---
_id: '63557'
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.
author:
- first_name: Michael
full_name: Konopik, Michael
last_name: Konopik
- first_name: Sigrid
full_name: Leyendecker, Sigrid
last_name: Leyendecker
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Rodrigo T.
full_name: Sato Martín de Almagro, Rodrigo T.
last_name: Sato Martín de Almagro
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. Multibody System Dynamics. Published online 2026.
doi:10.1007/s11044-025-10138-1
apa: Konopik, M., Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., & Sato Martín de Almagro,
R. T. (2026). On the variational discretisation of optimal control problems for
unconstrained Lagrangian dynamics. Multibody System Dynamics. https://doi.org/10.1007/s11044-025-10138-1
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={10.1007/s11044-025-10138-1},
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}
}'
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.” Multibody System Dynamics,
2026. https://doi.org/10.1007/s11044-025-10138-1.
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,” Multibody System Dynamics, 2026, doi: 10.1007/s11044-025-10138-1.'
mla: Konopik, Michael, et al. “On the Variational Discretisation of Optimal Control
Problems for Unconstrained Lagrangian Dynamics.” Multibody System Dynamics,
Springer Science and Business Media LLC, 2026, doi:10.1007/s11044-025-10138-1.
short: M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T. Sato Martín de Almagro,
Multibody System Dynamics (2026).
date_created: 2026-01-12T11:33:54Z
date_updated: 2026-01-12T11:35:27Z
department:
- _id: '636'
doi: 10.1007/s11044-025-10138-1
language:
- iso: eng
publication: Multibody System Dynamics
publication_identifier:
issn:
- 1384-5640
- 1573-272X
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: On the variational discretisation of optimal control problems for unconstrained
Lagrangian dynamics
type: journal_article
user_id: '87909'
year: '2026'
...
---
_id: '59792'
abstract:
- lang: eng
text: "Abstract\r\n 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 static turnpike to manifold turnpike
we extend the exponential turnpike property to the
exponential trim turnpike 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
trim turnpike theorem for the full problem. Finally,
we illustrate our results on the Kepler problem and the rigid body problem.\r\n"
author:
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
ama: Flaßkamp K, Maslovskaya S, Ober-Blöbaum S, Wembe Moafo BE. Trim turnpikes for
optimal control problems with symmetries. Mathematics of Control, Signals,
and Systems. Published online 2025. doi:10.1007/s00498-025-00408-w
apa: Flaßkamp, K., Maslovskaya, S., Ober-Blöbaum, S., & Wembe Moafo, B. E. (2025).
Trim turnpikes for optimal control problems with symmetries. Mathematics of
Control, Signals, and Systems. https://doi.org/10.1007/s00498-025-00408-w
bibtex: '@article{Flaßkamp_Maslovskaya_Ober-Blöbaum_Wembe Moafo_2025, title={Trim
turnpikes for optimal control problems with symmetries}, DOI={10.1007/s00498-025-00408-w},
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} }'
chicago: Flaßkamp, Kathrin, Sofya Maslovskaya, Sina Ober-Blöbaum, and Boris Edgar
Wembe Moafo. “Trim Turnpikes for Optimal Control Problems with Symmetries.” Mathematics
of Control, Signals, and Systems, 2025. https://doi.org/10.1007/s00498-025-00408-w.
ieee: 'K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, and B. E. Wembe Moafo, “Trim
turnpikes for optimal control problems with symmetries,” Mathematics of Control,
Signals, and Systems, 2025, doi: 10.1007/s00498-025-00408-w.'
mla: Flaßkamp, Kathrin, et al. “Trim Turnpikes for Optimal Control Problems with
Symmetries.” Mathematics of Control, Signals, and Systems, Springer Science
and Business Media LLC, 2025, doi:10.1007/s00498-025-00408-w.
short: K. Flaßkamp, S. Maslovskaya, S. Ober-Blöbaum, B.E. Wembe Moafo, Mathematics
of Control, Signals, and Systems (2025).
date_created: 2025-05-05T09:23:38Z
date_updated: 2025-05-05T09:24:09Z
department:
- _id: '636'
doi: 10.1007/s00498-025-00408-w
language:
- iso: eng
publication: Mathematics of Control, Signals, and Systems
publication_identifier:
issn:
- 0932-4194
- 1435-568X
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Trim turnpikes for optimal control problems with symmetries
type: journal_article
user_id: '87909'
year: '2025'
...
---
_id: '58544'
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. '
author:
- first_name: Denis
full_name: Kopylov, Denis
id: '98502'
last_name: Kopylov
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Laura
full_name: Ares, Laura
last_name: Ares
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
- first_name: Polina
full_name: Sharapova, Polina
id: '60286'
last_name: Sharapova
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
citation:
ama: Kopylov D, Offen C, Ares L, et al. 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., & Sperling, J. (n.d.). Multiphoton, multimode state
classification for nonlinear optical circuits .
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} }'
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 et al., “Multiphoton, multimode state classification for
nonlinear optical circuits .” .
mla: Kopylov, Denis, et al. Multiphoton, Multimode State Classification for Nonlinear
Optical Circuits .
short: D. Kopylov, C. Offen, L. Ares, B.E. Wembe Moafo, S. Ober-Blöbaum, T. Meier,
P. Sharapova, J. Sperling, (n.d.).
date_created: 2025-02-10T08:26:45Z
date_updated: 2025-02-10T08:36:12Z
department:
- _id: '623'
- _id: '15'
- _id: '636'
external_id:
arxiv:
- '2502.05123'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2502.05123
oa: '1'
publication_status: submitted
status: public
title: 'Multiphoton, multimode state classification for nonlinear optical circuits '
type: preprint
user_id: '85279'
year: '2025'
...
---
_id: '59794'
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.
author:
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Pranav
full_name: Singh, Pranav
last_name: Singh
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
citation:
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.
apa: Maslovskaya, S., Ober-Blöbaum, S., Offen, C., Singh, P., & Wembe Moafo,
B. E. (2025). Adaptive higher order reversible integrators for memory efficient
deep learning.
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} }'
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.
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.
mla: Maslovskaya, Sofya, et al. 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).
date_created: 2025-05-05T09:25:28Z
date_updated: 2025-09-30T15:16:09Z
ddc:
- '510'
department:
- _id: '636'
external_id:
arxiv:
- '2410.09537'
file:
- access_level: closed
content_type: application/pdf
creator: sofyam
date_created: 2025-05-05T09:28:02Z
date_updated: 2025-05-05T09:28:02Z
file_id: '59795'
file_name: 2410.09537v2.pdf
file_size: 1830758
relation: main_file
success: 1
file_date_updated: 2025-05-05T09:28:02Z
has_accepted_license: '1'
language:
- iso: eng
status: public
title: Adaptive higher order reversible integrators for memory efficient deep learning
type: preprint
user_id: '85279'
year: '2025'
...
---
_id: '62980'
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 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.
article_number: '033062'
author:
- first_name: Denis A.
full_name: Kopylov, Denis A.
last_name: Kopylov
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Laura
full_name: Ares, Laura
last_name: Ares
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
- first_name: Polina R.
full_name: Sharapova, Polina R.
id: '60286'
last_name: Sharapova
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
citation:
ama: Kopylov DA, Offen C, Ares L, et al. Multiphoton, multimode state classification
for nonlinear optical circuits. Physical Review Research. 2025;7(3). doi:10.1103/sv6z-v1gk
apa: Kopylov, D. A., Offen, C., Ares, L., Wembe Moafo, B. E., Ober-Blöbaum, S.,
Meier, T., Sharapova, P. R., & Sperling, J. (2025). Multiphoton, multimode
state classification for nonlinear optical circuits. Physical Review Research,
7(3), Article 033062. https://doi.org/10.1103/sv6z-v1gk
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={10.1103/sv6z-v1gk},
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} }'
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.” Physical Review
Research 7, no. 3 (2025). https://doi.org/10.1103/sv6z-v1gk.
ieee: 'D. A. Kopylov et al., “Multiphoton, multimode state classification
for nonlinear optical circuits,” Physical Review Research, vol. 7, no.
3, Art. no. 033062, 2025, doi: 10.1103/sv6z-v1gk.'
mla: Kopylov, Denis A., et al. “Multiphoton, Multimode State Classification for
Nonlinear Optical Circuits.” Physical Review Research, vol. 7, no. 3, 033062,
American Physical Society (APS), 2025, doi:10.1103/sv6z-v1gk.
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).
date_created: 2025-12-09T09:08:39Z
date_updated: 2025-12-09T09:10:01Z
department:
- _id: '15'
- _id: '569'
- _id: '170'
- _id: '293'
- _id: '706'
- _id: '636'
- _id: '35'
- _id: '230'
- _id: '429'
- _id: '623'
doi: 10.1103/sv6z-v1gk
intvolume: ' 7'
issue: '3'
language:
- iso: eng
project:
- _id: '53'
name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
zu funktionellen Strukturen'
- _id: '56'
name: TRR 142 - Project Area C
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: Physical Review Research
publication_identifier:
issn:
- 2643-1564
publication_status: published
publisher: American Physical Society (APS)
status: public
title: Multiphoton, multimode state classification for nonlinear optical circuits
type: journal_article
user_id: '16199'
volume: 7
year: '2025'
...
---
_id: '62979'
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.
author:
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
- first_name: Polina R.
full_name: Sharapova, Polina R.
id: '60286'
last_name: Sharapova
- first_name: Jan
full_name: Sperling, Jan
id: '75127'
last_name: Sperling
orcid: 0000-0002-5844-3205
- 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
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
citation:
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.
apa: Meier, T., Sharapova, P. R., Sperling, J., Ober-Blöbaum, S., Wembe Moafo, B.
E., & Offen, C. (2025). Multiphoton, multimode state classification for
nonlinear optical circuits.
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} }'
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.
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.
mla: Meier, Torsten, et al. Multiphoton, Multimode State Classification for Nonlinear
Optical Circuits. 2025.
short: T. Meier, P.R. Sharapova, J. Sperling, S. Ober-Blöbaum, B.E. Wembe Moafo,
C. Offen, (2025).
date_created: 2025-12-09T08:59:27Z
date_updated: 2025-12-09T09:10:23Z
department:
- _id: '15'
- _id: '170'
- _id: '293'
- _id: '706'
- _id: '636'
- _id: '230'
- _id: '623'
- _id: '429'
- _id: '35'
language:
- iso: eng
project:
- _id: '53'
name: 'TRR 142: Maßgeschneiderte nichtlineare Photonik: Von grundlegenden Konzepten
zu funktionellen Strukturen'
- _id: '56'
name: TRR 142 - Project Area C
- _id: '174'
name: 'TRR 142 ; TP: C10: Erzeugung und Charakterisierung von Quantenlicht in nichtlinearen
Systemen: Eine theoretische Analyse'
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
status: public
title: Multiphoton, multimode state classification for nonlinear optical circuits
type: preprint
user_id: '16199'
year: '2025'
...
---
_id: '59507'
abstract:
- lang: eng
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.
author:
- first_name: Boris Edgar
full_name: Wembe Moafo, Boris Edgar
id: '95394'
last_name: Wembe Moafo
- first_name: 'Cristian '
full_name: 'Offen, Cristian '
last_name: Offen
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Pranav
full_name: Singh, Pranav
last_name: Singh
citation:
ama: Wembe Moafo BE, Offen C, Maslovskaya S, Ober-Blöbaum S, Singh P. Commutator-free
Cayley methods. J Comput Appl Math. 477(15). doi:10.1016/j.cam.2025.117184
apa: Wembe Moafo, B. E., Offen, C., Maslovskaya, S., Ober-Blöbaum, S., & Singh,
P. (n.d.). Commutator-free Cayley methods. J. Comput. Appl. Math, 477(15).
https://doi.org/10.1016/j.cam.2025.117184
bibtex: '@article{Wembe Moafo_Offen_Maslovskaya_Ober-Blöbaum_Singh, title={Commutator-free
Cayley methods}, volume={477}, DOI={10.1016/j.cam.2025.117184},
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} }'
chicago: Wembe Moafo, Boris Edgar, Cristian Offen, Sofya Maslovskaya, Sina Ober-Blöbaum,
and Pranav Singh. “Commutator-Free Cayley Methods.” J. Comput. Appl. Math
477, no. 15 (n.d.). https://doi.org/10.1016/j.cam.2025.117184.
ieee: 'B. E. Wembe Moafo, C. Offen, S. Maslovskaya, S. Ober-Blöbaum, and P. Singh,
“Commutator-free Cayley methods,” J. Comput. Appl. Math, vol. 477, no.
15, doi: 10.1016/j.cam.2025.117184.'
mla: Wembe Moafo, Boris Edgar, et al. “Commutator-Free Cayley Methods.” J. Comput.
Appl. Math, vol. 477, no. 15, doi:10.1016/j.cam.2025.117184.
short: B.E. Wembe Moafo, C. Offen, S. Maslovskaya, S. Ober-Blöbaum, P. Singh, J.
Comput. Appl. Math 477 (n.d.).
date_created: 2025-04-10T14:42:52Z
date_updated: 2025-12-16T15:17:27Z
department:
- _id: '94'
doi: 10.1016/j.cam.2025.117184
intvolume: ' 477'
issue: '15'
language:
- iso: eng
publication: J. Comput. Appl. Math
publication_status: submitted
status: public
title: Commutator-free Cayley methods
type: journal_article
user_id: '95394'
volume: 477
year: '2025'
...
---
_id: '59797'
author:
- first_name: Michael
full_name: Konopik, Michael
last_name: Konopik
- first_name: Rodrigo
full_name: T. Sato Martín de Almagro, Rodrigo
last_name: T. Sato Martín de Almagro
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Sigrid
full_name: Leyendecker, Sigrid
last_name: Leyendecker
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. Journal of Nonlinear Science. 2025;36(11).
doi:10.1007/s00332-025-10229-5
apa: Konopik, M., T. Sato Martín de Almagro, R., Maslovskaya, S., Ober-Blöbaum,
S., & Leyendecker, S. (2025). Variational integrators for a new Lagrangian
approach to control affine systems with a quadratic Lagrange term. Journal
of Nonlinear Science, 36(11). https://doi.org/10.1007/s00332-025-10229-5
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={10.1007/s00332-025-10229-5},
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} }'
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.”
Journal of Nonlinear Science 36, no. 11 (2025). https://doi.org/10.1007/s00332-025-10229-5.
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,” Journal of Nonlinear
Science, vol. 36, no. 11, 2025, doi: 10.1007/s00332-025-10229-5.'
mla: Konopik, Michael, et al. “Variational Integrators for a New Lagrangian Approach
to Control Affine Systems with a Quadratic Lagrange Term.” Journal of Nonlinear
Science, vol. 36, no. 11, 2025, doi:10.1007/s00332-025-10229-5.
short: M. Konopik, R. T. Sato Martín de Almagro, S. Maslovskaya, S. Ober-Blöbaum,
S. Leyendecker, Journal of Nonlinear Science 36 (2025).
date_created: 2025-05-05T09:35:31Z
date_updated: 2026-01-06T18:26:57Z
department:
- _id: '636'
doi: 10.1007/s00332-025-10229-5
intvolume: ' 36'
issue: '11'
language:
- iso: eng
publication: Journal of Nonlinear Science
status: public
title: Variational integrators for a new Lagrangian approach to control affine systems
with a quadratic Lagrange term
type: journal_article
user_id: '87909'
volume: 36
year: '2025'
...
---
_id: '59799'
author:
- first_name: Michael
full_name: Konopik, Michael
last_name: Konopik
- first_name: Sigrid
full_name: Leyendecker, Sigrid
last_name: Leyendecker
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Rodrigo
full_name: T. Sato Martín de Almagro, Rodrigo
last_name: T. Sato Martín de Almagro
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.
Nonlinearity. 2025;38(11). doi:10.1088/1361-6544/ae1d08
apa: Konopik, M., Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., & T. Sato
Martín de Almagro, R. (2025). A new Lagrangian approach to optimal control of
second-order systems. Nonlinearity, 38(11). https://doi.org/10.1088/1361-6544/ae1d08
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={10.1088/1361-6544/ae1d08},
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} }'
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.” Nonlinearity 38, no. 11 (2025). https://doi.org/10.1088/1361-6544/ae1d08.
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,” Nonlinearity, vol. 38, no. 11, 2025, doi: 10.1088/1361-6544/ae1d08.'
mla: Konopik, Michael, et al. “A New Lagrangian Approach to Optimal Control of Second-Order
Systems.” Nonlinearity, vol. 38, no. 11, 2025, doi:10.1088/1361-6544/ae1d08.
short: M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. Sato Martín
de Almagro, Nonlinearity 38 (2025).
date_created: 2025-05-05T09:37:50Z
date_updated: 2026-01-06T18:24:40Z
department:
- _id: '636'
doi: 10.1088/1361-6544/ae1d08
intvolume: ' 38'
issue: '11'
language:
- iso: eng
publication: Nonlinearity
status: public
title: A new Lagrangian approach to optimal control of second-order systems
type: journal_article
user_id: '87909'
volume: 38
year: '2025'
...
---
_id: '53101'
abstract:
- lang: eng
text: In this work, we consider optimal control problems for mechanical systems
with fixed initial and free final state and a quadratic Lagrange term. Specifically,
the dynamics is described by a second order ODE containing an affine control term.
Classically, Pontryagin's maximum principle gives necessary optimality conditions
for the optimal control problem. For smooth problems, alternatively, a variational
approach based on an augmented objective can be followed. Here, we propose a new
Lagrangian approach leading to equivalent necessary optimality conditions in the
form of Euler-Lagrange equations. Thus, the differential geometric structure (similar
to classical Lagrangian dynamics) can be exploited in the framework of optimal
control problems. In particular, the formulation enables the symplectic discretisation
of the optimal control problem via variational integrators in a straightforward
way.
article_type: original
author:
- first_name: Sigrid
full_name: Leyendecker, Sigrid
last_name: Leyendecker
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Rodrigo T. Sato Martín de
full_name: Almagro, Rodrigo T. Sato Martín de
last_name: Almagro
- first_name: Flóra Orsolya
full_name: Szemenyei, Flóra Orsolya
last_name: Szemenyei
citation:
ama: Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Almagro RTSM de, Szemenyei FO.
A new Lagrangian approach to control affine systems with a quadratic Lagrange
term. Journal of Computational Dynamics. 2024;0(0):0-0. doi:10.3934/jcd.2024017
apa: Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., Almagro, R. T. S. M. de,
& Szemenyei, F. O. (2024). A new Lagrangian approach to control affine systems
with a quadratic Lagrange term. Journal of Computational Dynamics, 0(0),
0–0. https://doi.org/10.3934/jcd.2024017
bibtex: '@article{Leyendecker_Maslovskaya_Ober-Blöbaum_Almagro_Szemenyei_2024, title={A
new Lagrangian approach to control affine systems with a quadratic Lagrange term},
volume={0}, DOI={10.3934/jcd.2024017},
number={0}, journal={Journal of Computational Dynamics}, publisher={American Institute
of Mathematical Sciences (AIMS)}, author={Leyendecker, Sigrid and Maslovskaya,
Sofya and Ober-Blöbaum, Sina and Almagro, Rodrigo T. Sato Martín de and Szemenyei,
Flóra Orsolya}, year={2024}, pages={0–0} }'
chicago: 'Leyendecker, Sigrid, Sofya Maslovskaya, Sina Ober-Blöbaum, Rodrigo T.
Sato Martín de Almagro, and Flóra Orsolya Szemenyei. “A New Lagrangian Approach
to Control Affine Systems with a Quadratic Lagrange Term.” Journal of Computational
Dynamics 0, no. 0 (2024): 0–0. https://doi.org/10.3934/jcd.2024017.'
ieee: 'S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. S. M. de Almagro,
and F. O. Szemenyei, “A new Lagrangian approach to control affine systems with
a quadratic Lagrange term,” Journal of Computational Dynamics, vol. 0,
no. 0, pp. 0–0, 2024, doi: 10.3934/jcd.2024017.'
mla: Leyendecker, Sigrid, et al. “A New Lagrangian Approach to Control Affine Systems
with a Quadratic Lagrange Term.” Journal of Computational Dynamics, vol.
0, no. 0, American Institute of Mathematical Sciences (AIMS), 2024, pp. 0–0, doi:10.3934/jcd.2024017.
short: S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T.S.M. de Almagro, F.O.
Szemenyei, Journal of Computational Dynamics 0 (2024) 0–0.
date_created: 2024-03-28T15:58:02Z
date_updated: 2024-03-28T16:07:34Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.3934/jcd.2024017
has_accepted_license: '1'
issue: '0'
keyword:
- Optimal control problem
- Lagrangian system
- Hamiltonian system
- Variations
- Pontryagin's maximum principle.
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.aimsciences.org/article/doi/10.3934/jcd.2024017
oa: '1'
page: 0-0
publication: Journal of Computational Dynamics
publication_identifier:
issn:
- 2158-2491
- 2158-2505
publication_status: published
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: A new Lagrangian approach to control affine systems with a quadratic Lagrange
term
type: journal_article
user_id: '87909'
volume: '0'
year: '2024'
...
---
_id: '46469'
abstract:
- lang: eng
text: 'We show how to learn discrete field theories from observational data of fields
on a space-time lattice. For this, we train a neural network model of a discrete
Lagrangian density such that the discrete Euler--Lagrange equations are consistent
with the given training data. We, thus, obtain a structure-preserving machine
learning architecture. Lagrangian densities are not uniquely defined by the solutions
of a field theory. We introduce a technique to derive regularisers for the training
process which optimise numerical regularity of the discrete field theory. Minimisation
of the regularisers guarantees that close to the training data the discrete field
theory behaves robust and efficient when used in numerical simulations. Further,
we show how to identify structurally simple solutions of the underlying continuous
field theory such as travelling waves. This is possible even when travelling waves
are not present in the training data. This is compared to data-driven model order
reduction based approaches, which struggle to identify suitable latent spaces
containing structurally simple solutions when these are not present in the training
data. Ideas are demonstrated on examples based on the wave equation and the Schrödinger
equation. '
article_number: '013104'
article_type: original
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: Offen C, Ober-Blöbaum S. Learning of discrete models of variational PDEs from
data. Chaos. 2024;34(1). doi:10.1063/5.0172287
apa: Offen, C., & Ober-Blöbaum, S. (2024). Learning of discrete models of variational
PDEs from data. Chaos, 34(1), Article 013104. https://doi.org/10.1063/5.0172287
bibtex: '@article{Offen_Ober-Blöbaum_2024, title={Learning of discrete models of
variational PDEs from data}, volume={34}, DOI={10.1063/5.0172287},
number={1013104}, journal={Chaos}, publisher={AIP Publishing}, author={Offen,
Christian and Ober-Blöbaum, Sina}, year={2024} }'
chicago: Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of
Variational PDEs from Data.” Chaos 34, no. 1 (2024). https://doi.org/10.1063/5.0172287.
ieee: 'C. Offen and S. Ober-Blöbaum, “Learning of discrete models of variational
PDEs from data,” Chaos, vol. 34, no. 1, Art. no. 013104, 2024, doi: 10.1063/5.0172287.'
mla: Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational
PDEs from Data.” Chaos, vol. 34, no. 1, 013104, AIP Publishing, 2024, doi:10.1063/5.0172287.
short: C. Offen, S. Ober-Blöbaum, Chaos 34 (2024).
date_created: 2023-08-10T08:24:48Z
date_updated: 2024-08-12T13:45:43Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1063/5.0172287
external_id:
arxiv:
- '2308.05082 '
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2024-01-09T10:48:38Z
date_updated: 2024-01-09T10:48:38Z
file_id: '50376'
file_name: Accepted manuscript with AIP banner CHA23-AR-01370.pdf
file_size: 13222105
relation: main_file
title: Accepted Manuscript Chaos
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2024-01-09T11:19:49Z
date_updated: 2024-01-09T11:19:49Z
description: |-
We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train
a neural network model of a discrete Lagrangian density such that the discrete Euler–Lagrange equations are consistent
with the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian
densities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for
the training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers
guarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical
simulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory
such as travelling waves. This is possible even when travelling waves are not present in the training data. This is
compared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces
containing structurally simple solutions when these are not present in the training data. Ideas are demonstrated on
examples based on the wave equation and the Schrödinger equation.
file_id: '50390'
file_name: LDensityPDE_AIP.pdf
file_size: 12960884
relation: main_file
title: Learning of discrete models of variational PDEs from data
file_date_updated: 2024-01-09T11:19:49Z
has_accepted_license: '1'
intvolume: ' 34'
issue: '1'
language:
- iso: eng
oa: '1'
project:
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Chaos
publication_identifier:
issn:
- 1054-1500
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Christian-Offen/DLNN_pde
status: public
title: Learning of discrete models of variational PDEs from data
type: journal_article
user_id: '85279'
volume: 34
year: '2024'
...
---
_id: '59791'
author:
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Maslovskaya S, Ober-Blöbaum S. Symplectic Methods in Deep Learning. In: IFAC-PapersOnLine.
Vol 58. Elsevier BV; 2024:85-90. doi:10.1016/j.ifacol.2024.10.118'
apa: Maslovskaya, S., & Ober-Blöbaum, S. (2024). Symplectic Methods in Deep
Learning. IFAC-PapersOnLine, 58(17), 85–90. https://doi.org/10.1016/j.ifacol.2024.10.118
bibtex: '@inproceedings{Maslovskaya_Ober-Blöbaum_2024, title={Symplectic Methods
in Deep Learning}, volume={58}, DOI={10.1016/j.ifacol.2024.10.118},
number={17}, booktitle={IFAC-PapersOnLine}, publisher={Elsevier BV}, author={Maslovskaya,
Sofya and Ober-Blöbaum, Sina}, year={2024}, pages={85–90} }'
chicago: Maslovskaya, Sofya, and Sina Ober-Blöbaum. “Symplectic Methods in Deep
Learning.” In IFAC-PapersOnLine, 58:85–90. Elsevier BV, 2024. https://doi.org/10.1016/j.ifacol.2024.10.118.
ieee: 'S. Maslovskaya and S. Ober-Blöbaum, “Symplectic Methods in Deep Learning,”
in IFAC-PapersOnLine, 2024, vol. 58, no. 17, pp. 85–90, doi: 10.1016/j.ifacol.2024.10.118.'
mla: Maslovskaya, Sofya, and Sina Ober-Blöbaum. “Symplectic Methods in Deep Learning.”
IFAC-PapersOnLine, vol. 58, no. 17, Elsevier BV, 2024, pp. 85–90, doi:10.1016/j.ifacol.2024.10.118.
short: 'S. Maslovskaya, S. Ober-Blöbaum, in: IFAC-PapersOnLine, Elsevier BV, 2024,
pp. 85–90.'
date_created: 2025-05-05T09:21:13Z
date_updated: 2025-05-05T09:22:27Z
department:
- _id: '636'
doi: 10.1016/j.ifacol.2024.10.118
intvolume: ' 58'
issue: '17'
language:
- iso: eng
page: 85-90
publication: IFAC-PapersOnLine
publication_identifier:
issn:
- 2405-8963
publication_status: published
publisher: Elsevier BV
status: public
title: Symplectic Methods in Deep Learning
type: conference
user_id: '87909'
volume: 58
year: '2024'
...
---
_id: '34135'
abstract:
- lang: eng
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.
author:
- first_name: Yana
full_name: Lishkova, Yana
last_name: Lishkova
- first_name: Paul
full_name: Scherer, Paul
last_name: Scherer
- first_name: Steffen
full_name: Ridderbusch, Steffen
last_name: Ridderbusch
- first_name: Mateja
full_name: Jamnik, Mateja
last_name: Jamnik
- first_name: Pietro
full_name: Liò, Pietro
last_name: Liò
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
citation:
ama: 'Lishkova Y, Scherer P, Ridderbusch S, et al. Discrete Lagrangian Neural Networks
with Automatic Symmetry Discovery. In: IFAC-PapersOnLine. Vol 56. Elsevier;
2023:3203-3210. doi:10.1016/j.ifacol.2023.10.1457'
apa: Lishkova, Y., Scherer, P., Ridderbusch, S., Jamnik, M., Liò, P., Ober-Blöbaum,
S., & Offen, C. (2023). Discrete Lagrangian Neural Networks with Automatic
Symmetry Discovery. IFAC-PapersOnLine, 56(2), 3203–3210. https://doi.org/10.1016/j.ifacol.2023.10.1457
bibtex: '@inproceedings{Lishkova_Scherer_Ridderbusch_Jamnik_Liò_Ober-Blöbaum_Offen_2023,
title={Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery},
volume={56}, DOI={10.1016/j.ifacol.2023.10.1457},
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} }'
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 IFAC-PapersOnLine, 56:3203–10. Elsevier,
2023. https://doi.org/10.1016/j.ifacol.2023.10.1457.
ieee: 'Y. Lishkova et al., “Discrete Lagrangian Neural Networks with Automatic
Symmetry Discovery,” in IFAC-PapersOnLine, Yokohama, Japan, 2023, vol.
56, no. 2, pp. 3203–3210, doi: 10.1016/j.ifacol.2023.10.1457.'
mla: Lishkova, Yana, et al. “Discrete Lagrangian Neural Networks with Automatic
Symmetry Discovery.” IFAC-PapersOnLine, vol. 56, no. 2, Elsevier, 2023,
pp. 3203–10, doi:10.1016/j.ifacol.2023.10.1457.
short: 'Y. Lishkova, P. Scherer, S. Ridderbusch, M. Jamnik, P. Liò, S. Ober-Blöbaum,
C. Offen, in: IFAC-PapersOnLine, Elsevier, 2023, pp. 3203–3210.'
conference:
end_date: 2023-07-14
location: ' Yokohama, Japan'
name: The 22nd World Congress of the International Federation of Automatic Control
start_date: 2023-07-09
date_created: 2022-11-23T08:17:10Z
date_updated: 2023-12-29T14:26:00Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1016/j.ifacol.2023.10.1457
external_id:
arxiv:
- '2211.10830'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2023-04-17T08:05:55Z
date_updated: 2023-04-17T08:05:55Z
description: |-
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, 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.
file_id: '44037'
file_name: LNN_project.pdf
file_size: 576115
relation: main_file
title: Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery
file_date_updated: 2023-04-17T08:05:55Z
has_accepted_license: '1'
intvolume: ' 56'
issue: '2'
language:
- iso: eng
main_file_link:
- url: https://www.sciencedirect.com/science/article/pii/S2405896323018657
oa: '1'
page: 3203-3210
publication: IFAC-PapersOnLine
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/yanalish/SymDLNN
status: public
title: Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery
type: conference
user_id: '85279'
volume: 56
year: '2023'
...
---
_id: '42163'
abstract:
- lang: eng
text: 'The article shows how to learn models of dynamical systems from data which
are governed by an unknown variational PDE. Rather than employing reduction techniques,
we learn a discrete field theory governed by a discrete Lagrangian density $L_d$
that is modelled as a neural network. Careful regularisation of the loss function
for training $L_d$ is necessary to obtain a field theory that is suitable for
numerical computations: we derive a regularisation term which optimises the solvability
of the discrete Euler--Lagrange equations. Secondly, we develop a method to find
solutions to machine learned discrete field theories which constitute travelling
waves of the underlying continuous PDE.'
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Offen C, Ober-Blöbaum S. Learning discrete Lagrangians for variational PDEs
from data and detection of travelling waves. In: Nielsen F, Barbaresco F, eds.
Geometric Science of Information. Vol 14071. Lecture Notes in Computer
Science (LNCS). Springer, Cham.; 2023:569-579. doi:10.1007/978-3-031-38271-0_57'
apa: Offen, C., & Ober-Blöbaum, S. (2023). Learning discrete Lagrangians for
variational PDEs from data and detection of travelling waves. In F. Nielsen &
F. Barbaresco (Eds.), Geometric Science of Information (Vol. 14071, pp.
569–579). Springer, Cham. https://doi.org/10.1007/978-3-031-38271-0_57
bibtex: '@inproceedings{Offen_Ober-Blöbaum_2023, series={Lecture Notes in Computer
Science (LNCS)}, title={Learning discrete Lagrangians for variational PDEs from
data and detection of travelling waves}, volume={14071}, DOI={10.1007/978-3-031-38271-0_57},
booktitle={Geometric Science of Information}, publisher={Springer, Cham.}, author={Offen,
Christian and Ober-Blöbaum, Sina}, editor={Nielsen, F and Barbaresco, F}, year={2023},
pages={569–579}, collection={Lecture Notes in Computer Science (LNCS)} }'
chicago: Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians
for Variational PDEs from Data and Detection of Travelling Waves.” In Geometric
Science of Information, edited by F Nielsen and F Barbaresco, 14071:569–79.
Lecture Notes in Computer Science (LNCS). Springer, Cham., 2023. https://doi.org/10.1007/978-3-031-38271-0_57.
ieee: 'C. Offen and S. Ober-Blöbaum, “Learning discrete Lagrangians for variational
PDEs from data and detection of travelling waves,” in Geometric Science of
Information, Saint-Malo, Palais du Grand Large, France, 2023, vol. 14071,
pp. 569–579, doi: 10.1007/978-3-031-38271-0_57.'
mla: Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for
Variational PDEs from Data and Detection of Travelling Waves.” Geometric Science
of Information, edited by F Nielsen and F Barbaresco, vol. 14071, Springer,
Cham., 2023, pp. 569–79, doi:10.1007/978-3-031-38271-0_57.
short: 'C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric
Science of Information, Springer, Cham., 2023, pp. 569–579.'
conference:
end_date: 2023-09-01
location: Saint-Malo, Palais du Grand Large, France
name: ' GSI''23 6th International Conference on Geometric Science of Information'
start_date: 2023-08-30
date_created: 2023-02-16T11:32:48Z
date_updated: 2024-08-12T13:46:29Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1007/978-3-031-38271-0_57
editor:
- first_name: F
full_name: Nielsen, F
last_name: Nielsen
- first_name: F
full_name: Barbaresco, F
last_name: Barbaresco
external_id:
arxiv:
- '2302.08232 '
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2023-08-02T12:04:17Z
date_updated: 2023-08-02T12:04:17Z
description: |-
The article shows how to learn models of dynamical systems
from data which are governed by an unknown variational PDE. Rather
than employing reduction techniques, we learn a discrete field theory
governed by a discrete Lagrangian density Ld that is modelled as a neural network. Careful regularisation of the loss function for training Ld is
necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of
the discrete Euler–Lagrange equations. Secondly, we develop a method to
find solutions to machine learned discrete field theories which constitute
travelling waves of the underlying continuous PDE.
file_id: '46273'
file_name: LDensityLearning.pdf
file_size: 1938962
relation: main_file
title: Learning discrete Lagrangians for variational PDEs from data and detection
of travelling waves
file_date_updated: 2023-08-02T12:04:17Z
has_accepted_license: '1'
intvolume: ' 14071'
keyword:
- System identification
- discrete Lagrangians
- travelling waves
language:
- iso: eng
oa: '1'
page: 569-579
project:
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Geometric Science of Information
publication_identifier:
eisbn:
- 978-3-031-38271-0
publication_status: published
publisher: Springer, Cham.
quality_controlled: '1'
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Christian-Offen/LagrangianDensityML
series_title: Lecture Notes in Computer Science (LNCS)
status: public
title: Learning discrete Lagrangians for variational PDEs from data and detection
of travelling waves
type: conference
user_id: '85279'
volume: 14071
year: '2023'
...
---
_id: '29240'
abstract:
- lang: eng
text: "The principle of least action is one of the most fundamental physical principle.
It says that among all possible motions connecting two points in a phase space,
the system will exhibit those motions which extremise an action functional. Many
qualitative features of dynamical systems, such as the presence of conservation
laws and energy balance equations, are related to the existence of an action functional.
Incorporating variational structure into learning algorithms for dynamical systems
is, therefore, crucial in order to make sure that the learned model shares important
features with the exact physical system. In this paper we show how to incorporate
variational principles into trajectory predictions of learned dynamical systems.
The novelty of this work is that (1) our technique relies only on discrete position
data of observed trajectories. Velocities or conjugate momenta do not need to
be observed or approximated and no prior knowledge about the form of the variational
principle is assumed. Instead, they are recovered using backward error analysis.
(2) Moreover, our technique compensates discretisation errors when trajectories
are computed from the learned system. This is important when moderate to large
step-sizes are used and high accuracy is required. For this,\r\nwe introduce and
rigorously analyse the concept of inverse modified Lagrangians by developing an
inverse version of variational backward error analysis. (3) Finally, we introduce
a method to perform system identification from position observations only, based
on variational backward error analysis."
article_type: original
author:
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
citation:
ama: Ober-Blöbaum S, Offen C. Variational Learning of Euler–Lagrange Dynamics from
Data. Journal of Computational and Applied Mathematics. 2023;421:114780.
doi:10.1016/j.cam.2022.114780
apa: Ober-Blöbaum, S., & Offen, C. (2023). Variational Learning of Euler–Lagrange
Dynamics from Data. Journal of Computational and Applied Mathematics, 421,
114780. https://doi.org/10.1016/j.cam.2022.114780
bibtex: '@article{Ober-Blöbaum_Offen_2023, title={Variational Learning of Euler–Lagrange
Dynamics from Data}, volume={421}, DOI={10.1016/j.cam.2022.114780},
journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier},
author={Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={114780}
}'
chicago: 'Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange
Dynamics from Data.” Journal of Computational and Applied Mathematics 421
(2023): 114780. https://doi.org/10.1016/j.cam.2022.114780.'
ieee: 'S. Ober-Blöbaum and C. Offen, “Variational Learning of Euler–Lagrange Dynamics
from Data,” Journal of Computational and Applied Mathematics, vol. 421,
p. 114780, 2023, doi: 10.1016/j.cam.2022.114780.'
mla: Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange
Dynamics from Data.” Journal of Computational and Applied Mathematics,
vol. 421, Elsevier, 2023, p. 114780, doi:10.1016/j.cam.2022.114780.
short: S. Ober-Blöbaum, C. Offen, Journal of Computational and Applied Mathematics
421 (2023) 114780.
date_created: 2022-01-11T13:24:00Z
date_updated: 2023-08-10T08:42:39Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1016/j.cam.2022.114780
external_id:
arxiv:
- '2112.12619'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2022-06-28T15:25:50Z
date_updated: 2022-06-28T15:25:50Z
description: |-
The principle of least action is one of the most fundamental physical principle. It says that among all possible motions
connecting two points in a phase space, the system will exhibit those motions which extremise an action functional.
Many qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equa-
tions, are related to the existence of an action functional. Incorporating variational structure into learning algorithms
for dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features
with the exact physical system. In this paper we show how to incorporate variational principles into trajectory predic-
tions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position
data of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no
prior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward
error analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the
learned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,
we introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of
variational backward error analysis. (3) Finally, we introduce a method to perform system identification from position
observations only, based on variational backward error analysis.
file_id: '32274'
file_name: ShadowLagrangian_revision1_journal_style_arxiv.pdf
file_size: 3640770
relation: main_file
title: Variational Learning of Euler–Lagrange Dynamics from Data
file_date_updated: 2022-06-28T15:25:50Z
has_accepted_license: '1'
intvolume: ' 421'
keyword:
- Lagrangian learning
- variational backward error analysis
- modified Lagrangian
- variational integrators
- physics informed learning
language:
- iso: eng
oa: '1'
page: '114780'
publication: Journal of Computational and Applied Mathematics
publication_identifier:
issn:
- 0377-0427
publication_status: epub_ahead
publisher: Elsevier
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/Christian-Offen/LagrangianShadowIntegration
status: public
title: Variational Learning of Euler–Lagrange Dynamics from Data
type: journal_article
user_id: '85279'
volume: 421
year: '2023'
...
---
_id: '37654'
abstract:
- lang: eng
text: "Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate
prior physical knowledge when\r\nlearning the dynamical equations of Hamiltonian
systems. Hereby, the symplectic system structure is preserved despite\r\nthe data-driven
modeling approach. However, preserving symmetries requires additional attention.
In this research, we\r\nenhance the HNN with a Lie algebra framework to detect
and embed symmetries in the neural network. This approach\r\nallows to simultaneously
learn the symmetry group action and the total energy of the system. As illustrating
examples,\r\na pendulum on a cart and a two-body problem from astrodynamics are
considered."
article_number: '063115'
article_type: original
author:
- first_name: Eva
full_name: Dierkes, Eva
last_name: Dierkes
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
citation:
ama: Dierkes E, Offen C, Ober-Blöbaum S, Flaßkamp K. Hamiltonian Neural Networks
with Automatic Symmetry Detection. Chaos. 2023;33(6). doi:10.1063/5.0142969
apa: Dierkes, E., Offen, C., Ober-Blöbaum, S., & Flaßkamp, K. (2023). Hamiltonian
Neural Networks with Automatic Symmetry Detection. Chaos, 33(6),
Article 063115. https://doi.org/10.1063/5.0142969
bibtex: '@article{Dierkes_Offen_Ober-Blöbaum_Flaßkamp_2023, title={Hamiltonian Neural
Networks with Automatic Symmetry Detection}, volume={33}, DOI={10.1063/5.0142969},
number={6063115}, journal={Chaos}, publisher={AIP Publishing}, author={Dierkes,
Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}, year={2023}
}'
chicago: Dierkes, Eva, Christian Offen, Sina Ober-Blöbaum, and Kathrin Flaßkamp.
“Hamiltonian Neural Networks with Automatic Symmetry Detection.” Chaos
33, no. 6 (2023). https://doi.org/10.1063/5.0142969.
ieee: 'E. Dierkes, C. Offen, S. Ober-Blöbaum, and K. Flaßkamp, “Hamiltonian Neural
Networks with Automatic Symmetry Detection,” Chaos, vol. 33, no. 6, Art.
no. 063115, 2023, doi: 10.1063/5.0142969.'
mla: Dierkes, Eva, et al. “Hamiltonian Neural Networks with Automatic Symmetry Detection.”
Chaos, vol. 33, no. 6, 063115, AIP Publishing, 2023, doi:10.1063/5.0142969.
short: E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023).
date_created: 2023-01-20T09:10:06Z
date_updated: 2023-08-10T08:37:01Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1063/5.0142969
external_id:
arxiv:
- '2301.07928'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2023-04-26T16:20:56Z
date_updated: 2023-04-26T16:20:56Z
description: |-
Incorporating physical system knowledge into data-driven
system identification has been shown to be beneficial. The
approach presented in this article combines learning of an
energy-conserving model from data with detecting a Lie
group representation of the unknown system symmetry.
The proposed approach can improve the learned model
and reveal underlying symmetry simultaneously.
file_id: '44205'
file_name: JournalPaper_main.pdf
file_size: 5200111
relation: main_file
title: Hamiltonian Neural Networks with Automatic Symmetry Detection
file_date_updated: 2023-04-26T16:20:56Z
has_accepted_license: '1'
intvolume: ' 33'
issue: '6'
language:
- iso: eng
oa: '1'
publication: Chaos
publication_identifier:
issn:
- 1054-1500
publication_status: published
publisher: AIP Publishing
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/eva-dierkes/HNN_withSymmetries
status: public
title: Hamiltonian Neural Networks with Automatic Symmetry Detection
type: journal_article
user_id: '85279'
volume: 33
year: '2023'
...
---
_id: '21600'
abstract:
- lang: eng
text: Many problems in science and engineering require an efficient numerical approximation
of integrals or solutions to differential equations. For systems with rapidly
changing dynamics, an equidistant discretization is often inadvisable as it results
in prohibitively large errors or computational effort. To this end, adaptive schemes,
such as solvers based on Runge–Kutta pairs, have been developed which adapt the
step size based on local error estimations at each step. While the classical schemes
apply very generally and are highly efficient on regular systems, they can behave
suboptimally when an inefficient step rejection mechanism is triggered by structurally
complex systems such as chaotic systems. To overcome these issues, we propose
a method to tailor numerical schemes to the problem class at hand. This is achieved
by combining simple, classical quadrature rules or ODE solvers with data-driven
time-stepping controllers. Compared with learning solution operators to ODEs directly,
it generalizes better to unseen initial data as our approach employs classical
numerical schemes as base methods. At the same time it can make use of identified
structures of a problem class and, therefore, outperforms state-of-the-art adaptive
schemes. Several examples demonstrate superior efficiency. Source code is available
at https://github.com/lueckem/quadrature-ML.
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Eyke
full_name: Hüllermeier, Eyke
id: '48129'
last_name: Hüllermeier
- first_name: Marvin
full_name: Lücke, Marvin
last_name: Lücke
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Karlson
full_name: Pfannschmidt, Karlson
id: '13472'
last_name: Pfannschmidt
orcid: 0000-0001-9407-7903
citation:
ama: Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical
integration using reinforcement learning. SIAM Journal on Scientific Computing.
2023;45(2):A579-A595. doi:10.1137/21M1412682
apa: Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz,
S., & Pfannschmidt, K. (2023). Efficient time stepping for numerical integration
using reinforcement learning. SIAM Journal on Scientific Computing, 45(2),
A579–A595. https://doi.org/10.1137/21M1412682
bibtex: '@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023,
title={Efficient time stepping for numerical integration using reinforcement
learning}, volume={45}, DOI={10.1137/21M1412682},
number={2}, journal={SIAM Journal on Scientific Computing}, author={Dellnitz,
Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen,
Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, year={2023}, pages={A579–A595}
}'
chicago: 'Dellnitz, Michael, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum,
Christian Offen, Sebastian Peitz, and Karlson Pfannschmidt. “Efficient Time Stepping
for Numerical Integration Using Reinforcement Learning.” SIAM Journal on Scientific
Computing 45, no. 2 (2023): A579–95. https://doi.org/10.1137/21M1412682.'
ieee: 'M. Dellnitz et al., “Efficient time stepping for numerical integration
using reinforcement learning,” SIAM Journal on Scientific Computing, vol.
45, no. 2, pp. A579–A595, 2023, doi: 10.1137/21M1412682.'
mla: Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration
Using Reinforcement Learning.” SIAM Journal on Scientific Computing, vol.
45, no. 2, 2023, pp. A579–95, doi:10.1137/21M1412682.
short: M. Dellnitz, E. Hüllermeier, M. Lücke, S. Ober-Blöbaum, C. Offen, S. Peitz,
K. Pfannschmidt, SIAM Journal on Scientific Computing 45 (2023) A579–A595.
date_created: 2021-04-09T07:59:19Z
date_updated: 2023-08-25T09:24:50Z
ddc:
- '510'
department:
- _id: '101'
- _id: '636'
- _id: '355'
- _id: '655'
doi: 10.1137/21M1412682
external_id:
arxiv:
- arXiv:2104.03562
has_accepted_license: '1'
intvolume: ' 45'
issue: '2'
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/reader/10.1137/21M1412682
page: A579-A595
publication: SIAM Journal on Scientific Computing
publication_status: published
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/lueckem/quadrature-ML
status: public
title: Efficient time stepping for numerical integration using reinforcement learning
type: journal_article
user_id: '47427'
volume: 45
year: '2023'
...
---
_id: '47147'
alternative_title:
- GAMM Rundbriefe
author:
- first_name: Yana
full_name: Lishkova, Yana
last_name: Lishkova
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Sigrid
full_name: Leyendecker, Sigrid
last_name: Leyendecker
citation:
ama: Lishkova Y, Ober-Blöbaum S, Leyendecker S. Multirate Discrete Mechanics
and Optimal Control for a Flexible Satelite Model . Invited Mathematical Magazine
Article; 2023.
apa: Lishkova, Y., Ober-Blöbaum, S., & Leyendecker, S. (2023). Multirate
Discrete Mechanics and Optimal Control for a Flexible Satelite Model . Invited
Mathematical Magazine Article.
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} }'
chicago: Lishkova, Yana, Sina Ober-Blöbaum, and Sigrid Leyendecker. Multirate
Discrete Mechanics and Optimal Control for a Flexible Satelite Model . Invited
Mathematical Magazine Article, 2023.
ieee: Y. Lishkova, S. Ober-Blöbaum, and S. Leyendecker, Multirate Discrete Mechanics
and Optimal Control for a Flexible Satelite Model . Invited Mathematical Magazine
Article, 2023.
mla: Lishkova, Yana, et al. Multirate Discrete Mechanics and Optimal Control
for a Flexible Satelite Model . Invited Mathematical Magazine Article, 2023.
short: Y. Lishkova, S. Ober-Blöbaum, S. Leyendecker, Multirate Discrete Mechanics
and Optimal Control for a Flexible Satelite Model , Invited Mathematical Magazine
Article, 2023.
date_created: 2023-09-21T07:20:43Z
date_updated: 2023-09-21T07:27:15Z
language:
- iso: eng
publisher: Invited Mathematical Magazine Article
status: public
title: 'Multirate Discrete Mechanics and Optimal Control for a Flexible Satelite Model '
type: report
user_id: '15694'
year: '2023'
...
---
_id: '47148'
author:
- first_name: Y.
full_name: Lishkova, Y.
last_name: Lishkova
- first_name: M.
full_name: Bando, M.
last_name: Bando
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
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.'
apa: Lishkova, Y., Bando, M., & Ober-Blöbaum, S. (2023). Variational approach
for modelling and optimal control of electrodynamic tether motion.
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} }'
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.
mla: Lishkova, Y., et al. Variational Approach for Modelling and Optimal Control
of Electrodynamic Tether Motion. 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.'
date_created: 2023-09-21T07:25:40Z
date_updated: 2023-09-21T07:27:21Z
language:
- iso: eng
publisher: Accepted for the 74th International Astronautical Concress (IAC)
status: public
title: Variational approach for modelling and optimal control of electrodynamic tether
motion
type: conference
user_id: '15694'
year: '2023'
...
---
_id: '30490'
author:
- first_name: Jacky
full_name: Cresson, Jacky
last_name: Cresson
- first_name: Fernando
full_name: Jiménez, Fernando
last_name: Jiménez
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: Cresson J, Jiménez F, Ober-Blöbaum S. Continuous and discrete Noether’s fractional
conserved quantities for restricted calculus of variations. AIMS. 2022;14(1):57-89.
apa: Cresson, J., Jiménez, F., & Ober-Blöbaum, S. (2022). Continuous and discrete
Noether’s fractional conserved quantities for restricted calculus of variations.
AIMS, 14(1), 57–89.
bibtex: '@article{Cresson_Jiménez_Ober-Blöbaum_2022, title={Continuous and discrete
Noether’s fractional conserved quantities for restricted calculus of variations},
volume={14(1)}, journal={AIMS}, author={Cresson, Jacky and Jiménez, Fernando and
Ober-Blöbaum, Sina}, year={2022}, pages={57–89} }'
chicago: 'Cresson, Jacky, Fernando Jiménez, and Sina Ober-Blöbaum. “Continuous and
Discrete Noether’s Fractional Conserved Quantities for Restricted Calculus of
Variations.” AIMS 14(1) (2022): 57–89.'
ieee: J. Cresson, F. Jiménez, and S. Ober-Blöbaum, “Continuous and discrete Noether’s
fractional conserved quantities for restricted calculus of variations,” AIMS,
vol. 14(1), pp. 57–89, 2022.
mla: Cresson, Jacky, et al. “Continuous and Discrete Noether’s Fractional Conserved
Quantities for Restricted Calculus of Variations.” AIMS, vol. 14(1), 2022,
pp. 57–89.
short: J. Cresson, F. Jiménez, S. Ober-Blöbaum, AIMS 14(1) (2022) 57–89.
date_created: 2022-03-24T12:26:10Z
date_updated: 2022-03-24T12:26:32Z
department:
- _id: '636'
language:
- iso: eng
page: 57-89
publication: AIMS
status: public
title: Continuous and discrete Noether's fractional conserved quantities for restricted
calculus of variations
type: journal_article
user_id: '15694'
volume: 14(1)
year: '2022'
...