanical system and overall symplectic integrators in the state-adjoint space. Multi-body dynamics examples are solved numerically using the new approach. In addition, the new approach is compared to standard direct approaches in terms of computational performance and error convergence. The results highlight the advantages of the new approach, namely, better performance and convergence behaviour of state and costate variables consistent with variational error analysis and automatic preservation of certain first integrals."}],"status":"public","date_updated":"2026-01-12T11:35:27Z","publisher":"Springer Science and Business Media LLC","date_created":"2026-01-12T11:33:54Z","author":[{"last_name":"Konopik","full_name":"Konopik, Michael","first_name":"Michael"},{"first_name":"Sigrid","full_name":"Leyendecker, Sigrid","last_name":"Leyendecker"},{"last_name":"Maslovskaya","id":"87909","full_name":"Maslovskaya, Sofya","first_name":"Sofya"},{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"last_name":"Sato Martín de Almagro","full_name":"Sato Martín de Almagro, Rodrigo T.","first_name":"Rodrigo T."}],"title":"On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics","doi":"10.1007/s11044-025-10138-1","publication_identifier":{"issn":["1384-5640","1573-272X"]},"publication_status":"published","year":"2026","citation":{"apa":"Konopik, M., Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., &#38; Sato Martín de Almagro, R. T. (2026). On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics. <i>Multibody System Dynamics</i>. <a href=\"https://doi.org/10.1007/s11044-025-10138-1\">https://doi.org/10.1007/s11044-025-10138-1</a>","mla":"Konopik, Michael, et al. “On the Variational Discretisation of Optimal Control Problems for Unconstrained Lagrangian Dynamics.” <i>Multibody System Dynamics</i>, Springer Science and Business Media LLC, 2026, doi:<a href=\"https://doi.org/10.1007/s11044-025-10138-1\">10.1007/s11044-025-10138-1</a>.","short":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T. Sato Martín de Almagro, Multibody System Dynamics (2026).","bibtex":"@article{Konopik_Leyendecker_Maslovskaya_Ober-Blöbaum_Sato Martín de Almagro_2026, title={On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics}, DOI={<a href=\"https://doi.org/10.1007/s11044-025-10138-1\">10.1007/s11044-025-10138-1</a>}, journal={Multibody System Dynamics}, publisher={Springer Science and Business Media LLC}, author={Konopik, Michael and Leyendecker, Sigrid and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Sato Martín de Almagro, Rodrigo T.}, year={2026} }","ama":"Konopik M, Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Sato Martín de Almagro RT. On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics. <i>Multibody System Dynamics</i>. Published online 2026. doi:<a href=\"https://doi.org/10.1007/s11044-025-10138-1\">10.1007/s11044-025-10138-1</a>","ieee":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, and R. T. Sato Martín de Almagro, “On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics,” <i>Multibody System Dynamics</i>, 2026, doi: <a href=\"https://doi.org/10.1007/s11044-025-10138-1\">10.1007/s11044-025-10138-1</a>.","chicago":"Konopik, Michael, Sigrid Leyendecker, Sofya Maslovskaya, Sina Ober-Blöbaum, and Rodrigo T. Sato Martín de Almagro. “On the Variational Discretisation of Optimal Control Problems for Unconstrained Lagrangian Dynamics.” <i>Multibody System Dynamics</i>, 2026. <a href=\"https://doi.org/10.1007/s11044-025-10138-1\">https://doi.org/10.1007/s11044-025-10138-1</a>."}},{"language":[{"iso":"eng"}],"_id":"59792","department":[{"_id":"636"}],"user_id":"87909","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n          <jats:p>Motivated by mechanical systems with symmetries, we focus on optimal control problems possessing certain symmetries. Following recent works (Faulwasser in Math Control Signals Syst 34:759–788 2022; Trélat in Math Control Signals Syst 35:685–739 2023), which generalized the classical concept of <jats:italic>static turnpike to manifold turnpike</jats:italic> we extend the <jats:italic>exponential turnpike property</jats:italic> to the <jats:italic>exponential trim turnpike</jats:italic> for control systems with symmetries induced by abelian or non-abelian groups. Our analysis is mainly based on the geometric reduction of control systems with symmetries. More concretely, we first reduce the control system on the quotient space and state the turnpike theorem for the reduced problem. Then we use the group properties to obtain the <jats:italic>trim turnpike theorem</jats:italic> for the full problem. Finally, we illustrate our results on the Kepler problem and the rigid body problem.\r\n</jats:p>","lang":"eng"}],"status":"public","publication":"Mathematics of Control, Signals, and Systems","type":"journal_article","title":"Trim turnpikes for optimal control problems with symmetries","doi":"10.1007/s00498-025-00408-w","publisher":"Springer Science and Business Media LLC","date_updated":"2025-05-05T09:24:09Z","author":[{"full_name":"Flaßkamp, Kathrin","last_name":"Flaßkamp","first_name":"Kathrin"},{"last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","id":"87909","first_name":"Sofya"},{"first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum"},{"first_name":"Boris Edgar","full_name":"Wembe Moafo, Boris Edgar","id":"95394","last_name":"Wembe Moafo"}],"date_created":"2025-05-05T09:23:38Z","year":"2025","citation":{"ama":"Flaßkamp K, Maslovskaya S, Ober-Blöbaum S, Wembe Moafo BE. Trim turnpikes for optimal control problems with symmetries. <i>Mathematics of Control, Signals, and Systems</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>","chicago":"Flaßkamp, Kathrin, Sofya Maslovskaya, Sina Ober-Blöbaum, and Boris Edgar Wembe Moafo. “Trim Turnpikes for Optimal Control Problems with Symmetries.” <i>Mathematics of Control, Signals, and Systems</i>, 2025. <a href=\"https://doi.org/10.1007/s00498-025-00408-w\">https://doi.org/10.1007/s00498-025-00408-w</a>.","ieee":"K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, and B. E. Wembe Moafo, “Trim turnpikes for optimal control problems with symmetries,” <i>Mathematics of Control, Signals, and Systems</i>, 2025, doi: <a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>.","bibtex":"@article{Flaßkamp_Maslovskaya_Ober-Blöbaum_Wembe Moafo_2025, title={Trim turnpikes for optimal control problems with symmetries}, DOI={<a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>}, journal={Mathematics of Control, Signals, and Systems}, publisher={Springer Science and Business Media LLC}, author={Flaßkamp, Kathrin and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Wembe Moafo, Boris Edgar}, year={2025} }","mla":"Flaßkamp, Kathrin, et al. “Trim Turnpikes for Optimal Control Problems with Symmetries.” <i>Mathematics of Control, Signals, and Systems</i>, Springer Science and Business Media LLC, 2025, doi:<a href=\"https://doi.org/10.1007/s00498-025-00408-w\">10.1007/s00498-025-00408-w</a>.","short":"K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, B.E. Wembe Moafo, Mathematics of Control, Signals, and Systems (2025).","apa":"Flaßkamp, K., Maslovskaya, S., Ober-Blöbaum, S., &#38; Wembe Moafo, B. E. (2025). Trim turnpikes for optimal control problems with symmetries. <i>Mathematics of Control, Signals, and Systems</i>. <a href=\"https://doi.org/10.1007/s00498-025-00408-w\">https://doi.org/10.1007/s00498-025-00408-w</a>"},"publication_identifier":{"issn":["0932-4194","1435-568X"]},"publication_status":"published"},{"language":[{"iso":"eng"}],"department":[{"_id":"623"},{"_id":"15"},{"_id":"636"}],"user_id":"85279","_id":"58544","external_id":{"arxiv":["2502.05123"]},"status":"public","abstract":[{"lang":"eng","text":"We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which being in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes. "}],"type":"preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2502.05123"}],"title":"Multiphoton, multimode state classification for nonlinear optical circuits ","author":[{"first_name":"Denis","last_name":"Kopylov","full_name":"Kopylov, Denis","id":"98502"},{"first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian","id":"85279"},{"last_name":"Ares","full_name":"Ares, Laura","first_name":"Laura"},{"first_name":"Boris Edgar","id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"first_name":"Torsten","orcid":"0000-0001-8864-2072","last_name":"Meier","full_name":"Meier, Torsten","id":"344"},{"last_name":"Sharapova","id":"60286","full_name":"Sharapova, Polina","first_name":"Polina"},{"first_name":"Jan","id":"75127","full_name":"Sperling, Jan","last_name":"Sperling","orcid":"0000-0002-5844-3205"}],"date_created":"2025-02-10T08:26:45Z","oa":"1","date_updated":"2025-02-10T08:36:12Z","citation":{"apa":"Kopylov, D., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S., Meier, T., Sharapova, P., &#38; Sperling, J. (n.d.). <i>Multiphoton, multimode state classification for nonlinear optical circuits </i>.","mla":"Kopylov, Denis, et al. <i>Multiphoton, Multimode State Classification for Nonlinear Optical Circuits </i>.","bibtex":"@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling, title={Multiphoton, multimode state classification for nonlinear optical circuits }, author={Kopylov, Denis and Offen, Christian and Ares, Laura and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina and Sperling, Jan} }","short":"D. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier, P. Sharapova, J. Sperling, (n.d.).","ieee":"D. Kopylov <i>et al.</i>, “Multiphoton, multimode state classification for nonlinear optical circuits .” .","chicago":"Kopylov, Denis, Christian Offen, Laura Ares, Boris Edgar Wembe Moafo, Sina Ober-Blöbaum, Torsten Meier, Polina Sharapova, and Jan Sperling. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits ,” n.d.","ama":"Kopylov D, Offen C, Ares L, et al. Multiphoton, multimode state classification for nonlinear optical circuits ."},"year":"2025","publication_status":"submitted"},{"title":"Adaptive higher order reversible integrators for memory efficient deep learning","date_created":"2025-05-05T09:25:28Z","author":[{"first_name":"Sofya","id":"87909","full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"first_name":"Christian","full_name":"Offen, Christian","id":"85279","orcid":"0000-0002-5940-8057","last_name":"Offen"},{"first_name":"Pranav","last_name":"Singh","full_name":"Singh, Pranav"},{"last_name":"Wembe Moafo","full_name":"Wembe Moafo, Boris Edgar","id":"95394","first_name":"Boris Edgar"}],"date_updated":"2025-09-30T15:16:09Z","citation":{"apa":"Maslovskaya, S., Ober-Blöbaum, S., Offen, C., Singh, P., &#38; Wembe Moafo, B. E. (2025). <i>Adaptive higher order reversible integrators for memory efficient deep learning</i>.","bibtex":"@article{Maslovskaya_Ober-Blöbaum_Offen_Singh_Wembe Moafo_2025, title={Adaptive higher order reversible integrators for memory efficient deep learning}, author={Maslovskaya, Sofya and Ober-Blöbaum, Sina and Offen, Christian and Singh, Pranav and Wembe Moafo, Boris Edgar}, year={2025} }","mla":"Maslovskaya, Sofya, et al. <i>Adaptive Higher Order Reversible Integrators for Memory Efficient Deep Learning</i>. 2025.","short":"S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, B.E. Wembe Moafo, (2025).","ama":"Maslovskaya S, Ober-Blöbaum S, Offen C, Singh P, Wembe Moafo BE. Adaptive higher order reversible integrators for memory efficient deep learning. Published online 2025.","ieee":"S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, and B. E. Wembe Moafo, “Adaptive higher order reversible integrators for memory efficient deep learning.” 2025.","chicago":"Maslovskaya, Sofya, Sina Ober-Blöbaum, Christian Offen, Pranav Singh, and Boris Edgar Wembe Moafo. “Adaptive Higher Order Reversible Integrators for Memory Efficient Deep Learning,” 2025."},"year":"2025","has_accepted_license":"1","language":[{"iso":"eng"}],"file_date_updated":"2025-05-05T09:28:02Z","ddc":["510"],"user_id":"85279","department":[{"_id":"636"}],"external_id":{"arxiv":["2410.09537"]},"_id":"59794","file":[{"file_id":"59795","access_level":"closed","file_name":"2410.09537v2.pdf","file_size":1830758,"date_created":"2025-05-05T09:28:02Z","creator":"sofyam","date_updated":"2025-05-05T09:28:02Z","relation":"main_file","success":1,"content_type":"application/pdf"}],"status":"public","abstract":[{"lang":"eng","text":"The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, which leads to memory bottlenecks during training. Moreover, deep networks are often unable to handle time-series data appearing at irregular intervals. These issues can be resolved by considering continuous-depth networks based on the neural ODE framework in combination with reversible integration methods that allow for variable time-steps. Reversibility of the method ensures that the memory requirement for training is independent of network depth, while variable time-steps are required for assimilating time-series data on irregular intervals. However, at present, there are no known higher-order reversible methods with this property. High-order methods are especially important when a high level of accuracy in learning is required or when small time-steps are necessary due to large errors in time integration of neural ODEs, for instance in context of complex dynamical systems such as Kepler systems and molecular dynamics. The requirement of small time-steps when using a low-order method can significantly increase the computational cost of training as well as inference. In this work, we present an approach for constructing high-order reversible methods that allow adaptive time-stepping. Our numerical tests show the advantages in computational speed when applied to the task of learning dynamical systems."}],"type":"preprint"},{"publication":"Physical Review Research","type":"journal_article","abstract":[{"text":"<jats:p>We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which is in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes.</jats:p>","lang":"eng"}],"status":"public","_id":"62980","project":[{"_id":"53","name":"TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten zu funktionellen Strukturen"},{"name":"TRR 142 - Project Area C","_id":"56"},{"name":"TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen Systemen: Eine theoretische Analyse","_id":"174"},{"_id":"266","name":"PhoQC: Photonisches Quantencomputing"}],"department":[{"_id":"15"},{"_id":"569"},{"_id":"170"},{"_id":"293"},{"_id":"706"},{"_id":"636"},{"_id":"35"},{"_id":"230"},{"_id":"429"},{"_id":"623"}],"user_id":"16199","article_number":"033062","language":[{"iso":"eng"}],"publication_identifier":{"issn":["2643-1564"]},"publication_status":"published","issue":"3","year":"2025","intvolume":"         7","citation":{"ama":"Kopylov DA, Offen C, Ares L, et al. Multiphoton, multimode state classification for nonlinear optical circuits. <i>Physical Review Research</i>. 2025;7(3). doi:<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>","ieee":"D. A. Kopylov <i>et al.</i>, “Multiphoton, multimode state classification for nonlinear optical circuits,” <i>Physical Review Research</i>, vol. 7, no. 3, Art. no. 033062, 2025, doi: <a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>.","chicago":"Kopylov, Denis A., Christian Offen, Laura Ares, Boris Edgar Wembe Moafo, Sina Ober-Blöbaum, Torsten Meier, Polina R. Sharapova, and Jan Sperling. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits.” <i>Physical Review Research</i> 7, no. 3 (2025). <a href=\"https://doi.org/10.1103/sv6z-v1gk\">https://doi.org/10.1103/sv6z-v1gk</a>.","apa":"Kopylov, D. A., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S., Meier, T., Sharapova, P. R., &#38; Sperling, J. (2025). Multiphoton, multimode state classification for nonlinear optical circuits. <i>Physical Review Research</i>, <i>7</i>(3), Article 033062. <a href=\"https://doi.org/10.1103/sv6z-v1gk\">https://doi.org/10.1103/sv6z-v1gk</a>","short":"D.A. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier, P.R. Sharapova, J. Sperling, Physical Review Research 7 (2025).","bibtex":"@article{Kopylov_Offen_Ares_Wembe Moafo_Ober-Blöbaum_Meier_Sharapova_Sperling_2025, title={Multiphoton, multimode state classification for nonlinear optical circuits}, volume={7}, DOI={<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>}, number={3033062}, journal={Physical Review Research}, publisher={American Physical Society (APS)}, author={Kopylov, Denis A. and Offen, Christian and Ares, Laura and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina R. and Sperling, Jan}, year={2025} }","mla":"Kopylov, Denis A., et al. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits.” <i>Physical Review Research</i>, vol. 7, no. 3, 033062, American Physical Society (APS), 2025, doi:<a href=\"https://doi.org/10.1103/sv6z-v1gk\">10.1103/sv6z-v1gk</a>."},"publisher":"American Physical Society (APS)","date_updated":"2025-12-09T09:10:01Z","volume":7,"date_created":"2025-12-09T09:08:39Z","author":[{"full_name":"Kopylov, Denis A.","last_name":"Kopylov","first_name":"Denis A."},{"last_name":"Offen","orcid":"0000-0002-5940-8057","id":"85279","full_name":"Offen, Christian","first_name":"Christian"},{"first_name":"Laura","full_name":"Ares, Laura","last_name":"Ares"},{"first_name":"Boris Edgar","id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Torsten","id":"344","full_name":"Meier, Torsten","orcid":"0000-0001-8864-2072","last_name":"Meier"},{"first_name":"Polina R.","full_name":"Sharapova, Polina R.","id":"60286","last_name":"Sharapova"},{"full_name":"Sperling, Jan","id":"75127","orcid":"0000-0002-5844-3205","last_name":"Sperling","first_name":"Jan"}],"title":"Multiphoton, multimode state classification for nonlinear optical circuits","doi":"10.1103/sv6z-v1gk"},{"author":[{"first_name":"Torsten","last_name":"Meier","orcid":"0000-0001-8864-2072","full_name":"Meier, Torsten","id":"344"},{"id":"60286","full_name":"Sharapova, Polina R.","last_name":"Sharapova","first_name":"Polina R."},{"orcid":"0000-0002-5844-3205","last_name":"Sperling","id":"75127","full_name":"Sperling, Jan","first_name":"Jan"},{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","first_name":"Boris Edgar"},{"first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","id":"85279","full_name":"Offen, Christian"}],"date_created":"2025-12-09T08:59:27Z","date_updated":"2025-12-09T09:10:23Z","title":"Multiphoton, multimode state classification for nonlinear optical circuits","citation":{"apa":"Meier, T., Sharapova, P. R., Sperling, J., Ober-Blöbaum, S., Wembe Moafo, B. E., &#38; Offen, C. (2025). <i>Multiphoton, multimode state classification for nonlinear optical circuits</i>.","mla":"Meier, Torsten, et al. <i>Multiphoton, Multimode State Classification for Nonlinear Optical Circuits</i>. 2025.","bibtex":"@article{Meier_Sharapova_Sperling_Ober-Blöbaum_Wembe Moafo_Offen_2025, title={Multiphoton, multimode state classification for nonlinear optical circuits}, author={Meier, Torsten and Sharapova, Polina R. and Sperling, Jan and Ober-Blöbaum, Sina and Wembe Moafo, Boris Edgar and Offen, Christian}, year={2025} }","short":"T. Meier, P.R. Sharapova, J. Sperling, S. Ober-Blöbaum, B.E. Wembe Moafo, C. Offen, (2025).","ieee":"T. Meier, P. R. Sharapova, J. Sperling, S. Ober-Blöbaum, B. E. Wembe Moafo, and C. Offen, “Multiphoton, multimode state classification for nonlinear optical circuits.” 2025.","chicago":"Meier, Torsten, Polina R. Sharapova, Jan Sperling, Sina Ober-Blöbaum, Boris Edgar Wembe Moafo, and Christian Offen. “Multiphoton, Multimode State Classification for Nonlinear Optical Circuits,” 2025.","ama":"Meier T, Sharapova PR, Sperling J, Ober-Blöbaum S, Wembe Moafo BE, Offen C. Multiphoton, multimode state classification for nonlinear optical circuits. Published online 2025."},"year":"2025","department":[{"_id":"15"},{"_id":"170"},{"_id":"293"},{"_id":"706"},{"_id":"636"},{"_id":"230"},{"_id":"623"},{"_id":"429"},{"_id":"35"}],"user_id":"16199","_id":"62979","project":[{"name":"TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten zu funktionellen Strukturen","_id":"53"},{"name":"TRR 142 - Project Area C","_id":"56"},{"name":"TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen Systemen: Eine theoretische Analyse","_id":"174"},{"name":"PhoQC: Photonisches Quantencomputing","_id":"266"}],"language":[{"iso":"eng"}],"type":"preprint","status":"public","abstract":[{"lang":"eng","text":"We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which being in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes."}]},{"status":"public","abstract":[{"text":"Differential equations posed on quadratic matrix Lie groups arise in the context of classical mechanics and quantum dynamical systems. Lie group numerical integrators preserve the constants of motions defining the Lie group. Thus, they respect important physical laws of the dynamical system, such as unitarity and energy conservation in the context of quantum dynamical systems, for instance. In this article we develop a high-order commutator free Lie group integrator for non-autonomous differential equations evolving on quadratic Lie groups. Instead of matrix exponentials, which are expensive to evaluate and need to be approximated by appropriate rational functions in order to preserve the Lie group structure, the proposed method is obtained as a composition of Cayley transforms which naturally respect the structure of quadratic Lie groups while being computationally efficient to evaluate. Unlike Cayley-Magnus methods the method is also free from nested matrix commutators.","lang":"eng"}],"type":"journal_article","publication":"J. Comput. Appl. Math","language":[{"iso":"eng"}],"user_id":"95394","department":[{"_id":"94"}],"_id":"59507","citation":{"short":"B.E. Wembe Moafo, C. Offen, S. Maslovskaya, S. Ober-Blöbaum, P. Singh, J. Comput. Appl. Math 477 (n.d.).","mla":"Wembe Moafo, Boris Edgar, et al. “Commutator-Free Cayley Methods.” <i>J. Comput. Appl. Math</i>, vol. 477, no. 15, doi:<a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>.","bibtex":"@article{Wembe Moafo_Offen_Maslovskaya_Ober-Blöbaum_Singh, title={Commutator-free Cayley methods}, volume={477}, DOI={<a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>}, number={15}, journal={J. Comput. Appl. Math}, author={Wembe Moafo, Boris Edgar and Offen, Cristian  and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Singh, Pranav} }","apa":"Wembe Moafo, B. E., Offen, C., Maslovskaya, S., Ober-Blöbaum, S., &#38; Singh, P. (n.d.). Commutator-free Cayley methods. <i>J. Comput. Appl. Math</i>, <i>477</i>(15). <a href=\"https://doi.org/10.1016/j.cam.2025.117184\">https://doi.org/10.1016/j.cam.2025.117184</a>","ama":"Wembe Moafo BE, Offen C, Maslovskaya S, Ober-Blöbaum S, Singh P. Commutator-free Cayley methods. <i>J Comput Appl Math</i>. 477(15). doi:<a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>","chicago":"Wembe Moafo, Boris Edgar, Cristian  Offen, Sofya Maslovskaya, Sina Ober-Blöbaum, and Pranav Singh. “Commutator-Free Cayley Methods.” <i>J. Comput. Appl. Math</i> 477, no. 15 (n.d.). <a href=\"https://doi.org/10.1016/j.cam.2025.117184\">https://doi.org/10.1016/j.cam.2025.117184</a>.","ieee":"B. E. Wembe Moafo, C. Offen, S. Maslovskaya, S. Ober-Blöbaum, and P. Singh, “Commutator-free Cayley methods,” <i>J. Comput. Appl. Math</i>, vol. 477, no. 15, doi: <a href=\"https://doi.org/10.1016/j.cam.2025.117184\">10.1016/j.cam.2025.117184</a>."},"intvolume":"       477","year":"2025","issue":"15","publication_status":"submitted","doi":"10.1016/j.cam.2025.117184","title":"Commutator-free Cayley methods","date_created":"2025-04-10T14:42:52Z","author":[{"first_name":"Boris Edgar","id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo"},{"first_name":"Cristian ","full_name":"Offen, Cristian ","last_name":"Offen"},{"last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","id":"87909","first_name":"Sofya"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Pranav","full_name":"Singh, Pranav","last_name":"Singh"}],"volume":477,"date_updated":"2025-12-16T15:17:27Z"},{"status":"public","publication":"Journal of Nonlinear Science","type":"journal_article","language":[{"iso":"eng"}],"_id":"59797","department":[{"_id":"636"}],"user_id":"87909","year":"2025","intvolume":"        36","citation":{"ama":"Konopik M, T. Sato Martín de Almagro R, Maslovskaya S, Ober-Blöbaum S, Leyendecker S. Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term. <i>Journal of Nonlinear Science</i>. 2025;36(11). doi:<a href=\"https://doi.org/10.1007/s00332-025-10229-5\">10.1007/s00332-025-10229-5</a>","chicago":"Konopik, Michael, Rodrigo T. Sato Martín de Almagro, Sofya Maslovskaya, Sina Ober-Blöbaum, and Sigrid Leyendecker. “Variational Integrators for a New Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term.” <i>Journal of Nonlinear Science</i> 36, no. 11 (2025). <a href=\"https://doi.org/10.1007/s00332-025-10229-5\">https://doi.org/10.1007/s00332-025-10229-5</a>.","ieee":"M. Konopik, R. T. Sato Martín de Almagro, S. Maslovskaya, S. Ober-Blöbaum, and S. Leyendecker, “Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term,” <i>Journal of Nonlinear Science</i>, vol. 36, no. 11, 2025, doi: <a href=\"https://doi.org/10.1007/s00332-025-10229-5\">10.1007/s00332-025-10229-5</a>.","apa":"Konopik, M., T. Sato Martín de Almagro, R., Maslovskaya, S., Ober-Blöbaum, S., &#38; Leyendecker, S. (2025). Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term. <i>Journal of Nonlinear Science</i>, <i>36</i>(11). <a href=\"https://doi.org/10.1007/s00332-025-10229-5\">https://doi.org/10.1007/s00332-025-10229-5</a>","mla":"Konopik, Michael, et al. “Variational Integrators for a New Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term.” <i>Journal of Nonlinear Science</i>, vol. 36, no. 11, 2025, doi:<a href=\"https://doi.org/10.1007/s00332-025-10229-5\">10.1007/s00332-025-10229-5</a>.","bibtex":"@article{Konopik_T. Sato Martín de Almagro_Maslovskaya_Ober-Blöbaum_Leyendecker_2025, title={Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term}, volume={36}, DOI={<a href=\"https://doi.org/10.1007/s00332-025-10229-5\">10.1007/s00332-025-10229-5</a>}, number={11}, journal={Journal of Nonlinear Science}, author={Konopik, Michael and T. Sato Martín de Almagro, Rodrigo and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Leyendecker, Sigrid}, year={2025} }","short":"M. Konopik, R. T. Sato Martín de Almagro, S. Maslovskaya, S. Ober-Blöbaum, S. Leyendecker, Journal of Nonlinear Science 36 (2025)."},"issue":"11","title":"Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term","doi":"10.1007/s00332-025-10229-5","date_updated":"2026-01-06T18:26:57Z","volume":36,"author":[{"full_name":"Konopik, Michael","last_name":"Konopik","first_name":"Michael"},{"full_name":"T. Sato Martín de Almagro, Rodrigo","last_name":"T. Sato Martín de Almagro","first_name":"Rodrigo"},{"full_name":"Maslovskaya, Sofya","id":"87909","last_name":"Maslovskaya","first_name":"Sofya"},{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"last_name":"Leyendecker","full_name":"Leyendecker, Sigrid","first_name":"Sigrid"}],"date_created":"2025-05-05T09:35:31Z"},{"citation":{"ama":"Konopik M, Leyendecker S, Maslovskaya S, Ober-Blöbaum S, T. Sato Martín de Almagro R. A new Lagrangian approach to optimal control of second-order systems. <i>Nonlinearity</i>. 2025;38(11). doi:<a href=\"https://doi.org/10.1088/1361-6544/ae1d08\">10.1088/1361-6544/ae1d08</a>","chicago":"Konopik, Michael, Sigrid Leyendecker, Sofya Maslovskaya, Sina Ober-Blöbaum, and Rodrigo T. Sato Martín de Almagro. “A New Lagrangian Approach to Optimal Control of Second-Order Systems.” <i>Nonlinearity</i> 38, no. 11 (2025). <a href=\"https://doi.org/10.1088/1361-6544/ae1d08\">https://doi.org/10.1088/1361-6544/ae1d08</a>.","ieee":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, and R. T. Sato Martín de Almagro, “A new Lagrangian approach to optimal control of second-order systems,” <i>Nonlinearity</i>, vol. 38, no. 11, 2025, doi: <a href=\"https://doi.org/10.1088/1361-6544/ae1d08\">10.1088/1361-6544/ae1d08</a>.","apa":"Konopik, M., Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., &#38; T. Sato Martín de Almagro, R. (2025). A new Lagrangian approach to optimal control of second-order systems. <i>Nonlinearity</i>, <i>38</i>(11). <a href=\"https://doi.org/10.1088/1361-6544/ae1d08\">https://doi.org/10.1088/1361-6544/ae1d08</a>","bibtex":"@article{Konopik_Leyendecker_Maslovskaya_Ober-Blöbaum_T. Sato Martín de Almagro_2025, title={A new Lagrangian approach to optimal control of second-order systems}, volume={38}, DOI={<a href=\"https://doi.org/10.1088/1361-6544/ae1d08\">10.1088/1361-6544/ae1d08</a>}, number={11}, journal={Nonlinearity}, author={Konopik, Michael and Leyendecker, Sigrid and Maslovskaya, Sofya and Ober-Blöbaum, Sina and T. Sato Martín de Almagro, Rodrigo}, year={2025} }","mla":"Konopik, Michael, et al. “A New Lagrangian Approach to Optimal Control of Second-Order Systems.” <i>Nonlinearity</i>, vol. 38, no. 11, 2025, doi:<a href=\"https://doi.org/10.1088/1361-6544/ae1d08\">10.1088/1361-6544/ae1d08</a>.","short":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. Sato Martín de Almagro, Nonlinearity 38 (2025)."},"intvolume":"        38","year":"2025","issue":"11","doi":"10.1088/1361-6544/ae1d08","title":"A new Lagrangian approach to optimal control of second-order systems","author":[{"last_name":"Konopik","full_name":"Konopik, Michael","first_name":"Michael"},{"first_name":"Sigrid","last_name":"Leyendecker","full_name":"Leyendecker, Sigrid"},{"last_name":"Maslovskaya","id":"87909","full_name":"Maslovskaya, Sofya","first_name":"Sofya"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494","first_name":"Sina"},{"first_name":"Rodrigo","full_name":"T. Sato Martín de Almagro, Rodrigo","last_name":"T. Sato Martín de Almagro"}],"date_created":"2025-05-05T09:37:50Z","volume":38,"date_updated":"2026-01-06T18:24:40Z","status":"public","type":"journal_article","publication":"Nonlinearity","language":[{"iso":"eng"}],"user_id":"87909","department":[{"_id":"636"}],"_id":"59799"},{"issue":"0","year":"2024","publisher":"American Institute of Mathematical Sciences (AIMS)","date_created":"2024-03-28T15:58:02Z","title":"A new Lagrangian approach to control affine systems with a quadratic Lagrange term","publication":"Journal of Computational Dynamics","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."}],"keyword":["Optimal control problem","Lagrangian system","Hamiltonian system","Variations","Pontryagin's maximum principle."],"ddc":["510"],"language":[{"iso":"eng"}],"has_accepted_license":"1","publication_identifier":{"issn":["2158-2491","2158-2505"]},"publication_status":"published","page":"0-0","citation":{"apa":"Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., Almagro, R. T. S. M. de, &#38; Szemenyei, F. O. (2024). A new Lagrangian approach to control affine systems with a quadratic Lagrange term. <i>Journal of Computational Dynamics</i>, <i>0</i>(0), 0–0. <a href=\"https://doi.org/10.3934/jcd.2024017\">https://doi.org/10.3934/jcd.2024017</a>","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={<a href=\"https://doi.org/10.3934/jcd.2024017\">10.3934/jcd.2024017</a>}, 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} }","mla":"Leyendecker, Sigrid, et al. “A New Lagrangian Approach to Control Affine Systems with a Quadratic Lagrange Term.” <i>Journal of Computational Dynamics</i>, vol. 0, no. 0, American Institute of Mathematical Sciences (AIMS), 2024, pp. 0–0, doi:<a href=\"https://doi.org/10.3934/jcd.2024017\">10.3934/jcd.2024017</a>.","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.","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.” <i>Journal of Computational Dynamics</i> 0, no. 0 (2024): 0–0. <a href=\"https://doi.org/10.3934/jcd.2024017\">https://doi.org/10.3934/jcd.2024017</a>.","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,” <i>Journal of Computational Dynamics</i>, vol. 0, no. 0, pp. 0–0, 2024, doi: <a href=\"https://doi.org/10.3934/jcd.2024017\">10.3934/jcd.2024017</a>.","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. <i>Journal of Computational Dynamics</i>. 2024;0(0):0-0. doi:<a href=\"https://doi.org/10.3934/jcd.2024017\">10.3934/jcd.2024017</a>"},"oa":"1","date_updated":"2024-03-28T16:07:34Z","volume":"0","author":[{"first_name":"Sigrid","full_name":"Leyendecker, Sigrid","last_name":"Leyendecker"},{"last_name":"Maslovskaya","id":"87909","full_name":"Maslovskaya, Sofya","first_name":"Sofya"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Rodrigo T. Sato Martín de","full_name":"Almagro, Rodrigo T. Sato Martín de","last_name":"Almagro"},{"full_name":"Szemenyei, Flóra Orsolya","last_name":"Szemenyei","first_name":"Flóra Orsolya"}],"doi":"10.3934/jcd.2024017","main_file_link":[{"open_access":"1","url":"https://www.aimsciences.org/article/doi/10.3934/jcd.2024017"}],"type":"journal_article","status":"public","_id":"53101","department":[{"_id":"636"}],"user_id":"87909","article_type":"original"},{"year":"2024","issue":"1","quality_controlled":"1","title":"Learning of discrete models of variational PDEs from data","date_created":"2023-08-10T08:24:48Z","publisher":"AIP Publishing","file":[{"file_size":13222105,"title":"Accepted Manuscript Chaos","file_id":"50376","access_level":"open_access","file_name":"Accepted manuscript with AIP banner CHA23-AR-01370.pdf","date_updated":"2024-01-09T10:48:38Z","date_created":"2024-01-09T10:48:38Z","creator":"coffen","relation":"main_file","content_type":"application/pdf"},{"relation":"main_file","content_type":"application/pdf","file_size":12960884,"description":"We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train\na neural network model of a discrete Lagrangian density such that the discrete Euler–Lagrange equations are consistent\nwith the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian\ndensities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for\nthe training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers\nguarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical\nsimulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory\nsuch as travelling waves. This is possible even when travelling waves are not present in the training data. This is\ncompared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces\ncontaining structurally simple solutions when these are not present in the training data. Ideas are demonstrated on\nexamples based on the wave equation and the Schrödinger equation.","title":"Learning of discrete models of variational PDEs from data","file_name":"LDensityPDE_AIP.pdf","file_id":"50390","access_level":"open_access","date_updated":"2024-01-09T11:19:49Z","date_created":"2024-01-09T11:19:49Z","creator":"coffen"}],"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. "}],"publication":"Chaos","language":[{"iso":"eng"}],"ddc":["510"],"external_id":{"arxiv":["2308.05082 "]},"intvolume":"        34","citation":{"apa":"Offen, C., &#38; Ober-Blöbaum, S. (2024). Learning of discrete models of variational PDEs from data. <i>Chaos</i>, <i>34</i>(1), Article 013104. <a href=\"https://doi.org/10.1063/5.0172287\">https://doi.org/10.1063/5.0172287</a>","bibtex":"@article{Offen_Ober-Blöbaum_2024, title={Learning of discrete models of variational PDEs from data}, volume={34}, DOI={<a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>}, number={1013104}, journal={Chaos}, publisher={AIP Publishing}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2024} }","short":"C. Offen, S. Ober-Blöbaum, Chaos 34 (2024).","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” <i>Chaos</i>, vol. 34, no. 1, 013104, AIP Publishing, 2024, doi:<a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>.","ieee":"C. Offen and S. Ober-Blöbaum, “Learning of discrete models of variational PDEs from data,” <i>Chaos</i>, vol. 34, no. 1, Art. no. 013104, 2024, doi: <a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>.","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” <i>Chaos</i> 34, no. 1 (2024). <a href=\"https://doi.org/10.1063/5.0172287\">https://doi.org/10.1063/5.0172287</a>.","ama":"Offen C, Ober-Blöbaum S. Learning of discrete models of variational PDEs from data. <i>Chaos</i>. 2024;34(1). doi:<a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>"},"related_material":{"link":[{"relation":"software","description":"GitHub","url":"https://github.com/Christian-Offen/DLNN_pde"}]},"has_accepted_license":"1","publication_identifier":{"issn":["1054-1500"]},"publication_status":"published","doi":"10.1063/5.0172287","volume":34,"author":[{"id":"85279","full_name":"Offen, Christian","last_name":"Offen","orcid":"0000-0002-5940-8057","first_name":"Christian"},{"full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina"}],"date_updated":"2024-08-12T13:45:43Z","oa":"1","status":"public","type":"journal_article","file_date_updated":"2024-01-09T11:19:49Z","article_type":"original","article_number":"013104","department":[{"_id":"636"}],"user_id":"85279","_id":"46469","project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}]},{"language":[{"iso":"eng"}],"user_id":"87909","department":[{"_id":"636"}],"_id":"59791","status":"public","type":"conference","publication":"IFAC-PapersOnLine","doi":"10.1016/j.ifacol.2024.10.118","title":"Symplectic Methods in Deep Learning","date_created":"2025-05-05T09:21:13Z","author":[{"id":"87909","full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya","first_name":"Sofya"},{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"}],"volume":58,"publisher":"Elsevier BV","date_updated":"2025-05-05T09:22:27Z","citation":{"apa":"Maslovskaya, S., &#38; Ober-Blöbaum, S. (2024). Symplectic Methods in Deep Learning. <i>IFAC-PapersOnLine</i>, <i>58</i>(17), 85–90. <a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">https://doi.org/10.1016/j.ifacol.2024.10.118</a>","bibtex":"@inproceedings{Maslovskaya_Ober-Blöbaum_2024, title={Symplectic Methods in Deep Learning}, volume={58}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">10.1016/j.ifacol.2024.10.118</a>}, number={17}, booktitle={IFAC-PapersOnLine}, publisher={Elsevier BV}, author={Maslovskaya, Sofya and Ober-Blöbaum, Sina}, year={2024}, pages={85–90} }","short":"S. Maslovskaya, S. Ober-Blöbaum, in: IFAC-PapersOnLine, Elsevier BV, 2024, pp. 85–90.","mla":"Maslovskaya, Sofya, and Sina Ober-Blöbaum. “Symplectic Methods in Deep Learning.” <i>IFAC-PapersOnLine</i>, vol. 58, no. 17, Elsevier BV, 2024, pp. 85–90, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">10.1016/j.ifacol.2024.10.118</a>.","chicago":"Maslovskaya, Sofya, and Sina Ober-Blöbaum. “Symplectic Methods in Deep Learning.” In <i>IFAC-PapersOnLine</i>, 58:85–90. Elsevier BV, 2024. <a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">https://doi.org/10.1016/j.ifacol.2024.10.118</a>.","ieee":"S. Maslovskaya and S. Ober-Blöbaum, “Symplectic Methods in Deep Learning,” in <i>IFAC-PapersOnLine</i>, 2024, vol. 58, no. 17, pp. 85–90, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">10.1016/j.ifacol.2024.10.118</a>.","ama":"Maslovskaya S, Ober-Blöbaum S. Symplectic Methods in Deep Learning. In: <i>IFAC-PapersOnLine</i>. Vol 58. Elsevier BV; 2024:85-90. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">10.1016/j.ifacol.2024.10.118</a>"},"intvolume":"        58","page":"85-90","year":"2024","issue":"17","publication_status":"published","publication_identifier":{"issn":["2405-8963"]}},{"intvolume":"        56","page":"3203-3210","citation":{"apa":"Lishkova, Y., Scherer, P., Ridderbusch, S., Jamnik, M., Liò, P., Ober-Blöbaum, S., &#38; Offen, C. (2023). Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery. <i>IFAC-PapersOnLine</i>, <i>56</i>(2), 3203–3210. <a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">https://doi.org/10.1016/j.ifacol.2023.10.1457</a>","short":"Y. Lishkova, P. Scherer, S. Ridderbusch, M. Jamnik, P. Liò, S. Ober-Blöbaum, C. Offen, in: IFAC-PapersOnLine, Elsevier, 2023, pp. 3203–3210.","mla":"Lishkova, Yana, et al. “Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery.” <i>IFAC-PapersOnLine</i>, vol. 56, no. 2, Elsevier, 2023, pp. 3203–10, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>.","bibtex":"@inproceedings{Lishkova_Scherer_Ridderbusch_Jamnik_Liò_Ober-Blöbaum_Offen_2023, title={Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery}, volume={56}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>}, number={2}, booktitle={IFAC-PapersOnLine}, publisher={Elsevier}, author={Lishkova, Yana and Scherer, Paul and Ridderbusch, Steffen and Jamnik, Mateja and Liò, Pietro and Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={3203–3210} }","ieee":"Y. Lishkova <i>et al.</i>, “Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery,” in <i>IFAC-PapersOnLine</i>,  Yokohama, Japan, 2023, vol. 56, no. 2, pp. 3203–3210, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>.","chicago":"Lishkova, Yana, Paul Scherer, Steffen Ridderbusch, Mateja Jamnik, Pietro Liò, Sina Ober-Blöbaum, and Christian Offen. “Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery.” In <i>IFAC-PapersOnLine</i>, 56:3203–10. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">https://doi.org/10.1016/j.ifacol.2023.10.1457</a>.","ama":"Lishkova Y, Scherer P, Ridderbusch S, et al. Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery. In: <i>IFAC-PapersOnLine</i>. Vol 56. Elsevier; 2023:3203-3210. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>"},"has_accepted_license":"1","publication_status":"published","related_material":{"link":[{"url":"https://github.com/yanalish/SymDLNN","relation":"software","description":"GitHub"}]},"conference":{"location":" Yokohama, Japan","end_date":"2023-07-14","start_date":"2023-07-09","name":"The 22nd World Congress of the International Federation of Automatic Control"},"doi":"10.1016/j.ifacol.2023.10.1457","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S2405896323018657"}],"oa":"1","date_updated":"2023-12-29T14:26:00Z","volume":56,"author":[{"first_name":"Yana","last_name":"Lishkova","full_name":"Lishkova, Yana"},{"last_name":"Scherer","full_name":"Scherer, Paul","first_name":"Paul"},{"full_name":"Ridderbusch, Steffen","last_name":"Ridderbusch","first_name":"Steffen"},{"full_name":"Jamnik, Mateja","last_name":"Jamnik","first_name":"Mateja"},{"first_name":"Pietro","full_name":"Liò, Pietro","last_name":"Liò"},{"last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"},{"id":"85279","full_name":"Offen, Christian","last_name":"Offen","orcid":"0000-0002-5940-8057","first_name":"Christian"}],"status":"public","type":"conference","file_date_updated":"2023-04-17T08:05:55Z","_id":"34135","department":[{"_id":"636"}],"user_id":"85279","year":"2023","quality_controlled":"1","issue":"2","title":"Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery","publisher":"Elsevier","date_created":"2022-11-23T08:17:10Z","abstract":[{"text":"By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system will behave in time. If the dynamics exhibit additional symmetries, then the motion fulfils additional conservation laws, such as conservation of energy (time invariance), momentum (translation invariance), or angular momentum (rotational invariance). To learn a system representation, one could learn the discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function Ld which defines them. Based on ideas from Lie group theory, in this work we introduce a framework to learn a discrete Lagrangian along with its symmetry group from discrete observations of motions and, therefore, identify conserved quantities. The learning process does not restrict the form of the Lagrangian, does not require velocity or momentum observations or predictions and incorporates a cost term which safeguards against unwanted solutions and against potential numerical issues in forward simulations. The learnt discrete quantities are related to their continuous analogues using variational backward error analysis and numerical results demonstrate the improvement such models can have both qualitatively and quantitatively even in the presence of noise.","lang":"eng"}],"file":[{"relation":"main_file","file_id":"44037","access_level":"open_access","description":"By one of the most fundamental principles in physics, a dynamical system will\nexhibit those motions which extremise an action functional. This leads to the formation of\nthe Euler-Lagrange equations, which serve as a model of how the system will behave in time.\nIf the dynamics exhibit additional symmetries, then the motion fulfils additional conservation\nlaws, such as conservation of energy (time invariance), momentum (translation invariance), or\nangular momentum (rotational invariance). To learn a system representation, one could learn\nthe discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function\nLd which defines them. Based on ideas from Lie group theory, we introduce a framework to learn\na discrete Lagrangian along with its symmetry group from discrete observations of motions and,\ntherefore, identify conserved quantities. The learning process does not restrict the form of the\nLagrangian, does not require velocity or momentum observations or predictions and incorporates\na cost term which safeguards against unwanted solutions and against potential numerical issues\nin forward simulations. The learnt discrete quantities are related to their continuous analogues\nusing variational backward error analysis and numerical results demonstrate the improvement\nsuch models can have both qualitatively and quantitatively even in the presence of noise.","title":"Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery","date_created":"2023-04-17T08:05:55Z","date_updated":"2023-04-17T08:05:55Z","content_type":"application/pdf","file_name":"LNN_project.pdf","file_size":576115,"creator":"coffen"}],"publication":"IFAC-PapersOnLine","ddc":["510"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["2211.10830"]}},{"publication":"Geometric Science of Information","abstract":[{"lang":"eng","text":"The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that is modelled as a neural network. Careful regularisation of the loss function for training $L_d$ is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler--Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE."}],"file":[{"content_type":"application/pdf","relation":"main_file","creator":"coffen","date_created":"2023-08-02T12:04:17Z","date_updated":"2023-08-02T12:04:17Z","access_level":"open_access","file_id":"46273","file_name":"LDensityLearning.pdf","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","file_size":1938962,"description":"The article shows how to learn models of dynamical systems\nfrom data which are governed by an unknown variational PDE. Rather\nthan employing reduction techniques, we learn a discrete field theory\ngoverned by a discrete Lagrangian density Ld that is modelled as a neural network. Careful regularisation of the loss function for training Ld is\nnecessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of\nthe discrete Euler–Lagrange equations. Secondly, we develop a method to\nfind solutions to machine learned discrete field theories which constitute\ntravelling waves of the underlying continuous PDE."}],"external_id":{"arxiv":["2302.08232 "]},"ddc":["510"],"keyword":["System identification","discrete Lagrangians","travelling waves"],"language":[{"iso":"eng"}],"quality_controlled":"1","year":"2023","publisher":"Springer, Cham.","date_created":"2023-02-16T11:32:48Z","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","type":"conference","editor":[{"full_name":"Nielsen, F","last_name":"Nielsen","first_name":"F"},{"first_name":"F","full_name":"Barbaresco, F","last_name":"Barbaresco"}],"status":"public","project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"_id":"42163","series_title":"Lecture Notes in Computer Science (LNCS)","user_id":"85279","department":[{"_id":"636"}],"file_date_updated":"2023-08-02T12:04:17Z","publication_status":"published","has_accepted_license":"1","publication_identifier":{"eisbn":["978-3-031-38271-0"]},"related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/Christian-Offen/LagrangianDensityML"}]},"citation":{"ama":"Offen C, Ober-Blöbaum S. Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In: Nielsen F, Barbaresco F, eds. <i>Geometric Science of Information</i>. Vol 14071. Lecture Notes in Computer Science (LNCS). Springer, Cham.; 2023:569-579. doi:<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” In <i>Geometric Science of Information</i>, edited by F Nielsen and F Barbaresco, 14071:569–79. Lecture Notes in Computer Science (LNCS). Springer, Cham., 2023. <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">https://doi.org/10.1007/978-3-031-38271-0_57</a>.","ieee":"C. Offen and S. Ober-Blöbaum, “Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves,” in <i>Geometric Science of Information</i>, Saint-Malo, Palais du Grand Large, France, 2023, vol. 14071, pp. 569–579, doi: <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>.","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2023). Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In F. Nielsen &#38; F. Barbaresco (Eds.), <i>Geometric Science of Information</i> (Vol. 14071, pp. 569–579). Springer, Cham. <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">https://doi.org/10.1007/978-3-031-38271-0_57</a>","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” <i>Geometric Science of Information</i>, edited by F Nielsen and F Barbaresco, vol. 14071, Springer, Cham., 2023, pp. 569–79, doi:<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>.","bibtex":"@inproceedings{Offen_Ober-Blöbaum_2023, series={Lecture Notes in Computer Science (LNCS)}, title={Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves}, volume={14071}, DOI={<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>}, booktitle={Geometric Science of Information}, publisher={Springer, Cham.}, author={Offen, Christian and Ober-Blöbaum, Sina}, editor={Nielsen, F and Barbaresco, F}, year={2023}, pages={569–579}, collection={Lecture Notes in Computer Science (LNCS)} }","short":"C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric Science of Information, Springer, Cham., 2023, pp. 569–579."},"intvolume":"     14071","page":"569-579","date_updated":"2024-08-12T13:46:29Z","oa":"1","author":[{"orcid":"0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian","id":"85279","first_name":"Christian"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494","first_name":"Sina"}],"volume":14071,"doi":"10.1007/978-3-031-38271-0_57","conference":{"name":"  GSI'23 6th International Conference on Geometric Science of Information","start_date":"2023-08-30","end_date":"2023-09-01","location":"Saint-Malo, Palais du Grand Large, France"}},{"has_accepted_license":"1","publication_identifier":{"issn":["0377-0427"]},"publication_status":"epub_ahead","related_material":{"link":[{"relation":"software","url":"https://github.com/Christian-Offen/LagrangianShadowIntegration"}]},"intvolume":"       421","page":"114780","citation":{"apa":"Ober-Blöbaum, S., &#38; Offen, C. (2023). Variational Learning of Euler–Lagrange Dynamics from Data. <i>Journal of Computational and Applied Mathematics</i>, <i>421</i>, 114780. <a href=\"https://doi.org/10.1016/j.cam.2022.114780\">https://doi.org/10.1016/j.cam.2022.114780</a>","mla":"Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” <i>Journal of Computational and Applied Mathematics</i>, vol. 421, Elsevier, 2023, p. 114780, doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>.","bibtex":"@article{Ober-Blöbaum_Offen_2023, title={Variational Learning of Euler–Lagrange Dynamics from Data}, volume={421}, DOI={<a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>}, journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier}, author={Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={114780} }","short":"S. Ober-Blöbaum, C. Offen, Journal of Computational and Applied Mathematics 421 (2023) 114780.","ieee":"S. Ober-Blöbaum and C. Offen, “Variational Learning of Euler–Lagrange Dynamics from Data,” <i>Journal of Computational and Applied Mathematics</i>, vol. 421, p. 114780, 2023, doi: <a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>.","chicago":"Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange Dynamics from Data.” <i>Journal of Computational and Applied Mathematics</i> 421 (2023): 114780. <a href=\"https://doi.org/10.1016/j.cam.2022.114780\">https://doi.org/10.1016/j.cam.2022.114780</a>.","ama":"Ober-Blöbaum S, Offen C. Variational Learning of Euler–Lagrange Dynamics from Data. <i>Journal of Computational and Applied Mathematics</i>. 2023;421:114780. doi:<a href=\"https://doi.org/10.1016/j.cam.2022.114780\">10.1016/j.cam.2022.114780</a>"},"date_updated":"2023-08-10T08:42:39Z","oa":"1","volume":421,"author":[{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","id":"85279","full_name":"Offen, Christian"}],"doi":"10.1016/j.cam.2022.114780","type":"journal_article","status":"public","_id":"29240","department":[{"_id":"636"}],"user_id":"85279","article_type":"original","file_date_updated":"2022-06-28T15:25:50Z","quality_controlled":"1","year":"2023","publisher":"Elsevier","date_created":"2022-01-11T13:24:00Z","title":"Variational Learning of Euler–Lagrange Dynamics from Data","publication":"Journal of Computational and Applied Mathematics","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."}],"file":[{"date_updated":"2022-06-28T15:25:50Z","date_created":"2022-06-28T15:25:50Z","title":"Variational Learning of Euler–Lagrange Dynamics from Data","description":"The principle of least action is one of the most fundamental physical principle. It says that among all possible motions\nconnecting two points in a phase space, the system will exhibit those motions which extremise an action functional.\nMany qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equa-\ntions, are related to the existence of an action functional. Incorporating variational structure into learning algorithms\nfor dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features\nwith the exact physical system. In this paper we show how to incorporate variational principles into trajectory predic-\ntions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position\ndata of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no\nprior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward\nerror analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the\nlearned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,\nwe introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of\nvariational backward error analysis. (3) Finally, we introduce a method to perform system identification from position\nobservations only, based on variational backward error analysis.","access_level":"open_access","file_id":"32274","relation":"main_file","creator":"coffen","file_size":3640770,"file_name":"ShadowLagrangian_revision1_journal_style_arxiv.pdf","content_type":"application/pdf"}],"external_id":{"arxiv":["2112.12619"]},"keyword":["Lagrangian learning","variational backward error analysis","modified Lagrangian","variational integrators","physics informed learning"],"ddc":["510"],"language":[{"iso":"eng"}]},{"doi":"10.1063/5.0142969","volume":33,"author":[{"first_name":"Eva","last_name":"Dierkes","full_name":"Dierkes, Eva"},{"first_name":"Christian","full_name":"Offen, Christian","id":"85279","orcid":"0000-0002-5940-8057","last_name":"Offen"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494","first_name":"Sina"},{"last_name":"Flaßkamp","full_name":"Flaßkamp, Kathrin","first_name":"Kathrin"}],"date_updated":"2023-08-10T08:37:01Z","oa":"1","intvolume":"        33","citation":{"short":"E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023).","bibtex":"@article{Dierkes_Offen_Ober-Blöbaum_Flaßkamp_2023, title={Hamiltonian Neural Networks with Automatic Symmetry Detection}, volume={33}, DOI={<a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>}, number={6063115}, journal={Chaos}, publisher={AIP Publishing}, author={Dierkes, Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}, year={2023} }","mla":"Dierkes, Eva, et al. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” <i>Chaos</i>, vol. 33, no. 6, 063115, AIP Publishing, 2023, doi:<a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>.","apa":"Dierkes, E., Offen, C., Ober-Blöbaum, S., &#38; Flaßkamp, K. (2023). Hamiltonian Neural Networks with Automatic Symmetry Detection. <i>Chaos</i>, <i>33</i>(6), Article 063115. <a href=\"https://doi.org/10.1063/5.0142969\">https://doi.org/10.1063/5.0142969</a>","chicago":"Dierkes, Eva, Christian Offen, Sina Ober-Blöbaum, and Kathrin Flaßkamp. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” <i>Chaos</i> 33, no. 6 (2023). <a href=\"https://doi.org/10.1063/5.0142969\">https://doi.org/10.1063/5.0142969</a>.","ieee":"E. Dierkes, C. Offen, S. Ober-Blöbaum, and K. Flaßkamp, “Hamiltonian Neural Networks with Automatic Symmetry Detection,” <i>Chaos</i>, vol. 33, no. 6, Art. no. 063115, 2023, doi: <a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>.","ama":"Dierkes E, Offen C, Ober-Blöbaum S, Flaßkamp K. Hamiltonian Neural Networks with Automatic Symmetry Detection. <i>Chaos</i>. 2023;33(6). doi:<a href=\"https://doi.org/10.1063/5.0142969\">10.1063/5.0142969</a>"},"related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/eva-dierkes/HNN_withSymmetries"}]},"has_accepted_license":"1","publication_identifier":{"issn":["1054-1500"]},"publication_status":"published","file_date_updated":"2023-04-26T16:20:56Z","article_type":"original","article_number":"063115","department":[{"_id":"636"}],"user_id":"85279","_id":"37654","status":"public","type":"journal_article","title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","date_created":"2023-01-20T09:10:06Z","publisher":"AIP Publishing","year":"2023","issue":"6","language":[{"iso":"eng"}],"ddc":["510"],"external_id":{"arxiv":["2301.07928"]},"file":[{"access_level":"open_access","file_id":"44205","file_name":"JournalPaper_main.pdf","title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","description":"Incorporating physical system knowledge into data-driven\nsystem identification has been shown to be beneficial. The\napproach presented in this article combines learning of an\nenergy-conserving model from data with detecting a Lie\ngroup representation of the unknown system symmetry.\nThe proposed approach can improve the learned model\nand reveal underlying symmetry simultaneously.","file_size":5200111,"creator":"coffen","date_created":"2023-04-26T16:20:56Z","date_updated":"2023-04-26T16:20:56Z","relation":"main_file","content_type":"application/pdf"}],"abstract":[{"text":"Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when\r\nlearning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite\r\nthe data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we\r\nenhance the HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach\r\nallows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples,\r\na pendulum on a cart and a two-body problem from astrodynamics are considered.","lang":"eng"}],"publication":"Chaos"},{"abstract":[{"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.","lang":"eng"}],"publication":"SIAM Journal on Scientific Computing","language":[{"iso":"eng"}],"ddc":["510"],"external_id":{"arxiv":["arXiv:2104.03562"]},"year":"2023","issue":"2","title":"Efficient time stepping for numerical integration using reinforcement  learning","date_created":"2021-04-09T07:59:19Z","status":"public","type":"journal_article","user_id":"47427","department":[{"_id":"101"},{"_id":"636"},{"_id":"355"},{"_id":"655"}],"_id":"21600","citation":{"apa":"Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz, S., &#38; Pfannschmidt, K. (2023). Efficient time stepping for numerical integration using reinforcement  learning. <i>SIAM Journal on Scientific Computing</i>, <i>45</i>(2), A579–A595. <a href=\"https://doi.org/10.1137/21M1412682\">https://doi.org/10.1137/21M1412682</a>","mla":"Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration Using Reinforcement  Learning.” <i>SIAM Journal on Scientific Computing</i>, vol. 45, no. 2, 2023, pp. A579–95, doi:<a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>.","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.","bibtex":"@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023, title={Efficient time stepping for numerical integration using reinforcement  learning}, volume={45}, DOI={<a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>}, number={2}, journal={SIAM Journal on Scientific Computing}, author={Dellnitz, Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen, Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, year={2023}, pages={A579–A595} }","ama":"Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical integration using reinforcement  learning. <i>SIAM Journal on Scientific Computing</i>. 2023;45(2):A579-A595. doi:<a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>","chicago":"Dellnitz, Michael, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum, Christian Offen, Sebastian Peitz, and Karlson Pfannschmidt. “Efficient Time Stepping for Numerical Integration Using Reinforcement  Learning.” <i>SIAM Journal on Scientific Computing</i> 45, no. 2 (2023): A579–95. <a href=\"https://doi.org/10.1137/21M1412682\">https://doi.org/10.1137/21M1412682</a>.","ieee":"M. Dellnitz <i>et al.</i>, “Efficient time stepping for numerical integration using reinforcement  learning,” <i>SIAM Journal on Scientific Computing</i>, vol. 45, no. 2, pp. A579–A595, 2023, doi: <a href=\"https://doi.org/10.1137/21M1412682\">10.1137/21M1412682</a>."},"page":"A579-A595","intvolume":"        45","related_material":{"link":[{"url":"https://github.com/lueckem/quadrature-ML","description":"GitHub","relation":"software"}]},"publication_status":"published","has_accepted_license":"1","main_file_link":[{"url":"https://epubs.siam.org/doi/reader/10.1137/21M1412682"}],"doi":"10.1137/21M1412682","author":[{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"},{"full_name":"Hüllermeier, Eyke","id":"48129","last_name":"Hüllermeier","first_name":"Eyke"},{"last_name":"Lücke","full_name":"Lücke, Marvin","first_name":"Marvin"},{"full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina"},{"first_name":"Christian","full_name":"Offen, Christian","id":"85279","last_name":"Offen","orcid":"0000-0002-5940-8057"},{"full_name":"Peitz, Sebastian","id":"47427","orcid":"0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"},{"first_name":"Karlson","id":"13472","full_name":"Pfannschmidt, Karlson","last_name":"Pfannschmidt","orcid":"0000-0001-9407-7903"}],"volume":45,"date_updated":"2023-08-25T09:24:50Z"},{"citation":{"chicago":"Lishkova, Yana, Sina Ober-Blöbaum, and Sigrid Leyendecker. <i>Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model </i>. Invited Mathematical Magazine Article, 2023.","ieee":"Y. Lishkova, S. Ober-Blöbaum, and S. Leyendecker, <i>Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model </i>. Invited Mathematical Magazine Article, 2023.","ama":"Lishkova Y, Ober-Blöbaum S, Leyendecker S. <i>Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model </i>. Invited Mathematical Magazine Article; 2023.","apa":"Lishkova, Y., Ober-Blöbaum, S., &#38; Leyendecker, S. (2023). <i>Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model </i>. Invited Mathematical Magazine Article.","short":"Y. Lishkova, S. Ober-Blöbaum, S. Leyendecker, Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model , Invited Mathematical Magazine Article, 2023.","mla":"Lishkova, Yana, et al. <i>Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model </i>. Invited Mathematical Magazine Article, 2023.","bibtex":"@book{Lishkova_Ober-Blöbaum_Leyendecker_2023, title={Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model }, publisher={Invited Mathematical Magazine Article}, author={Lishkova, Yana and Ober-Blöbaum, Sina and Leyendecker, Sigrid}, year={2023} }"},"year":"2023","title":"Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model ","date_created":"2023-09-21T07:20:43Z","author":[{"full_name":"Lishkova, Yana","last_name":"Lishkova","first_name":"Yana"},{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Sigrid","last_name":"Leyendecker","full_name":"Leyendecker, Sigrid"}],"publisher":"Invited Mathematical Magazine Article","date_updated":"2023-09-21T07:27:15Z","status":"public","type":"report","language":[{"iso":"eng"}],"alternative_title":["GAMM Rundbriefe"],"user_id":"15694","_id":"47147"},{"language":[{"iso":"eng"}],"user_id":"15694","_id":"47148","status":"public","type":"conference","title":"Variational approach for modelling and optimal control of electrodynamic tether motion","date_created":"2023-09-21T07:25:40Z","author":[{"last_name":"Lishkova","full_name":"Lishkova, Y.","first_name":"Y."},{"first_name":"M.","full_name":"Bando, M.","last_name":"Bando"},{"last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina"}],"publisher":"Accepted for the 74th International Astronautical Concress (IAC)","date_updated":"2023-09-21T07:27:21Z","citation":{"ama":"Lishkova Y, Bando M, Ober-Blöbaum S. Variational approach for modelling and optimal control of electrodynamic tether motion. In: Accepted for the 74th International Astronautical Concress (IAC); 2023.","chicago":"Lishkova, Y., M. Bando, and Sina Ober-Blöbaum. “Variational Approach for Modelling and Optimal Control of Electrodynamic Tether Motion.” Accepted for the 74th International Astronautical Concress (IAC), 2023.","ieee":"Y. Lishkova, M. Bando, and S. Ober-Blöbaum, “Variational approach for modelling and optimal control of electrodynamic tether motion,” 2023.","bibtex":"@inproceedings{Lishkova_Bando_Ober-Blöbaum_2023, title={Variational approach for modelling and optimal control of electrodynamic tether motion}, publisher={Accepted for the 74th International Astronautical Concress (IAC)}, author={Lishkova, Y. and Bando, M. and Ober-Blöbaum, Sina}, year={2023} }","mla":"Lishkova, Y., et al. <i>Variational Approach for Modelling and Optimal Control of Electrodynamic Tether Motion</i>. Accepted for the 74th International Astronautical Concress (IAC), 2023.","short":"Y. Lishkova, M. Bando, S. Ober-Blöbaum, in: Accepted for the 74th International Astronautical Concress (IAC), 2023.","apa":"Lishkova, Y., Bando, M., &#38; Ober-Blöbaum, S. (2023). <i>Variational approach for modelling and optimal control of electrodynamic tether motion</i>."},"year":"2023"},{"date_updated":"2022-03-24T12:26:32Z","author":[{"first_name":"Jacky","full_name":"Cresson, Jacky","last_name":"Cresson"},{"first_name":"Fernando","full_name":"Jiménez, Fernando","last_name":"Jiménez"},{"last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494","first_name":"Sina"}],"date_created":"2022-03-24T12:26:10Z","volume":"14(1)","title":"Continuous and discrete Noether's fractional conserved quantities for restricted calculus of variations","year":"2022","citation":{"ieee":"J. Cresson, F. Jiménez, and S. 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Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations. <i>AIMS</i>, <i>14(1)</i>, 57–89.","ama":"Cresson J, Jiménez F, Ober-Blöbaum S. Continuous and discrete Noether’s fractional conserved quantities for restricted calculus of variations. <i>AIMS</i>. 2022;14(1):57-89."},"page":"57-89","_id":"30490","user_id":"15694","department":[{"_id":"636"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"AIMS","status":"public"}]