[{"doi":"10.1007/s11044-025-10138-1","user_id":"87909","language":[{"iso":"eng"}],"_id":"63557","publisher":"Springer Science and Business Media LLC","date_updated":"2026-01-12T11:35:27Z","publication_status":"published","author":[{"full_name":"Konopik, Michael","first_name":"Michael","last_name":"Konopik"},{"full_name":"Leyendecker, Sigrid","last_name":"Leyendecker","first_name":"Sigrid"},{"full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya","first_name":"Sofya","id":"87909"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina","id":"16494"},{"first_name":"Rodrigo T.","last_name":"Sato Martín de Almagro","full_name":"Sato Martín de Almagro, Rodrigo T."}],"publication_identifier":{"issn":["1384-5640","1573-272X"]},"year":"2026","title":"On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics","status":"public","department":[{"_id":"636"}],"type":"journal_article","date_created":"2026-01-12T11:33:54Z","abstract":[{"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.","lang":"eng"}],"citation":{"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>","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} }","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>.","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>.","short":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T. Sato Martín de Almagro, Multibody System Dynamics (2026).","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>","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>."},"publication":"Multibody System Dynamics"},{"citation":{"mla":"Wembe Moafo, Boris Edgar, et al. <i>Cayley Commutator-Free Methods for Krotov-Type Algorithms in Quantum Optimal Control</i>. 2026, doi:<a href=\"https://doi.org/10.48550/ARXIV.2603.11697\">10.48550/ARXIV.2603.11697</a>.","bibtex":"@inproceedings{Wembe Moafo_Ali_Meier_Ober-Blöbaum_2026, title={Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control}, DOI={<a href=\"https://doi.org/10.48550/ARXIV.2603.11697\">10.48550/ARXIV.2603.11697</a>}, author={Wembe Moafo, Boris Edgar and Ali, Usman and Meier, Torsten and Ober-Blöbaum, Sina}, year={2026} }","ama":"Wembe Moafo BE, Ali U, Meier T, Ober-Blöbaum S. Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control. In: ; 2026. doi:<a href=\"https://doi.org/10.48550/ARXIV.2603.11697\">10.48550/ARXIV.2603.11697</a>","ieee":"B. E. Wembe Moafo, U. Ali, T. Meier, and S. Ober-Blöbaum, “Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control,” presented at the European Control Conference, Reykjavík, Iceland, 2026, doi: <a href=\"https://doi.org/10.48550/ARXIV.2603.11697\">10.48550/ARXIV.2603.11697</a>.","apa":"Wembe Moafo, B. E., Ali, U., Meier, T., &#38; Ober-Blöbaum, S. (2026). <i>Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control</i>. European Control Conference, Reykjavík, Iceland. <a href=\"https://doi.org/10.48550/ARXIV.2603.11697\">https://doi.org/10.48550/ARXIV.2603.11697</a>","short":"B.E. Wembe Moafo, U. Ali, T. Meier, S. Ober-Blöbaum, in: 2026.","chicago":"Wembe Moafo, Boris Edgar, Usman Ali, Torsten Meier, and Sina Ober-Blöbaum. “Cayley Commutator-Free Methods for Krotov-Type Algorithms in Quantum Optimal Control,” 2026. <a href=\"https://doi.org/10.48550/ARXIV.2603.11697\">https://doi.org/10.48550/ARXIV.2603.11697</a>."},"abstract":[{"lang":"eng","text":"This paper presents a class of structure-preserving numerical methods for quantum optimal control problems, based on commutator-free Cayley integrators. Starting from the Krotov framework, we reformulate the forward and backward propagation steps using Cayley-type schemes that preserve unitarity and symmetry at the discrete level. This approach eliminates the need for matrix exponentials and commutators, leading to significant computational savings while maintaining higher-order accuracy. We first recall the standard linear setting and then extend the formulation to nonlinear Schrödinger and Gross-Pitaevskii equations using a Cayley-polynomial interpolation strategy. Numerical experiments on state-transfer problems illustrate that the CF-Cayley method achieves the same accuracy as high-order exponential or Cayley-Magnus schemes at substantially lower cost, especially for longtime or highly oscillatory dynamics. In the nonlinear regime, the structure-preserving properties of the method ensure stability and norm conservation, making it a robust tool for large-scale quantum control simulations. The proposed framework thus bridges geometric integration and optimal control, offering an efficient and reliable alternative to existing exponential-based propagators."}],"date_created":"2026-06-01T09:38:06Z","department":[{"_id":"94"}],"type":"conference","conference":{"end_date":"2026-07-10","start_date":"2026-07-07","name":"European Control Conference","location":"Reykjavík, Iceland"},"author":[{"orcid":"0000-0002-6085-8071","last_name":"Wembe Moafo","first_name":"Boris Edgar","full_name":"Wembe Moafo, Boris Edgar","id":"95394"},{"full_name":"Ali, Usman","last_name":"Ali","first_name":"Usman"},{"id":"344","orcid":"0000-0001-8864-2072","first_name":"Torsten","last_name":"Meier","full_name":"Meier, Torsten"},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"}],"title":"Cayley Commutator-free Methods for Krotov-Type Algorithms in Quantum Optimal Control","year":"2026","status":"public","date_updated":"2026-06-01T09:40:38Z","_id":"65746","language":[{"iso":"eng"}],"doi":"10.48550/ARXIV.2603.11697","user_id":"95394"},{"date_created":"2026-06-01T09:31:15Z","department":[{"_id":"94"}],"type":"preprint","citation":{"bibtex":"@article{Maslovskaya_Ober-Blöbaum_Wembe Moafo, title={Non static exponential turnpike property for optimal control problems with symmetries and boundary conditions}, author={Maslovskaya, Sofya and Ober-Blöbaum, Sina and Wembe Moafo, Boris Edgar} }","ama":"Maslovskaya S, Ober-Blöbaum S, Wembe Moafo BE. Non static exponential turnpike property for optimal control problems with symmetries and boundary conditions.","mla":"Maslovskaya, Sofya, et al. <i>Non Static Exponential Turnpike Property for Optimal Control Problems with Symmetries and Boundary Conditions</i>.","short":"S. Maslovskaya, S. Ober-Blöbaum, B.E. Wembe Moafo, (n.d.).","chicago":"Maslovskaya, Sofya, Sina Ober-Blöbaum, and Boris Edgar Wembe Moafo. “Non Static Exponential Turnpike Property for Optimal Control Problems with Symmetries and Boundary Conditions,” n.d.","ieee":"S. Maslovskaya, S. Ober-Blöbaum, and B. E. Wembe Moafo, “Non static exponential turnpike property for optimal control problems with symmetries and boundary conditions.” .","apa":"Maslovskaya, S., Ober-Blöbaum, S., &#38; Wembe Moafo, B. E. (n.d.). <i>Non static exponential turnpike property for optimal control problems with symmetries and boundary conditions</i>."},"abstract":[{"lang":"eng","text":"Optimal control problems with symmetries often admit a non stationary turnpike property called trim turnpike, which characterizes the convergence of optimal solutions to certain symmetry induced trajectories called trim primitives. In this paper we establish an exponential trim turnpike property for a class of optimal control problems with structural properties related to Abelian Lie group symmetries. The key ingredient of our approach is the introduction of an appropriate reduced optimal control problem. We show that extremals of the original problem can be characterized through a reduced Hamiltonian boundary value problem that coincides with the optimality system of the reduced problem. Under a hyperbolicity assumption on the equilibrium of the corresponding reduced Hamiltonian system we prove that optimal trajectories remain exponentially close, up to boundary layers near the endpoints, to a trim primitive defined by the static reduced problem. The theoretical results are illustrated on three representative examples: linear and nonlinear problems with quadratic cost and the Kepler orbital transfer problem."}],"_id":"65744","language":[{"iso":"eng"}],"user_id":"95394","author":[{"full_name":"Maslovskaya, Sofya","first_name":"Sofya","last_name":"Maslovskaya","id":"87909"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","orcid":"0000-0002-6085-8071","first_name":"Boris Edgar","id":"95394"}],"year":"2026","title":"Non static exponential turnpike property for optimal control problems with symmetries and boundary conditions","status":"public","publication_status":"submitted","date_updated":"2026-06-01T09:35:13Z"},{"date_created":"2026-06-05T07:37:43Z","type":"journal_article","department":[{"_id":"623"},{"_id":"15"},{"_id":"170"},{"_id":"706"},{"_id":"429"}],"publication":"Journal of Physics A: Mathematical and Theoretical","issue":"22","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n                  <jats:p>In this work, we address the numerical identification of entanglement in dynamical scenarios. To this end, we consider different programs based on the restriction of the evolution to the set of separable (i.e., non-entangled) states, together with the discretization of the space of variables for numerical computations. As a first approach, we apply linear splitting methods to the restricted, continuous equations of motion derived from variational principles. We utilize an exchange interaction Hamiltonian to confirm that the numerical and analytical solutions coincide in the limit of small time steps. The application to different Hamiltonians shows the wide applicability of the method to detect dynamical entanglement. To avoid the derivation of analytical solutions for complex dynamics, we consider variational, numerical integration schemes, introducing a variational discretization for Lagrangians linear in velocities. Here, we examine and compare two approaches: one in which the system is discretized before the restriction is applied, and another in which the restriction precedes the discretization. We find that the ‘first-discretize-then-restrict’ method becomes numerically unstable, already for the example of an exchange-interaction Hamiltonian, which can be an important consideration for the numerical analysis of constrained quantum dynamics. Thereby, broadly applicable numerical tools, including their limitations, for studying entanglement over time are established for assessing the entangling power of processes that are used in quantum information theory.</jats:p>"}],"article_number":"225303","language":[{"iso":"eng"}],"doi":"10.1088/1751-8121/ae6d51","title":"Numerical approaches to entangling dynamics from variational principles","year":"2026","author":[{"full_name":"Offen, Christian","last_name":"Offen","first_name":"Christian"},{"id":"95394","orcid":"0000-0002-6085-8071","last_name":"Wembe Moafo","first_name":"Boris Edgar","full_name":"Wembe Moafo, Boris Edgar"},{"last_name":"Ares","first_name":"Laura","full_name":"Ares, Laura"},{"id":"75127","full_name":"Sperling, Jan","last_name":"Sperling","orcid":"0000-0002-5844-3205","first_name":"Jan"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"}],"publication_identifier":{"issn":["1751-8113","1751-8121"]},"publication_status":"published","date_updated":"2026-06-05T07:38:44Z","intvolume":"        59","citation":{"bibtex":"@article{Offen_Wembe Moafo_Ares_Sperling_Ober-Blöbaum_2026, title={Numerical approaches to entangling dynamics from variational principles}, volume={59}, DOI={<a href=\"https://doi.org/10.1088/1751-8121/ae6d51\">10.1088/1751-8121/ae6d51</a>}, number={22225303}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing}, author={Offen, Christian and Wembe Moafo, Boris Edgar and Ares, Laura and Sperling, Jan and Ober-Blöbaum, Sina}, year={2026} }","ama":"Offen C, Wembe Moafo BE, Ares L, Sperling J, Ober-Blöbaum S. Numerical approaches to entangling dynamics from variational principles. <i>Journal of Physics A: Mathematical and Theoretical</i>. 2026;59(22). doi:<a href=\"https://doi.org/10.1088/1751-8121/ae6d51\">10.1088/1751-8121/ae6d51</a>","mla":"Offen, Christian, et al. “Numerical Approaches to Entangling Dynamics from Variational Principles.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 59, no. 22, 225303, IOP Publishing, 2026, doi:<a href=\"https://doi.org/10.1088/1751-8121/ae6d51\">10.1088/1751-8121/ae6d51</a>.","chicago":"Offen, Christian, Boris Edgar Wembe Moafo, Laura Ares, Jan Sperling, and Sina Ober-Blöbaum. “Numerical Approaches to Entangling Dynamics from Variational Principles.” <i>Journal of Physics A: Mathematical and Theoretical</i> 59, no. 22 (2026). <a href=\"https://doi.org/10.1088/1751-8121/ae6d51\">https://doi.org/10.1088/1751-8121/ae6d51</a>.","short":"C. Offen, B.E. Wembe Moafo, L. Ares, J. Sperling, S. Ober-Blöbaum, Journal of Physics A: Mathematical and Theoretical 59 (2026).","ieee":"C. Offen, B. E. Wembe Moafo, L. Ares, J. Sperling, and S. Ober-Blöbaum, “Numerical approaches to entangling dynamics from variational principles,” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 59, no. 22, Art. no. 225303, 2026, doi: <a href=\"https://doi.org/10.1088/1751-8121/ae6d51\">10.1088/1751-8121/ae6d51</a>.","apa":"Offen, C., Wembe Moafo, B. E., Ares, L., Sperling, J., &#38; Ober-Blöbaum, S. (2026). Numerical approaches to entangling dynamics from variational principles. <i>Journal of Physics A: Mathematical and Theoretical</i>, <i>59</i>(22), Article 225303. <a href=\"https://doi.org/10.1088/1751-8121/ae6d51\">https://doi.org/10.1088/1751-8121/ae6d51</a>"},"_id":"65777","publisher":"IOP Publishing","user_id":"75127","volume":59,"status":"public"},{"type":"journal_article","department":[{"_id":"636"}],"date_created":"2025-05-05T09:23:38Z","abstract":[{"lang":"eng","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>"}],"publication":"Mathematics of Control, Signals, and Systems","citation":{"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>.","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>.","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>","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} }","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>","short":"K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, B.E. Wembe Moafo, Mathematics of Control, Signals, and Systems (2025).","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>."},"doi":"10.1007/s00498-025-00408-w","user_id":"87909","language":[{"iso":"eng"}],"_id":"59792","publisher":"Springer Science and Business Media LLC","date_updated":"2025-05-05T09:24:09Z","publication_status":"published","title":"Trim turnpikes for optimal control problems with symmetries","year":"2025","status":"public","publication_identifier":{"issn":["0932-4194","1435-568X"]},"author":[{"first_name":"Kathrin","last_name":"Flaßkamp","full_name":"Flaßkamp, Kathrin"},{"id":"87909","full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya","first_name":"Sofya"},{"id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Boris Edgar","last_name":"Wembe Moafo","full_name":"Wembe Moafo, Boris Edgar","id":"95394"}]},{"date_updated":"2025-09-30T15:16:09Z","has_accepted_license":"1","year":"2025","status":"public","title":"Adaptive higher order reversible integrators for memory efficient deep learning","author":[{"full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya","first_name":"Sofya","id":"87909"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"id":"85279","orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen","full_name":"Offen, Christian"},{"full_name":"Singh, Pranav","last_name":"Singh","first_name":"Pranav"},{"id":"95394","first_name":"Boris Edgar","last_name":"Wembe Moafo","full_name":"Wembe Moafo, Boris Edgar"}],"ddc":["510"],"user_id":"85279","_id":"59794","language":[{"iso":"eng"}],"abstract":[{"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.","lang":"eng"}],"file_date_updated":"2025-05-05T09:28:02Z","citation":{"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.","short":"S. Maslovskaya, S. Ober-Blöbaum, C. Offen, P. Singh, B.E. Wembe Moafo, (2025).","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>.","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.","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.","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."},"type":"preprint","department":[{"_id":"636"}],"external_id":{"arxiv":["2410.09537"]},"file":[{"file_size":1830758,"access_level":"closed","file_name":"2410.09537v2.pdf","date_updated":"2025-05-05T09:28:02Z","relation":"main_file","content_type":"application/pdf","success":1,"file_id":"59795","creator":"sofyam","date_created":"2025-05-05T09:28:02Z"}],"date_created":"2025-05-05T09:25:28Z"},{"date_updated":"2025-12-09T09:10:01Z","publication_status":"published","intvolume":"         7","title":"Multiphoton, multimode state classification for nonlinear optical circuits","year":"2025","publication_identifier":{"issn":["2643-1564"]},"author":[{"full_name":"Kopylov, Denis A.","first_name":"Denis A.","last_name":"Kopylov"},{"full_name":"Offen, Christian","last_name":"Offen","orcid":"0000-0002-5940-8057","first_name":"Christian","id":"85279"},{"full_name":"Ares, Laura","first_name":"Laura","last_name":"Ares"},{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","last_name":"Wembe Moafo","first_name":"Boris Edgar"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina","id":"16494"},{"last_name":"Meier","orcid":"0000-0001-8864-2072","first_name":"Torsten","full_name":"Meier, Torsten","id":"344"},{"first_name":"Polina R.","last_name":"Sharapova","full_name":"Sharapova, Polina R.","id":"60286"},{"full_name":"Sperling, Jan","first_name":"Jan","orcid":"0000-0002-5844-3205","last_name":"Sperling","id":"75127"}],"doi":"10.1103/sv6z-v1gk","article_number":"033062","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","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>"}],"publication":"Physical Review Research","issue":"3","type":"journal_article","department":[{"_id":"15"},{"_id":"569"},{"_id":"170"},{"_id":"293"},{"_id":"706"},{"_id":"636"},{"_id":"35"},{"_id":"230"},{"_id":"429"},{"_id":"623"}],"date_created":"2025-12-09T09:08:39Z","status":"public","user_id":"16199","volume":7,"_id":"62980","publisher":"American Physical Society (APS)","project":[{"name":"TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten zu funktionellen Strukturen","_id":"53"},{"_id":"56","name":"TRR 142 - Project Area C"},{"name":"TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen Systemen: Eine theoretische Analyse","_id":"174"},{"_id":"266","name":"PhoQC: Photonisches Quantencomputing"}],"citation":{"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>.","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).","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>.","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>.","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} }","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>"}},{"date_created":"2025-04-10T14:42:52Z","department":[{"_id":"94"}],"type":"journal_article","citation":{"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} }","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>","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>.","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>","short":"B.E. Wembe Moafo, C. Offen, S. Maslovskaya, S. Ober-Blöbaum, P. Singh, J. Comput. Appl. Math 477 (n.d.).","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>."},"publication":"J. Comput. Appl. Math","issue":"15","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"}],"_id":"59507","language":[{"iso":"eng"}],"volume":477,"doi":"10.1016/j.cam.2025.117184","user_id":"95394","author":[{"id":"95394","full_name":"Wembe Moafo, Boris Edgar","first_name":"Boris Edgar","last_name":"Wembe Moafo"},{"full_name":"Offen, Cristian ","first_name":"Cristian ","last_name":"Offen"},{"first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya","id":"87909"},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"},{"first_name":"Pranav","last_name":"Singh","full_name":"Singh, Pranav"}],"title":"Commutator-free Cayley methods","status":"public","year":"2025","intvolume":"       477","date_updated":"2025-12-16T15:17:27Z","publication_status":"submitted"},{"title":"Second order optimality conditions in a new Lagrangian formulation for optimal control problems","status":"public","year":"2025","author":[{"last_name":"Konopik","first_name":"Michael","full_name":"Konopik, Michael"},{"full_name":"Leyendecker, Sigrid","last_name":"Leyendecker","first_name":"Sigrid"},{"first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya"},{"last_name":"Sina Ober-Blöbaum","first_name":"Sina Ober-Blöbaum","full_name":"Sina Ober-Blöbaum, Sina Ober-Blöbaum"},{"full_name":"Almagro, Rodrigo T. Sato Martín de","last_name":"Almagro","first_name":"Rodrigo T. Sato Martín de"}],"date_updated":"2026-01-06T18:29:15Z","language":[{"iso":"eng"}],"_id":"63510","user_id":"87909","publication":"arXiv:2507.06024","citation":{"bibtex":"@article{Konopik_Leyendecker_Maslovskaya_Sina Ober-Blöbaum_Almagro_2025, title={Second order optimality conditions in a new Lagrangian formulation for optimal control problems}, journal={arXiv:2507.06024}, author={Konopik, Michael and Leyendecker, Sigrid and Maslovskaya, Sofya and Sina Ober-Blöbaum, Sina Ober-Blöbaum and Almagro, Rodrigo T. Sato Martín de}, year={2025} }","ama":"Konopik M, Leyendecker S, Maslovskaya S, Sina Ober-Blöbaum SO-B, Almagro RTSM de. Second order optimality conditions in a new Lagrangian formulation for optimal control problems. <i>arXiv:250706024</i>. Published online 2025.","mla":"Konopik, Michael, et al. “Second Order Optimality Conditions in a New Lagrangian Formulation for Optimal Control Problems.” <i>ArXiv:2507.06024</i>, 2025.","chicago":"Konopik, Michael, Sigrid Leyendecker, Sofya Maslovskaya, Sina Ober-Blöbaum Sina Ober-Blöbaum, and Rodrigo T. Sato Martín de Almagro. “Second Order Optimality Conditions in a New Lagrangian Formulation for Optimal Control Problems.” <i>ArXiv:2507.06024</i>, 2025.","short":"M. Konopik, S. Leyendecker, S. Maslovskaya, S.O.-B. Sina Ober-Blöbaum, R.T.S.M. de Almagro, ArXiv:2507.06024 (2025).","ieee":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. O.-B. Sina Ober-Blöbaum, and R. T. S. M. de Almagro, “Second order optimality conditions in a new Lagrangian formulation for optimal control problems,” <i>arXiv:2507.06024</i>. 2025.","apa":"Konopik, M., Leyendecker, S., Maslovskaya, S., Sina Ober-Blöbaum, S. O.-B., &#38; Almagro, R. T. S. M. de. (2025). Second order optimality conditions in a new Lagrangian formulation for optimal control problems. In <i>arXiv:2507.06024</i>."},"abstract":[{"text":"It has been shown recently that optimal control problems with the dynamical constraint given by a second order system admit a regular Lagrangian formulation. This implies that the optimality conditions can be obtained in a new form based on the variational approach. In this paper we extend the first order necessary optimality conditions obtained previously to second order optimality conditions. This results in a complete characterization of the optimality conditions in a new Lagrangian form.","lang":"eng"}],"external_id":{"arxiv":["2507.06024"]},"date_created":"2026-01-06T18:28:18Z","type":"preprint","department":[{"_id":"636"}]},{"_id":"59797","language":[{"iso":"eng"}],"volume":36,"user_id":"87909","doi":"10.1007/s00332-025-10229-5","author":[{"last_name":"Konopik","first_name":"Michael","full_name":"Konopik, Michael"},{"full_name":"T. Sato Martín de Almagro, Rodrigo","first_name":"Rodrigo","last_name":"T. Sato Martín de Almagro"},{"full_name":"Maslovskaya, Sofya","first_name":"Sofya","last_name":"Maslovskaya","id":"87909"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"last_name":"Leyendecker","first_name":"Sigrid","full_name":"Leyendecker, Sigrid"}],"status":"public","title":"Variational integrators for a new Lagrangian approach to control affine systems with a quadratic Lagrange term","year":"2025","intvolume":"        36","date_updated":"2026-01-06T18:26:57Z","date_created":"2025-05-05T09:35:31Z","department":[{"_id":"636"}],"type":"journal_article","citation":{"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>.","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>","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>.","short":"M. Konopik, R. T. Sato Martín de Almagro, S. Maslovskaya, S. Ober-Blöbaum, S. Leyendecker, Journal of Nonlinear Science 36 (2025).","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>.","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} }"},"issue":"11","publication":"Journal of Nonlinear Science"},{"date_updated":"2026-01-06T18:24:40Z","intvolume":"        38","title":"A new Lagrangian approach to optimal control of second-order systems","status":"public","year":"2025","author":[{"first_name":"Michael","last_name":"Konopik","full_name":"Konopik, Michael"},{"first_name":"Sigrid","last_name":"Leyendecker","full_name":"Leyendecker, Sigrid"},{"id":"87909","full_name":"Maslovskaya, Sofya","first_name":"Sofya","last_name":"Maslovskaya"},{"id":"16494","first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina"},{"last_name":"T. Sato Martín de Almagro","first_name":"Rodrigo","full_name":"T. Sato Martín de Almagro, Rodrigo"}],"user_id":"87909","doi":"10.1088/1361-6544/ae1d08","volume":38,"_id":"59799","language":[{"iso":"eng"}],"publication":"Nonlinearity","issue":"11","citation":{"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} }","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>","short":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. Sato Martín de Almagro, Nonlinearity 38 (2025).","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>.","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>.","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>"},"type":"journal_article","department":[{"_id":"636"}],"date_created":"2025-05-05T09:37:50Z"},{"user_id":"85279","_id":"58544","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2502.05123"}],"date_updated":"2025-02-10T08:36:12Z","publication_status":"submitted","author":[{"id":"98502","last_name":"Kopylov","first_name":"Denis","full_name":"Kopylov, Denis"},{"orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen","full_name":"Offen, Christian","id":"85279"},{"full_name":"Ares, Laura","last_name":"Ares","first_name":"Laura"},{"id":"95394","first_name":"Boris Edgar","last_name":"Wembe Moafo","full_name":"Wembe Moafo, Boris Edgar"},{"last_name":"Ober-Blöbaum","first_name":"Sina","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"id":"344","orcid":"0000-0001-8864-2072","last_name":"Meier","first_name":"Torsten","full_name":"Meier, Torsten"},{"id":"60286","full_name":"Sharapova, Polina","last_name":"Sharapova","first_name":"Polina"},{"id":"75127","orcid":"0000-0002-5844-3205","last_name":"Sperling","first_name":"Jan","full_name":"Sperling, Jan"}],"year":"2025","status":"public","title":"Multiphoton, multimode state classification for nonlinear optical circuits ","oa":"1","department":[{"_id":"623"},{"_id":"15"},{"_id":"636"}],"type":"preprint","date_created":"2025-02-10T08:26:45Z","external_id":{"arxiv":["2502.05123"]},"abstract":[{"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. ","lang":"eng"}],"citation":{"short":"D. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier, P. Sharapova, J. Sperling, (n.d.).","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.","ieee":"D. Kopylov <i>et al.</i>, “Multiphoton, multimode state classification for nonlinear optical circuits .” .","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>.","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} }","ama":"Kopylov D, Offen C, Ares L, et al. Multiphoton, multimode state classification for nonlinear optical circuits .","mla":"Kopylov, Denis, et al. <i>Multiphoton, Multimode State Classification for Nonlinear Optical Circuits </i>."}},{"user_id":"85279","ddc":["510"],"publisher":"American Mathematical Society","_id":"53805","has_accepted_license":"1","status":"public","oa":"1","external_id":{"arxiv":["arXiv:2404.19626"]},"quality_controlled":"1","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"file_date_updated":"2025-05-02T13:20:31Z","citation":{"short":"C. Offen, Mathematics of Computation (2025).","chicago":"Offen, Christian. “Machine Learning of Continuous and Discrete Variational ODEs with Convergence Guarantee and Uncertainty Quantification.” <i>Mathematics of Computation</i>, 2025. <a href=\"https://doi.org/10.1090/mcom/4120\">https://doi.org/10.1090/mcom/4120</a>.","apa":"Offen, C. (2025). Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification. <i>Mathematics of Computation</i>. <a href=\"https://doi.org/10.1090/mcom/4120\">https://doi.org/10.1090/mcom/4120</a>","ieee":"C. Offen, “Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification,” <i>Mathematics of Computation</i>, 2025, doi: <a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>.","ama":"Offen C. Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification. <i>Mathematics of Computation</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>","bibtex":"@article{Offen_2025, title={Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification}, DOI={<a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>}, journal={Mathematics of Computation}, publisher={American Mathematical Society}, author={Offen, Christian}, year={2025} }","mla":"Offen, Christian. “Machine Learning of Continuous and Discrete Variational ODEs with Convergence Guarantee and Uncertainty Quantification.” <i>Mathematics of Computation</i>, American Mathematical Society, 2025, doi:<a href=\"https://doi.org/10.1090/mcom/4120\">10.1090/mcom/4120</a>."},"doi":"10.1090/mcom/4120","language":[{"iso":"eng"}],"publication_status":"epub_ahead","date_updated":"2025-06-29T13:03:55Z","article_type":"original","year":"2025","title":"Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification","author":[{"full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen","id":"85279"}],"type":"journal_article","department":[{"_id":"636"}],"file":[{"relation":"main_file","date_updated":"2025-05-02T13:20:31Z","file_name":"L_Collocation_ODE_mcom-l-template.pdf","file_size":1819189,"access_level":"open_access","title":"Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification ","file_id":"59759","content_type":"application/pdf","creator":"coffen","description":"The article introduces a method to learn dynamical systems that\nare governed by Euler–Lagrange equations from data. The method is based on\nGaussian process regression and identifies continuous or discrete Lagrangians\nand is, therefore, structure preserving by design. A rigorous proof of con-\nvergence as the distance between observation data points converges to zero\nand lower bounds for convergence rates are provided. Next to convergence\nguarantees, the method allows for quantification of model uncertainty, which\ncan provide a basis of adaptive sampling techniques. We provide efficient uncertainty quantification of any observable that is linear in the Lagrangian,\nincluding of Hamiltonian functions (energy) and symplectic structures, which\nis of interest in the context of system identification. The article overcomes\nmajor practical and theoretical difficulties related to the ill-posedness of the\nidentification task of (discrete) Lagrangians through a careful design of geometric regularisation strategies and through an exploit of a relation to convex\nminimisation problems in reproducing kernel Hilbert spaces.","date_created":"2025-05-02T13:20:31Z"}],"date_created":"2024-04-30T16:04:40Z","related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/Christian-Offen/Lagrangian_GP"}]},"abstract":[{"lang":"eng","text":"The article introduces a method to learn dynamical systems that are governed by Euler–Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore, structure preserving by design. A rigorous proof of convergence as the distance between observation data points converges to zero and lower bounds for convergence rates are provided. Next to convergence guarantees, the method allows for quantification of model uncertainty, which can provide a basis of adaptive sampling techniques. We provide efficient uncertainty quantification of any observable that is linear in the Lagrangian, including of Hamiltonian functions (energy) and symplectic structures, which is of interest in the context of system identification. The article overcomes major practical and theoretical difficulties related to the ill-posedness of the identification task of (discrete) Lagrangians through a careful design of geometric regularisation strategies and through an exploit of a relation to convex minimisation problems in reproducing kernel Hilbert spaces."}],"publication":"Mathematics of Computation"},{"status":"public","has_accepted_license":"1","_id":"53101","publisher":"American Institute of Mathematical Sciences (AIMS)","page":"0-0","volume":"0","ddc":["510"],"user_id":"87909","citation":{"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>.","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>","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>.","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>.","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} }","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","publication_identifier":{"issn":["2158-2491","2158-2505"]},"author":[{"first_name":"Sigrid","last_name":"Leyendecker","full_name":"Leyendecker, Sigrid"},{"id":"87909","first_name":"Sofya","last_name":"Maslovskaya","full_name":"Maslovskaya, Sofya"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494"},{"full_name":"Almagro, Rodrigo T. Sato Martín de","first_name":"Rodrigo T. Sato Martín de","last_name":"Almagro"},{"full_name":"Szemenyei, Flóra Orsolya","last_name":"Szemenyei","first_name":"Flóra Orsolya"}],"year":"2024","title":"A new Lagrangian approach to control affine systems with a quadratic Lagrange term","article_type":"original","date_updated":"2024-03-28T16:07:34Z","publication_status":"published","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://www.aimsciences.org/article/doi/10.3934/jcd.2024017","open_access":"1"}],"doi":"10.3934/jcd.2024017","publication":"Journal of Computational Dynamics","issue":"0","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."}],"date_created":"2024-03-28T15:58:02Z","department":[{"_id":"636"}],"type":"journal_article","keyword":["Optimal control problem","Lagrangian system","Hamiltonian system","Variations","Pontryagin's maximum principle."]},{"status":"public","has_accepted_license":"1","_id":"46469","publisher":"AIP Publishing","user_id":"85279","ddc":["510"],"volume":34,"file_date_updated":"2024-01-09T11:19:49Z","citation":{"short":"C. Offen, S. Ober-Blöbaum, Chaos 34 (2024).","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” <i>Chaos</i> 34, no. 1 (2024). <a href=\"https://doi.org/10.1063/5.0172287\">https://doi.org/10.1063/5.0172287</a>.","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2024). Learning of discrete models of variational PDEs from data. <i>Chaos</i>, <i>34</i>(1), Article 013104. <a href=\"https://doi.org/10.1063/5.0172287\">https://doi.org/10.1063/5.0172287</a>","ieee":"C. Offen and S. Ober-Blöbaum, “Learning of discrete models of variational PDEs from data,” <i>Chaos</i>, vol. 34, no. 1, Art. no. 013104, 2024, doi: <a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>.","ama":"Offen C, Ober-Blöbaum S. Learning of discrete models of variational PDEs from data. <i>Chaos</i>. 2024;34(1). doi:<a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>","bibtex":"@article{Offen_Ober-Blöbaum_2024, title={Learning of discrete models of variational PDEs from data}, volume={34}, DOI={<a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>}, number={1013104}, journal={Chaos}, publisher={AIP Publishing}, author={Offen, Christian and Ober-Blöbaum, Sina}, year={2024} }","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational PDEs from Data.” <i>Chaos</i>, vol. 34, no. 1, 013104, AIP Publishing, 2024, doi:<a href=\"https://doi.org/10.1063/5.0172287\">10.1063/5.0172287</a>."},"quality_controlled":"1","project":[{"_id":"52","name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"external_id":{"arxiv":["2308.05082 "]},"oa":"1","year":"2024","title":"Learning of discrete models of variational PDEs from data","author":[{"full_name":"Offen, Christian","first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","id":"85279"},{"id":"16494","full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"}],"publication_identifier":{"issn":["1054-1500"]},"publication_status":"published","date_updated":"2024-08-12T13:45:43Z","article_type":"original","intvolume":"        34","article_number":"013104","language":[{"iso":"eng"}],"doi":"10.1063/5.0172287","issue":"1","publication":"Chaos","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. "}],"related_material":{"link":[{"url":"https://github.com/Christian-Offen/DLNN_pde","relation":"software","description":"GitHub"}]},"file":[{"date_created":"2024-01-09T10:48:38Z","creator":"coffen","title":"Accepted Manuscript Chaos","content_type":"application/pdf","file_id":"50376","date_updated":"2024-01-09T10:48:38Z","relation":"main_file","file_size":13222105,"access_level":"open_access","file_name":"Accepted manuscript with AIP banner CHA23-AR-01370.pdf"},{"date_updated":"2024-01-09T11:19:49Z","relation":"main_file","file_size":12960884,"access_level":"open_access","file_name":"LDensityPDE_AIP.pdf","title":"Learning of discrete models of variational PDEs from data","content_type":"application/pdf","file_id":"50390","creator":"coffen","description":"We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train\na neural network model of a discrete Lagrangian density such that the discrete Euler–Lagrange equations are consistent\nwith the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian\ndensities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for\nthe training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers\nguarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical\nsimulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory\nsuch as travelling waves. This is possible even when travelling waves are not present in the training data. This is\ncompared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces\ncontaining structurally simple solutions when these are not present in the training data. Ideas are demonstrated on\nexamples based on the wave equation and the Schrödinger equation.","date_created":"2024-01-09T11:19:49Z"}],"date_created":"2023-08-10T08:24:48Z","type":"journal_article","department":[{"_id":"636"}]},{"publication_status":"submitted","date_updated":"2024-08-12T13:43:32Z","title":"Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification","year":"2024","author":[{"orcid":"0000-0002-5940-8057","last_name":"Offen","first_name":"Christian","full_name":"Offen, Christian","id":"85279"}],"language":[{"iso":"eng"}],"related_material":{"link":[{"url":"https://github.com/Christian-Offen/Lagrangian_GP_PDE","relation":"software","description":"GitHub"}]},"abstract":[{"text":"We introduce a method based on Gaussian process regression to identify discrete variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a geometric machine learning technique in the sense that the variational structure of the true field theory is reflected in the data-driven model by design. We provide a rigorous convergence statement of the method. The proof circumvents challenges posed by the ambiguity of discrete Lagrangian densities in the inverse problem of variational calculus.\r\nMoreover, our method can be used to quantify model uncertainty in the equations of motions and any linear observable of the discrete field theory. This is illustrated on the example of the discrete wave equation and Schrödinger equation.\r\nThe article constitutes an extension of our previous article  arXiv:2404.19626 for the data-driven identification of (discrete) Lagrangians for variational dynamics from an ode setting to the setting of discrete pdes.","lang":"eng"}],"keyword":["System identification","inverse problem of variational calculus","Gaussian process","Lagrangian learning","physics informed machine learning","geometry aware learning"],"type":"preprint","department":[{"_id":"636"}],"file":[{"creator":"coffen","description":"We introduce a method based on Gaussian process regression to identify discrete\nvariational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a geometric machine learning technique in the sense that the variational structure of the true field theory is reflected in the data-driven model by design.\nWe provide a rigorous convergence statement of the method.\nThe proof circumvents challenges posed by the ambiguity of discrete Lagrangian densities in the inverse problem of variational calculus.\nMoreover, our method can be used to quantify model uncertainty in the equations of motions and any linear observable of the discrete field theory.\nThis is illustrated on the example of the discrete wave equation and Schrödinger equation.\nThe article constitutes an extension of our previous article for the data-driven identification of (discrete) Lagrangians for variational dynamics from an ode setting to the setting of discrete pdes.","date_created":"2024-07-10T13:39:32Z","relation":"main_file","date_updated":"2024-07-10T13:39:32Z","file_name":"L_Collocation.pdf","access_level":"open_access","file_size":4569314,"title":"Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification","file_id":"55160","content_type":"application/pdf"}],"date_created":"2024-07-10T13:43:50Z","has_accepted_license":"1","status":"public","user_id":"85279","ddc":["510"],"page":"28","_id":"55159","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"file_date_updated":"2024-07-10T13:39:32Z","citation":{"ieee":"C. Offen, “Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification.” .","apa":"Offen, C. (n.d.). <i>Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification</i>.","chicago":"Offen, Christian. “Machine Learning of Discrete Field Theories with Guaranteed Convergence and Uncertainty Quantification,” n.d.","short":"C. Offen, (n.d.).","mla":"Offen, Christian. <i>Machine Learning of Discrete Field Theories with Guaranteed Convergence and Uncertainty Quantification</i>.","bibtex":"@article{Offen, title={Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification}, author={Offen, Christian} }","ama":"Offen C. Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification."},"oa":"1","external_id":{"arxiv":["2407.07642"]}},{"title":"Symplectic Methods in Deep Learning","year":"2024","author":[{"full_name":"Maslovskaya, Sofya","first_name":"Sofya","last_name":"Maslovskaya","id":"87909"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina","id":"16494"}],"publication_identifier":{"issn":["2405-8963"]},"publication_status":"published","date_updated":"2025-05-05T09:22:27Z","intvolume":"        58","language":[{"iso":"eng"}],"doi":"10.1016/j.ifacol.2024.10.118","publication":"IFAC-PapersOnLine","issue":"17","date_created":"2025-05-05T09:21:13Z","type":"conference","department":[{"_id":"636"}],"status":"public","page":"85-90","_id":"59791","publisher":"Elsevier BV","user_id":"87909","volume":58,"citation":{"chicago":"Maslovskaya, Sofya, and Sina Ober-Blöbaum. “Symplectic Methods in Deep Learning.” In <i>IFAC-PapersOnLine</i>, 58:85–90. Elsevier BV, 2024. <a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">https://doi.org/10.1016/j.ifacol.2024.10.118</a>.","short":"S. Maslovskaya, S. Ober-Blöbaum, in: IFAC-PapersOnLine, Elsevier BV, 2024, pp. 85–90.","apa":"Maslovskaya, S., &#38; Ober-Blöbaum, S. (2024). Symplectic Methods in Deep Learning. <i>IFAC-PapersOnLine</i>, <i>58</i>(17), 85–90. <a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">https://doi.org/10.1016/j.ifacol.2024.10.118</a>","ieee":"S. Maslovskaya and S. Ober-Blöbaum, “Symplectic Methods in Deep Learning,” in <i>IFAC-PapersOnLine</i>, 2024, vol. 58, no. 17, pp. 85–90, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">10.1016/j.ifacol.2024.10.118</a>.","ama":"Maslovskaya S, Ober-Blöbaum S. Symplectic Methods in Deep Learning. In: <i>IFAC-PapersOnLine</i>. Vol 58. Elsevier BV; 2024:85-90. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">10.1016/j.ifacol.2024.10.118</a>","bibtex":"@inproceedings{Maslovskaya_Ober-Blöbaum_2024, title={Symplectic Methods in Deep Learning}, volume={58}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2024.10.118\">10.1016/j.ifacol.2024.10.118</a>}, number={17}, booktitle={IFAC-PapersOnLine}, publisher={Elsevier BV}, author={Maslovskaya, Sofya and Ober-Blöbaum, Sina}, year={2024}, pages={85–90} }","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>."}},{"citation":{"short":"F. Jean, S. Maslovskaya, (2024).","chicago":"Jean, Frédéric, and Sofya Maslovskaya. “Inverse Optimal Control Problem in the Non Autonomous Linear-Quadratic Case,” 2024.","apa":"Jean, F., &#38; Maslovskaya, S. (2024). <i>Inverse optimal control problem in the non autonomous linear-quadratic case</i>.","ieee":"F. Jean and S. Maslovskaya, “Inverse optimal control problem in the non autonomous linear-quadratic case.” 2024.","ama":"Jean F, Maslovskaya S. Inverse optimal control problem in the non autonomous linear-quadratic case. Published online 2024.","bibtex":"@article{Jean_Maslovskaya_2024, title={Inverse optimal control problem in the non autonomous linear-quadratic case}, author={Jean, Frédéric and Maslovskaya, Sofya}, year={2024} }","mla":"Jean, Frédéric, and Sofya Maslovskaya. <i>Inverse Optimal Control Problem in the Non Autonomous Linear-Quadratic Case</i>. 2024."},"date_created":"2025-05-05T09:42:19Z","department":[{"_id":"636"}],"type":"preprint","author":[{"full_name":"Jean, Frédéric","first_name":"Frédéric","last_name":"Jean"},{"id":"87909","full_name":"Maslovskaya, Sofya","first_name":"Sofya","last_name":"Maslovskaya"}],"year":"2024","title":"Inverse optimal control problem in the non autonomous linear-quadratic case","status":"public","date_updated":"2025-05-05T09:43:05Z","_id":"59801","language":[{"iso":"eng"}],"user_id":"87909"},{"abstract":[{"text":"By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system will behave in time. If the dynamics exhibit additional symmetries, then the motion fulfils additional conservation laws, such as conservation of energy (time invariance), momentum (translation invariance), or angular momentum (rotational invariance). To learn a system representation, one could learn the discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function Ld which defines them. Based on ideas from Lie group theory, in this work we introduce a framework to learn a discrete Lagrangian along with its symmetry group from discrete observations of motions and, therefore, identify conserved quantities. The learning process does not restrict the form of the Lagrangian, does not require velocity or momentum observations or predictions and incorporates a cost term which safeguards against unwanted solutions and against potential numerical issues in forward simulations. The learnt discrete quantities are related to their continuous analogues using variational backward error analysis and numerical results demonstrate the improvement such models can have both qualitatively and quantitatively even in the presence of noise.","lang":"eng"}],"related_material":{"link":[{"description":"GitHub","url":"https://github.com/yanalish/SymDLNN","relation":"software"}]},"issue":"2","publication":"IFAC-PapersOnLine","department":[{"_id":"636"}],"type":"conference","date_created":"2022-11-23T08:17:10Z","file":[{"relation":"main_file","date_updated":"2023-04-17T08:05:55Z","file_name":"LNN_project.pdf","file_size":576115,"access_level":"open_access","title":"Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery","file_id":"44037","content_type":"application/pdf","creator":"coffen","description":"By one of the most fundamental principles in physics, a dynamical system will\nexhibit those motions which extremise an action functional. This leads to the formation of\nthe Euler-Lagrange equations, which serve as a model of how the system will behave in time.\nIf the dynamics exhibit additional symmetries, then the motion fulfils additional conservation\nlaws, such as conservation of energy (time invariance), momentum (translation invariance), or\nangular momentum (rotational invariance). To learn a system representation, one could learn\nthe discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function\nLd which defines them. Based on ideas from Lie group theory, we introduce a framework to learn\na discrete Lagrangian along with its symmetry group from discrete observations of motions and,\ntherefore, identify conserved quantities. The learning process does not restrict the form of the\nLagrangian, does not require velocity or momentum observations or predictions and incorporates\na cost term which safeguards against unwanted solutions and against potential numerical issues\nin forward simulations. The learnt discrete quantities are related to their continuous analogues\nusing variational backward error analysis and numerical results demonstrate the improvement\nsuch models can have both qualitatively and quantitatively even in the presence of noise.","date_created":"2023-04-17T08:05:55Z"}],"intvolume":"        56","date_updated":"2023-12-29T14:26:00Z","publication_status":"published","author":[{"first_name":"Yana","last_name":"Lishkova","full_name":"Lishkova, Yana"},{"full_name":"Scherer, Paul","first_name":"Paul","last_name":"Scherer"},{"full_name":"Ridderbusch, Steffen","last_name":"Ridderbusch","first_name":"Steffen"},{"full_name":"Jamnik, Mateja","first_name":"Mateja","last_name":"Jamnik"},{"full_name":"Liò, Pietro","last_name":"Liò","first_name":"Pietro"},{"first_name":"Sina","last_name":"Ober-Blöbaum","full_name":"Ober-Blöbaum, Sina","id":"16494"},{"id":"85279","full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","first_name":"Christian","last_name":"Offen"}],"title":"Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery","year":"2023","doi":"10.1016/j.ifacol.2023.10.1457","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S2405896323018657"}],"quality_controlled":"1","citation":{"ieee":"Y. Lishkova <i>et al.</i>, “Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery,” in <i>IFAC-PapersOnLine</i>,  Yokohama, Japan, 2023, vol. 56, no. 2, pp. 3203–3210, doi: <a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>.","apa":"Lishkova, Y., Scherer, P., Ridderbusch, S., Jamnik, M., Liò, P., Ober-Blöbaum, S., &#38; Offen, C. (2023). Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery. <i>IFAC-PapersOnLine</i>, <i>56</i>(2), 3203–3210. <a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">https://doi.org/10.1016/j.ifacol.2023.10.1457</a>","short":"Y. Lishkova, P. Scherer, S. Ridderbusch, M. Jamnik, P. Liò, S. Ober-Blöbaum, C. Offen, in: IFAC-PapersOnLine, Elsevier, 2023, pp. 3203–3210.","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>.","mla":"Lishkova, Yana, et al. “Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery.” <i>IFAC-PapersOnLine</i>, vol. 56, no. 2, Elsevier, 2023, pp. 3203–10, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>.","bibtex":"@inproceedings{Lishkova_Scherer_Ridderbusch_Jamnik_Liò_Ober-Blöbaum_Offen_2023, title={Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery}, volume={56}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>}, number={2}, booktitle={IFAC-PapersOnLine}, publisher={Elsevier}, author={Lishkova, Yana and Scherer, Paul and Ridderbusch, Steffen and Jamnik, Mateja and Liò, Pietro and Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={3203–3210} }","ama":"Lishkova Y, Scherer P, Ridderbusch S, et al. Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery. In: <i>IFAC-PapersOnLine</i>. Vol 56. Elsevier; 2023:3203-3210. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2023.10.1457\">10.1016/j.ifacol.2023.10.1457</a>"},"file_date_updated":"2023-04-17T08:05:55Z","oa":"1","external_id":{"arxiv":["2211.10830"]},"has_accepted_license":"1","conference":{"location":" Yokohama, Japan","start_date":"2023-07-09","name":"The 22nd World Congress of the International Federation of Automatic Control","end_date":"2023-07-14"},"status":"public","volume":56,"ddc":["510"],"user_id":"85279","_id":"34135","publisher":"Elsevier","page":"3203-3210"},{"publication_identifier":{"eisbn":["978-3-031-38271-0"]},"author":[{"first_name":"Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","full_name":"Offen, Christian","id":"85279"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494"}],"title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","year":"2023","intvolume":"     14071","date_updated":"2024-08-12T13:46:29Z","publication_status":"published","language":[{"iso":"eng"}],"series_title":"Lecture Notes in Computer Science (LNCS)","doi":"10.1007/978-3-031-38271-0_57","publication":"Geometric Science of Information","related_material":{"link":[{"url":"https://github.com/Christian-Offen/LagrangianDensityML","relation":"software","description":"GitHub"}]},"abstract":[{"lang":"eng","text":"The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that is modelled as a neural network. Careful regularisation of the loss function for training $L_d$ is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler--Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE."}],"date_created":"2023-02-16T11:32:48Z","file":[{"file_id":"46273","content_type":"application/pdf","title":"Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves","file_name":"LDensityLearning.pdf","access_level":"open_access","file_size":1938962,"relation":"main_file","date_updated":"2023-08-02T12:04:17Z","date_created":"2023-08-02T12:04:17Z","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.","creator":"coffen"}],"department":[{"_id":"636"}],"keyword":["System identification","discrete Lagrangians","travelling waves"],"type":"conference","conference":{"start_date":"2023-08-30","name":"  GSI'23 6th International Conference on Geometric Science of Information","location":"Saint-Malo, Palais du Grand Large, France","end_date":"2023-09-01"},"status":"public","has_accepted_license":"1","_id":"42163","publisher":"Springer, Cham.","page":"569-579","editor":[{"first_name":"F","last_name":"Nielsen","full_name":"Nielsen, F"},{"full_name":"Barbaresco, F","first_name":"F","last_name":"Barbaresco"}],"volume":14071,"ddc":["510"],"user_id":"85279","citation":{"ama":"Offen C, Ober-Blöbaum S. Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In: Nielsen F, Barbaresco F, eds. <i>Geometric Science of Information</i>. Vol 14071. Lecture Notes in Computer Science (LNCS). Springer, Cham.; 2023:569-579. doi:<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>","bibtex":"@inproceedings{Offen_Ober-Blöbaum_2023, series={Lecture Notes in Computer Science (LNCS)}, title={Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves}, volume={14071}, DOI={<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>}, booktitle={Geometric Science of Information}, publisher={Springer, Cham.}, author={Offen, Christian and Ober-Blöbaum, Sina}, editor={Nielsen, F and Barbaresco, F}, year={2023}, pages={569–579}, collection={Lecture Notes in Computer Science (LNCS)} }","mla":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” <i>Geometric Science of Information</i>, edited by F Nielsen and F Barbaresco, vol. 14071, Springer, Cham., 2023, pp. 569–79, doi:<a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>.","chicago":"Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” In <i>Geometric Science of Information</i>, edited by F Nielsen and F Barbaresco, 14071:569–79. Lecture Notes in Computer Science (LNCS). Springer, Cham., 2023. <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">https://doi.org/10.1007/978-3-031-38271-0_57</a>.","short":"C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric Science of Information, Springer, Cham., 2023, pp. 569–579.","apa":"Offen, C., &#38; Ober-Blöbaum, S. (2023). Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In F. Nielsen &#38; F. Barbaresco (Eds.), <i>Geometric Science of Information</i> (Vol. 14071, pp. 569–579). Springer, Cham. <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">https://doi.org/10.1007/978-3-031-38271-0_57</a>","ieee":"C. Offen and S. Ober-Blöbaum, “Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves,” in <i>Geometric Science of Information</i>, Saint-Malo, Palais du Grand Large, France, 2023, vol. 14071, pp. 569–579, doi: <a href=\"https://doi.org/10.1007/978-3-031-38271-0_57\">10.1007/978-3-031-38271-0_57</a>."},"file_date_updated":"2023-08-02T12:04:17Z","project":[{"name":"PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"quality_controlled":"1","external_id":{"arxiv":["2302.08232 "]},"oa":"1"}]