---
_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: '55159'
abstract:
- lang: eng
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."
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
citation:
ama: Offen C. Machine learning of discrete field theories with guaranteed convergence
and uncertainty quantification.
apa: Offen, C. (n.d.). Machine learning of discrete field theories with guaranteed
convergence and uncertainty quantification.
bibtex: '@article{Offen, title={Machine learning of discrete field theories with
guaranteed convergence and uncertainty quantification}, author={Offen, Christian}
}'
chicago: Offen, Christian. “Machine Learning of Discrete Field Theories with Guaranteed
Convergence and Uncertainty Quantification,” n.d.
ieee: C. Offen, “Machine learning of discrete field theories with guaranteed convergence
and uncertainty quantification.” .
mla: Offen, Christian. Machine Learning of Discrete Field Theories with Guaranteed
Convergence and Uncertainty Quantification.
short: C. Offen, (n.d.).
date_created: 2024-07-10T13:43:50Z
date_updated: 2024-08-12T13:43:32Z
ddc:
- '510'
department:
- _id: '636'
external_id:
arxiv:
- '2407.07642'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2024-07-10T13:39:32Z
date_updated: 2024-07-10T13:39:32Z
description: |-
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.
Moreover, 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.
The 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.
file_id: '55160'
file_name: L_Collocation.pdf
file_size: 4569314
relation: main_file
title: Machine learning of discrete field theories with guaranteed convergence and
uncertainty quantification
file_date_updated: 2024-07-10T13:39:32Z
has_accepted_license: '1'
keyword:
- System identification
- inverse problem of variational calculus
- Gaussian process
- Lagrangian learning
- physics informed machine learning
- geometry aware learning
language:
- iso: eng
oa: '1'
page: '28'
project:
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication_status: submitted
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Christian-Offen/Lagrangian_GP_PDE
status: public
title: Machine learning of discrete field theories with guaranteed convergence and
uncertainty quantification
type: preprint
user_id: '85279'
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: '59801'
author:
- first_name: Frédéric
full_name: Jean, Frédéric
last_name: Jean
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
citation:
ama: Jean F, Maslovskaya S. Inverse optimal control problem in the non autonomous
linear-quadratic case. Published online 2024.
apa: Jean, F., & Maslovskaya, S. (2024). Inverse optimal control problem
in the non autonomous linear-quadratic case.
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} }'
chicago: Jean, Frédéric, and Sofya Maslovskaya. “Inverse Optimal Control Problem
in the Non Autonomous Linear-Quadratic Case,” 2024.
ieee: F. Jean and S. Maslovskaya, “Inverse optimal control problem in the non autonomous
linear-quadratic case.” 2024.
mla: Jean, Frédéric, and Sofya Maslovskaya. Inverse Optimal Control Problem in
the Non Autonomous Linear-Quadratic Case. 2024.
short: F. Jean, S. Maslovskaya, (2024).
date_created: 2025-05-05T09:42:19Z
date_updated: 2025-05-05T09:43:05Z
department:
- _id: '636'
language:
- iso: eng
status: public
title: Inverse optimal control problem in the non autonomous linear-quadratic case
type: preprint
user_id: '87909'
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: '29236'
abstract:
- lang: eng
text: The numerical solution of an ordinary differential equation can be interpreted
as the exact solution of a nearby modified equation. Investigating the behaviour
of numerical solutions by analysing the modified equation is known as backward
error analysis. If the original and modified equation share structural properties,
then the exact and approximate solution share geometric features such as the existence
of conserved quantities. Conjugate symplectic methods preserve a modified symplectic
form and a modified Hamiltonian when applied to a Hamiltonian system. We show
how a blended version of variational and symplectic techniques can be used to
compute modified symplectic and Hamiltonian structures. In contrast to other approaches,
our backward error analysis method does not rely on an ansatz but computes the
structures systematically, provided that a variational formulation of the method
is known. The technique is illustrated on the example of symmetric linear multistep
methods with matrix coefficients.
article_type: original
author:
- first_name: Robert
full_name: McLachlan, Robert
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
citation:
ama: McLachlan R, Offen C. Backward error analysis for conjugate symplectic methods.
Journal of Geometric Mechanics. 2023;15(1):98-115. doi:10.3934/jgm.2023005
apa: McLachlan, R., & Offen, C. (2023). Backward error analysis for conjugate
symplectic methods. Journal of Geometric Mechanics, 15(1), 98–115.
https://doi.org/10.3934/jgm.2023005
bibtex: '@article{McLachlan_Offen_2023, title={Backward error analysis for conjugate
symplectic methods}, volume={15}, DOI={10.3934/jgm.2023005},
number={1}, journal={Journal of Geometric Mechanics}, publisher={AIMS Press},
author={McLachlan, Robert and Offen, Christian}, year={2023}, pages={98–115} }'
chicago: 'McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate
Symplectic Methods.” Journal of Geometric Mechanics 15, no. 1 (2023): 98–115.
https://doi.org/10.3934/jgm.2023005.'
ieee: 'R. McLachlan and C. Offen, “Backward error analysis for conjugate symplectic
methods,” Journal of Geometric Mechanics, vol. 15, no. 1, pp. 98–115, 2023,
doi: 10.3934/jgm.2023005.'
mla: McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate
Symplectic Methods.” Journal of Geometric Mechanics, vol. 15, no. 1, AIMS
Press, 2023, pp. 98–115, doi:10.3934/jgm.2023005.
short: R. McLachlan, C. Offen, Journal of Geometric Mechanics 15 (2023) 98–115.
date_created: 2022-01-11T12:48:39Z
date_updated: 2023-08-10T08:40:30Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.3934/jgm.2023005
external_id:
arxiv:
- '2201.03911'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2022-08-12T16:48:59Z
date_updated: 2022-08-12T16:48:59Z
description: The numerical solution of an ordinary differential equation can be
interpreted as the exact solution of a nearby modified equation. Investigating
the behaviour of numerical solutions by analysing the modified equation is known
as backward error analysis. If the original and modified equation share structural
properties, then the exact and approximate solution share geometric features such
as the existence of conserved quantities. Conjugate symplectic methods preserve
a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian
system. We show how a blended version of variational and symplectic techniques
can be used to compute modified symplectic and Hamiltonian structures. In contrast
to other approaches, our backward error analysis method does not rely on an ansatz
but computes the structures systematically, provided that a variational formulation
of the method is known. The technique is illustrated on the example of symmetric
linear multistep methods with matrix coefficients.
file_id: '32801'
file_name: BEA_MultiStep_Matrix.pdf
file_size: 827030
relation: main_file
title: Backward error analysis for conjugate symplectic methods
file_date_updated: 2022-08-12T16:48:59Z
has_accepted_license: '1'
intvolume: ' 15'
issue: '1'
keyword:
- variational integrators
- backward error analysis
- Euler--Lagrange equations
- multistep methods
- conjugate symplectic methods
language:
- iso: eng
oa: '1'
page: 98-115
publication: Journal of Geometric Mechanics
publication_status: published
publisher: AIMS Press
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/Christian-Offen/BEAConjugateSymplectic
status: public
title: Backward error analysis for conjugate symplectic methods
type: journal_article
user_id: '85279'
volume: 15
year: '2023'
...
---
_id: '37654'
abstract:
- lang: eng
text: "Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate
prior physical knowledge when\r\nlearning the dynamical equations of Hamiltonian
systems. Hereby, the symplectic system structure is preserved despite\r\nthe data-driven
modeling approach. However, preserving symmetries requires additional attention.
In this research, we\r\nenhance the HNN with a Lie algebra framework to detect
and embed symmetries in the neural network. This approach\r\nallows to simultaneously
learn the symmetry group action and the total energy of the system. As illustrating
examples,\r\na pendulum on a cart and a two-body problem from astrodynamics are
considered."
article_number: '063115'
article_type: original
author:
- first_name: Eva
full_name: Dierkes, Eva
last_name: Dierkes
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
citation:
ama: Dierkes E, Offen C, Ober-Blöbaum S, Flaßkamp K. Hamiltonian Neural Networks
with Automatic Symmetry Detection. Chaos. 2023;33(6). doi:10.1063/5.0142969
apa: Dierkes, E., Offen, C., Ober-Blöbaum, S., & Flaßkamp, K. (2023). Hamiltonian
Neural Networks with Automatic Symmetry Detection. Chaos, 33(6),
Article 063115. https://doi.org/10.1063/5.0142969
bibtex: '@article{Dierkes_Offen_Ober-Blöbaum_Flaßkamp_2023, title={Hamiltonian Neural
Networks with Automatic Symmetry Detection}, volume={33}, DOI={10.1063/5.0142969},
number={6063115}, journal={Chaos}, publisher={AIP Publishing}, author={Dierkes,
Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}, year={2023}
}'
chicago: Dierkes, Eva, Christian Offen, Sina Ober-Blöbaum, and Kathrin Flaßkamp.
“Hamiltonian Neural Networks with Automatic Symmetry Detection.” Chaos
33, no. 6 (2023). https://doi.org/10.1063/5.0142969.
ieee: 'E. Dierkes, C. Offen, S. Ober-Blöbaum, and K. Flaßkamp, “Hamiltonian Neural
Networks with Automatic Symmetry Detection,” Chaos, vol. 33, no. 6, Art.
no. 063115, 2023, doi: 10.1063/5.0142969.'
mla: Dierkes, Eva, et al. “Hamiltonian Neural Networks with Automatic Symmetry Detection.”
Chaos, vol. 33, no. 6, 063115, AIP Publishing, 2023, doi:10.1063/5.0142969.
short: E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023).
date_created: 2023-01-20T09:10:06Z
date_updated: 2023-08-10T08:37:01Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1063/5.0142969
external_id:
arxiv:
- '2301.07928'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2023-04-26T16:20:56Z
date_updated: 2023-04-26T16:20:56Z
description: |-
Incorporating physical system knowledge into data-driven
system identification has been shown to be beneficial. The
approach presented in this article combines learning of an
energy-conserving model from data with detecting a Lie
group representation of the unknown system symmetry.
The proposed approach can improve the learned model
and reveal underlying symmetry simultaneously.
file_id: '44205'
file_name: JournalPaper_main.pdf
file_size: 5200111
relation: main_file
title: Hamiltonian Neural Networks with Automatic Symmetry Detection
file_date_updated: 2023-04-26T16:20:56Z
has_accepted_license: '1'
intvolume: ' 33'
issue: '6'
language:
- iso: eng
oa: '1'
publication: Chaos
publication_identifier:
issn:
- 1054-1500
publication_status: published
publisher: AIP Publishing
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/eva-dierkes/HNN_withSymmetries
status: public
title: Hamiltonian Neural Networks with Automatic Symmetry Detection
type: journal_article
user_id: '85279'
volume: 33
year: '2023'
...
---
_id: '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: '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'
...
---
_id: '30861'
abstract:
- lang: eng
text: AbstractWe consider the problem of maximization
of metabolite production in bacterial cells formulated as a dynamical optimal
control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions
are concatenations of singular and bang arcs and exhibit the chattering or Fuller
phenomenon, which is problematic for applications. To avoid chattering, we introduce
a reduced model which is still biologically relevant and retains the important
structural features of the original problem. Using a combination of analytical
and numerical methods, we show that the singular arc is dominant in the studied
DOCPs and exhibits the turnpike property. This property
is further used in order to design simple and realistic suboptimal control strategies.
author:
- first_name: Jean-Baptiste
full_name: Caillau, Jean-Baptiste
last_name: Caillau
- first_name: Walid
full_name: Djema, Walid
last_name: Djema
- first_name: Jean-Luc
full_name: Gouzé, Jean-Luc
last_name: Gouzé
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Jean-Baptiste
full_name: Pomet, Jean-Baptiste
last_name: Pomet
citation:
ama: Caillau J-B, Djema W, Gouzé J-L, Maslovskaya S, Pomet J-B. Turnpike Property
in Optimal Microbial Metabolite Production. Journal of Optimization Theory
and Applications. Published online 2022. doi:10.1007/s10957-022-02023-0
apa: Caillau, J.-B., Djema, W., Gouzé, J.-L., Maslovskaya, S., & Pomet, J.-B.
(2022). Turnpike Property in Optimal Microbial Metabolite Production. Journal
of Optimization Theory and Applications. https://doi.org/10.1007/s10957-022-02023-0
bibtex: '@article{Caillau_Djema_Gouzé_Maslovskaya_Pomet_2022, title={Turnpike Property
in Optimal Microbial Metabolite Production}, DOI={10.1007/s10957-022-02023-0},
journal={Journal of Optimization Theory and Applications}, publisher={Springer
Science and Business Media LLC}, author={Caillau, Jean-Baptiste and Djema, Walid
and Gouzé, Jean-Luc and Maslovskaya, Sofya and Pomet, Jean-Baptiste}, year={2022}
}'
chicago: Caillau, Jean-Baptiste, Walid Djema, Jean-Luc Gouzé, Sofya Maslovskaya,
and Jean-Baptiste Pomet. “Turnpike Property in Optimal Microbial Metabolite Production.”
Journal of Optimization Theory and Applications, 2022. https://doi.org/10.1007/s10957-022-02023-0.
ieee: 'J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, and J.-B. Pomet, “Turnpike
Property in Optimal Microbial Metabolite Production,” Journal of Optimization
Theory and Applications, 2022, doi: 10.1007/s10957-022-02023-0.'
mla: Caillau, Jean-Baptiste, et al. “Turnpike Property in Optimal Microbial Metabolite
Production.” Journal of Optimization Theory and Applications, Springer
Science and Business Media LLC, 2022, doi:10.1007/s10957-022-02023-0.
short: J.-B. Caillau, W. Djema, J.-L. Gouzé, S. Maslovskaya, J.-B. Pomet, Journal
of Optimization Theory and Applications (2022).
date_created: 2022-04-08T17:23:13Z
date_updated: 2022-04-08T18:23:02Z
department:
- _id: '636'
doi: 10.1007/s10957-022-02023-0
keyword:
- Applied Mathematics
- Management Science and Operations Research
- Control and Optimization
language:
- iso: eng
publication: Journal of Optimization Theory and Applications
publication_identifier:
issn:
- 0022-3239
- 1573-2878
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Turnpike Property in Optimal Microbial Metabolite Production
type: journal_article
user_id: '87909'
year: '2022'
...
---
_id: '30733'
abstract:
- lang: eng
text: Hamilton-Jacobi reachability methods for safety-critical control have been
well studied, but the safety guarantees derived rely on the accuracy of the numerical
computation. Thus, it is crucial to understand and account for any inaccuracies
that occur due to uncertainty in the underlying dynamics and environment as well
as the induced numerical errors. To this end, we propose a framework for modeling
the error of the value function inherent in Hamilton-Jacobi reachability using
a Gaussian process. The derived safety controller can be used in conjuncture with
arbitrary controllers to provide a safe hybrid control law. The marginal likelihood
of the Gaussian process then provides a confidence metric used to determine switches
between a least restrictive controller and a safety controller. We test both the
prediction as well as the correction capabilities of the presented method in a
classical pursuit-evasion example.
author:
- first_name: Nikolaus
full_name: Vertovec, Nikolaus
id: '93930'
last_name: Vertovec
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Kostas
full_name: Margellos, Kostas
last_name: Margellos
citation:
ama: 'Vertovec N, Ober-Blöbaum S, Margellos K. Verification of safety critical control
policies using kernel methods. In: ; 2022:1870-1875.'
apa: Vertovec, N., Ober-Blöbaum, S., & Margellos, K. (2022). Verification
of safety critical control policies using kernel methods. 1870–1875.
bibtex: '@inproceedings{Vertovec_Ober-Blöbaum_Margellos_2022, title={Verification
of safety critical control policies using kernel methods}, author={Vertovec, Nikolaus
and Ober-Blöbaum, Sina and Margellos, Kostas}, year={2022}, pages={1870–1875}
}'
chicago: Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Verification
of Safety Critical Control Policies Using Kernel Methods,” 1870–75, 2022.
ieee: N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Verification of safety critical
control policies using kernel methods,” London, 2022, pp. 1870–1875.
mla: Vertovec, Nikolaus, et al. Verification of Safety Critical Control Policies
Using Kernel Methods. 2022, pp. 1870–75.
short: 'N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: 2022, pp. 1870–1875.'
conference:
end_date: 2022-07-15
location: London
name: 2022 European Control Conference (ECC)
start_date: 2022-07-12
date_created: 2022-03-31T11:14:13Z
date_updated: 2023-11-29T10:00:18Z
ddc:
- '510'
department:
- _id: '636'
has_accepted_license: '1'
language:
- iso: eng
page: 1870-1875
status: public
title: Verification of safety critical control policies using kernel methods
type: conference
user_id: '15694'
year: '2022'
...
---
_id: '44624'
author:
- first_name: Timm
full_name: Faulwasser, Timm
last_name: Faulwasser
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Manuel
full_name: Schaller, Manuel
last_name: Schaller
- first_name: Karl
full_name: Worthmann, Karl
last_name: Worthmann
citation:
ama: Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Schaller M, Worthmann K. Manifold
turnpikes, trims, and symmetries. Mathematics of Control, Signals, and Systems.
2022;34:759-788.
apa: Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., Schaller, M., & Worthmann,
K. (2022). Manifold turnpikes, trims, and symmetries. Mathematics of Control,
Signals, and Systems, 34, 759–788.
bibtex: '@article{Faulwasser_Flaßkamp_Ober-Blöbaum_Schaller_Worthmann_2022, title={Manifold
turnpikes, trims, and symmetries}, volume={34}, journal={Mathematics of Control,
Signals, and Systems}, publisher={Springer}, author={Faulwasser, Timm and Flaßkamp,
Kathrin and Ober-Blöbaum, Sina and Schaller, Manuel and Worthmann, Karl}, year={2022},
pages={759–788} }'
chicago: 'Faulwasser, Timm, Kathrin Flaßkamp, Sina Ober-Blöbaum, Manuel Schaller,
and Karl Worthmann. “Manifold Turnpikes, Trims, and Symmetries.” Mathematics
of Control, Signals, and Systems 34 (2022): 759–88.'
ieee: T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, M. Schaller, and K. Worthmann,
“Manifold turnpikes, trims, and symmetries,” Mathematics of Control, Signals,
and Systems, vol. 34, pp. 759–788, 2022.
mla: Faulwasser, Timm, et al. “Manifold Turnpikes, Trims, and Symmetries.” Mathematics
of Control, Signals, and Systems, vol. 34, Springer, 2022, pp. 759–88.
short: T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, M. Schaller, K. Worthmann, Mathematics
of Control, Signals, and Systems 34 (2022) 759–788.
date_created: 2023-05-08T09:04:06Z
date_updated: 2023-05-08T09:04:26Z
department:
- _id: '636'
intvolume: ' 34'
language:
- iso: eng
page: 759-788
publication: Mathematics of Control, Signals, and Systems
publisher: Springer
status: public
title: Manifold turnpikes, trims, and symmetries
type: journal_article
user_id: '15694'
volume: 34
year: '2022'
...
---
_id: '19941'
abstract:
- lang: eng
text: "In backward error analysis, an approximate solution to an equation is compared
to the exact solution to a nearby ‘modified’ equation. In numerical ordinary differential
equations, the two agree up to any power of the step size. If the differential
equation has a geometric property then the modified equation may share it. In
this way, known properties of differential equations can be applied to the approximation.
But for partial differential equations, the known modified equations are of higher
order, limiting applicability of the theory. Therefore, we study symmetric solutions
of discretized\r\npartial differential equations that arise from a discrete variational
principle. These symmetric solutions obey infinite-dimensional functional equations.
We show that these equations admit second-order modified equations which are Hamiltonian
and also possess first-order Lagrangians in modified coordinates. The modified
equation and its associated structures are computed explicitly for the case of
rotating travelling waves in the nonlinear wave equation."
article_type: original
author:
- first_name: Robert I
full_name: McLachlan, Robert I
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
citation:
ama: McLachlan RI, Offen C. Backward error analysis for variational discretisations
of partial differential equations. Journal of Geometric Mechanics. 2022;14(3):447-471.
doi:10.3934/jgm.2022014
apa: McLachlan, R. I., & Offen, C. (2022). Backward error analysis for variational
discretisations of partial differential equations. Journal of Geometric Mechanics,
14(3), 447–471. https://doi.org/10.3934/jgm.2022014
bibtex: '@article{McLachlan_Offen_2022, title={Backward error analysis for variational
discretisations of partial differential equations}, volume={14}, DOI={10.3934/jgm.2022014},
number={3}, journal={Journal of Geometric Mechanics}, publisher={AIMS}, author={McLachlan,
Robert I and Offen, Christian}, year={2022}, pages={447–471} }'
chicago: 'McLachlan, Robert I, and Christian Offen. “Backward Error Analysis for
Variational Discretisations of Partial Differential Equations.” Journal of
Geometric Mechanics 14, no. 3 (2022): 447–71. https://doi.org/10.3934/jgm.2022014.'
ieee: 'R. I. McLachlan and C. Offen, “Backward error analysis for variational discretisations
of partial differential equations,” Journal of Geometric Mechanics, vol.
14, no. 3, pp. 447–471, 2022, doi: 10.3934/jgm.2022014.'
mla: McLachlan, Robert I., and Christian Offen. “Backward Error Analysis for Variational
Discretisations of Partial Differential Equations.” Journal of Geometric Mechanics,
vol. 14, no. 3, AIMS, 2022, pp. 447–71, doi:10.3934/jgm.2022014.
short: R.I. McLachlan, C. Offen, Journal of Geometric Mechanics 14 (2022) 447–471.
date_created: 2020-10-06T16:33:19Z
date_updated: 2023-08-10T08:44:55Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.3934/jgm.2022014
external_id:
arxiv:
- '2006.14172'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2022-06-13T09:11:38Z
date_updated: 2022-06-13T09:11:38Z
description: |-
In backward error analysis, an approximate solution to an equa-
tion is compared to the exact solution to a nearby ‘modified’ equation. In
numerical ordinary differential equations, the two agree up to any power of
the step size. If the differential equation has a geometric property then the
modified equation may share it. In this way, known properties of differential
equations can be applied to the approximation. But for partial differential
equations, the known modified equations are of higher order, limiting appli-
cability of the theory. Therefore, we study symmetric solutions of discretized
partial differential equations that arise from a discrete variational principle.
These symmetric solutions obey infinite-dimensional functional equations. We
show that these equations admit second-order modified equations which are
Hamiltonian and also possess first-order Lagrangians in modified coordinates.
The modified equation and its associated structures are computed explicitly
for the case of rotating travelling waves in the nonlinear wave equation.
file_id: '31859'
file_name: 2_BlendedBEASymmPDE.pdf
file_size: 1507248
relation: main_file
title: Backward error analysis for variational discretisations of PDEs
file_date_updated: 2022-06-13T09:11:38Z
has_accepted_license: '1'
intvolume: ' 14'
issue: '3'
language:
- iso: eng
oa: '1'
page: 447 - 471
publication: Journal of Geometric Mechanics
publication_status: published
publisher: AIMS
related_material:
link:
- relation: software
url: https://github.com/Christian-Offen/multisymplectic
status: public
title: Backward error analysis for variational discretisations of partial differential
equations
type: journal_article
user_id: '85279'
volume: 14
year: '2022'
...
---
_id: '23382'
abstract:
- lang: eng
text: Hamiltonian systems are differential equations which describe systems in classical
mechanics, plasma physics, and sampling problems. They exhibit many structural
properties, such as a lack of attractors and the presence of conservation laws.
To predict Hamiltonian dynamics based on discrete trajectory observations, incorporation
of prior knowledge about Hamiltonian structure greatly improves predictions. This
is typically done by learning the system's Hamiltonian and then integrating the
Hamiltonian vector field with a symplectic integrator. For this, however, Hamiltonian
data needs to be approximated based on the trajectory observations. Moreover,
the numerical integrator introduces an additional discretisation error. In this
paper, we show that an inverse modified Hamiltonian structure adapted to the geometric
integrator can be learned directly from observations. A separate approximation
step for the Hamiltonian data avoided. The inverse modified data compensates for
the discretisation error such that the discretisation error is eliminated. The
technique is developed for Gaussian Processes.
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. Symplectic integration of learned Hamiltonian systems.
Chaos: An Interdisciplinary Journal of Nonlinear Science. 2022;32(1). doi:10.1063/5.0065913'
apa: 'Offen, C., & Ober-Blöbaum, S. (2022). Symplectic integration of learned
Hamiltonian systems. Chaos: An Interdisciplinary Journal of Nonlinear Science,
32(1). https://doi.org/10.1063/5.0065913'
bibtex: '@article{Offen_Ober-Blöbaum_2022, title={Symplectic integration of learned
Hamiltonian systems}, volume={32(1)}, DOI={10.1063/5.0065913},
journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP},
author={Offen, Christian and Ober-Blöbaum, Sina}, year={2022} }'
chicago: 'Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned
Hamiltonian Systems.” Chaos: An Interdisciplinary Journal of Nonlinear Science
32(1) (2022). https://doi.org/10.1063/5.0065913.'
ieee: 'C. Offen and S. Ober-Blöbaum, “Symplectic integration of learned Hamiltonian
systems,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.
32(1), 2022, doi: 10.1063/5.0065913.'
mla: 'Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned
Hamiltonian Systems.” Chaos: An Interdisciplinary Journal of Nonlinear Science,
vol. 32(1), AIP, 2022, doi:10.1063/5.0065913.'
short: 'C. Offen, S. Ober-Blöbaum, Chaos: An Interdisciplinary Journal of Nonlinear
Science 32(1) (2022).'
date_created: 2021-08-11T08:24:02Z
date_updated: 2023-08-10T08:48:14Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1063/5.0065913
external_id:
arxiv:
- '2108.02492'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2021-12-13T14:56:15Z
date_updated: 2021-12-13T14:56:15Z
file_id: '28734'
file_name: SymplecticShadowIntegration_AIP.pdf
file_size: 2285059
relation: main_file
file_date_updated: 2021-12-13T14:56:15Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://aip.scitation.org/doi/abs/10.1063/5.0065913
oa: '1'
publication: 'Chaos: An Interdisciplinary Journal of Nonlinear Science'
publication_status: published
publisher: AIP
quality_controlled: '1'
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Christian-Offen/symplectic-shadow-integration
status: public
title: Symplectic integration of learned Hamiltonian systems
type: journal_article
user_id: '85279'
volume: 32(1)
year: '2022'
...
---
_id: '29421'
author:
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: M.
full_name: Vermeeren, M.
last_name: Vermeeren
citation:
ama: 'Ober-Blöbaum S, Vermeeren M. Superconvergence of galerkin variational integrators.
In: IFAC-PapersOnLine, ed. 7th IIFAC Workshop on Lagrangian and Hamiltonian
Methods for Nonlinear Control LHMNC. Vol 54(19). ; 2021:327-333.'
apa: 'Ober-Blöbaum, S., & Vermeeren, M. (2021). Superconvergence of galerkin
variational integrators. In IFAC-PapersOnLine (Ed.), 7th IIFAC Workshop on
Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC: Vol. 54(19)
(pp. 327–333).'
bibtex: '@inproceedings{Ober-Blöbaum_Vermeeren_2021, title={Superconvergence of
galerkin variational integrators}, volume={54(19)}, booktitle={7th IIFAC Workshop
on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC}, author={Ober-Blöbaum,
Sina and Vermeeren, M.}, editor={IFAC-PapersOnLine}, year={2021}, pages={327–333}
}'
chicago: Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational
Integrators.” In 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for
Nonlinear Control LHMNC, edited by IFAC-PapersOnLine, 54(19):327–33, 2021.
ieee: S. Ober-Blöbaum and M. Vermeeren, “Superconvergence of galerkin variational
integrators,” in 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for
Nonlinear Control LHMNC, 2021, vol. 54(19), pp. 327–333.
mla: Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational
Integrators.” 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for
Nonlinear Control LHMNC, edited by IFAC-PapersOnLine, vol. 54(19), 2021, pp.
327–33.
short: 'S. Ober-Blöbaum, M. Vermeeren, in: IFAC-PapersOnLine (Ed.), 7th IIFAC Workshop
on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC, 2021, pp. 327–333.'
corporate_editor:
- IFAC-PapersOnLine
date_created: 2022-01-18T14:27:56Z
date_updated: 2022-01-21T13:36:53Z
department:
- _id: '636'
language:
- iso: eng
page: 327-333
publication: 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear
Control LHMNC
status: public
title: Superconvergence of galerkin variational integrators
type: conference
user_id: '15694'
volume: 54(19)
year: '2021'
...
---
_id: '29543'
article_number: '109804'
author:
- first_name: Walid
full_name: Djema, Walid
last_name: Djema
- first_name: Laetitia
full_name: Giraldi, Laetitia
last_name: Giraldi
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Olivier
full_name: Bernard, Olivier
last_name: Bernard
citation:
ama: Djema W, Giraldi L, Maslovskaya S, Bernard O. Turnpike features in optimal
selection of species represented by quota models. Automatica. 2021;132.
doi:10.1016/j.automatica.2021.109804
apa: Djema, W., Giraldi, L., Maslovskaya, S., & Bernard, O. (2021). Turnpike
features in optimal selection of species represented by quota models. Automatica,
132, Article 109804. https://doi.org/10.1016/j.automatica.2021.109804
bibtex: '@article{Djema_Giraldi_Maslovskaya_Bernard_2021, title={Turnpike features
in optimal selection of species represented by quota models}, volume={132}, DOI={10.1016/j.automatica.2021.109804},
number={109804}, journal={Automatica}, publisher={Elsevier BV}, author={Djema,
Walid and Giraldi, Laetitia and Maslovskaya, Sofya and Bernard, Olivier}, year={2021}
}'
chicago: Djema, Walid, Laetitia Giraldi, Sofya Maslovskaya, and Olivier Bernard.
“Turnpike Features in Optimal Selection of Species Represented by Quota Models.”
Automatica 132 (2021). https://doi.org/10.1016/j.automatica.2021.109804.
ieee: 'W. Djema, L. Giraldi, S. Maslovskaya, and O. Bernard, “Turnpike features
in optimal selection of species represented by quota models,” Automatica,
vol. 132, Art. no. 109804, 2021, doi: 10.1016/j.automatica.2021.109804.'
mla: Djema, Walid, et al. “Turnpike Features in Optimal Selection of Species Represented
by Quota Models.” Automatica, vol. 132, 109804, Elsevier BV, 2021, doi:10.1016/j.automatica.2021.109804.
short: W. Djema, L. Giraldi, S. Maslovskaya, O. Bernard, Automatica 132 (2021).
date_created: 2022-01-26T13:13:06Z
date_updated: 2022-01-26T13:15:33Z
department:
- _id: '636'
doi: 10.1016/j.automatica.2021.109804
intvolume: ' 132'
keyword:
- Electrical and Electronic Engineering
- Control and Systems Engineering
language:
- iso: eng
publication: Automatica
publication_identifier:
issn:
- 0005-1098
publication_status: published
publisher: Elsevier BV
status: public
title: Turnpike features in optimal selection of species represented by quota models
type: journal_article
user_id: '87909'
volume: 132
year: '2021'
...
---
_id: '22894'
abstract:
- lang: eng
text: "The first order optimality conditions of optimal control problems (OCPs)
can\r\nbe regarded as boundary value problems for Hamiltonian systems. Variational
or\r\nsymplectic discretisation methods are classically known for their excellent\r\nlong
term behaviour. As boundary value problems are posed on intervals of\r\nfixed,
moderate length, it is not immediately clear whether methods can profit\r\nfrom
structure preservation in this context. When parameters are present,\r\nsolutions
can undergo bifurcations, for instance, two solutions can merge and\r\nannihilate
one another as parameters are varied. We will show that generic\r\nbifurcations
of an OCP are preserved under discretisation when the OCP is\r\neither directly
discretised to a discrete OCP (direct method) or translated\r\ninto a Hamiltonian
boundary value problem using first order necessary\r\nconditions of optimality
which is then solved using a symplectic integrator\r\n(indirect method). Moreover,
certain bifurcations break when a non-symplectic\r\nscheme is used. The general
phenomenon is illustrated on the example of a cut\r\nlocus of an ellipsoid."
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. Bifurcation preserving discretisations of optimal
control problems. 2021;54(19):334-339. doi:https://doi.org/10.1016/j.ifacol.2021.11.099
apa: 'Offen, C., & Ober-Blöbaum, S. (2021). Bifurcation preserving discretisations
of optimal control problems: Vol. 54(19) (pp. 334–339). https://doi.org/10.1016/j.ifacol.2021.11.099'
bibtex: '@article{Offen_Ober-Blöbaum_2021, series={IFAC-PapersOnLine}, title={Bifurcation
preserving discretisations of optimal control problems}, volume={54(19)}, DOI={https://doi.org/10.1016/j.ifacol.2021.11.099},
author={Offen, Christian and Ober-Blöbaum, Sina}, year={2021}, pages={334–339},
collection={IFAC-PapersOnLine} }'
chicago: Offen, Christian, and Sina Ober-Blöbaum. “Bifurcation Preserving Discretisations
of Optimal Control Problems.” IFAC-PapersOnLine, 2021. https://doi.org/10.1016/j.ifacol.2021.11.099.
ieee: 'C. Offen and S. Ober-Blöbaum, “Bifurcation preserving discretisations of
optimal control problems,” vol. 54(19). pp. 334–339, 2021, doi: https://doi.org/10.1016/j.ifacol.2021.11.099.'
mla: Offen, Christian, and Sina Ober-Blöbaum. Bifurcation Preserving Discretisations
of Optimal Control Problems. 2021, pp. 334–39, doi:https://doi.org/10.1016/j.ifacol.2021.11.099.
short: C. Offen, S. Ober-Blöbaum, 54(19) (2021) 334–339.
conference:
end_date: 2021-10-13
location: Berlin, Germany
name: 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control,
LHMNC 2021
start_date: 2021-10-11
date_created: 2021-07-29T09:38:32Z
date_updated: 2023-11-29T10:19:41Z
ddc:
- '510'
department:
- _id: '636'
doi: https://doi.org/10.1016/j.ifacol.2021.11.099
external_id:
arxiv:
- '2107.13853'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2021-07-29T09:37:49Z
date_updated: 2021-07-29T09:37:49Z
file_id: '22895'
file_name: ifacconf.pdf
file_size: 3125220
relation: main_file
file_date_updated: 2021-07-29T09:37:49Z
has_accepted_license: '1'
keyword:
- optimal control
- catastrophe theory
- bifurcations
- variational methods
- symplectic integrators
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/S2405896321021236
oa: '1'
page: 334-339
publication_identifier:
issn:
- 2405-8963
publication_status: published
quality_controlled: '1'
related_material:
link:
- description: GitHub/Zenodo
relation: software
url: https://doi.org/10.5281/zenodo.4562664
series_title: IFAC-PapersOnLine
status: public
title: Bifurcation preserving discretisations of optimal control problems
type: conference
user_id: '15694'
volume: 54(19)
year: '2021'
...
---
_id: '21572'
author:
- first_name: Steffen
full_name: Ridderbusch, Steffen
last_name: Ridderbusch
- 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: Paul
full_name: Goulart, Paul
last_name: Goulart
citation:
ama: 'Ridderbusch S, Offen C, Ober-Blöbaum S, Goulart P. Learning ODE Models with
Qualitative Structure Using Gaussian Processes . In: 2021 60th IEEE Conference
on Decision and Control (CDC). IEEE; 2021:2896. doi:10.1109/CDC45484.2021.9683426'
apa: Ridderbusch, S., Offen, C., Ober-Blöbaum, S., & Goulart, P. (2021). Learning
ODE Models with Qualitative Structure Using Gaussian Processes . 2021 60th
IEEE Conference on Decision and Control (CDC), 2896. https://doi.org/10.1109/CDC45484.2021.9683426
bibtex: '@inproceedings{Ridderbusch_Offen_Ober-Blöbaum_Goulart_2021, title={Learning
ODE Models with Qualitative Structure Using Gaussian Processes }, DOI={10.1109/CDC45484.2021.9683426},
booktitle={2021 60th IEEE Conference on Decision and Control (CDC)}, publisher={IEEE},
author={Ridderbusch, Steffen and Offen, Christian and Ober-Blöbaum, Sina and Goulart,
Paul}, year={2021}, pages={2896} }'
chicago: Ridderbusch, Steffen, Christian Offen, Sina Ober-Blöbaum, and Paul Goulart.
“Learning ODE Models with Qualitative Structure Using Gaussian Processes .” In
2021 60th IEEE Conference on Decision and Control (CDC), 2896. IEEE, 2021.
https://doi.org/10.1109/CDC45484.2021.9683426.
ieee: 'S. Ridderbusch, C. Offen, S. Ober-Blöbaum, and P. Goulart, “Learning ODE
Models with Qualitative Structure Using Gaussian Processes ,” in 2021 60th
IEEE Conference on Decision and Control (CDC), Austin, TX, USA, 2021, p. 2896,
doi: 10.1109/CDC45484.2021.9683426.'
mla: Ridderbusch, Steffen, et al. “Learning ODE Models with Qualitative Structure
Using Gaussian Processes .” 2021 60th IEEE Conference on Decision and Control
(CDC), IEEE, 2021, p. 2896, doi:10.1109/CDC45484.2021.9683426.
short: 'S. Ridderbusch, C. Offen, S. Ober-Blöbaum, P. Goulart, in: 2021 60th IEEE
Conference on Decision and Control (CDC), IEEE, 2021, p. 2896.'
conference:
end_date: 2021-12-17
location: Austin, TX, USA
name: 60th IEEE Conference on Decision and Control (CDC)
start_date: 2021-12-14
date_created: 2021-03-30T10:27:44Z
date_updated: 2023-11-29T10:24:55Z
department:
- _id: '636'
doi: 10.1109/CDC45484.2021.9683426
external_id:
arxiv:
- '2011.05364'
language:
- iso: eng
page: '2896'
publication: 2021 60th IEEE Conference on Decision and Control (CDC)
publication_identifier:
eisbn:
- 978-1-6654-3659-5
publication_status: published
publisher: IEEE
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Crown421/StructureGPs-paper
status: public
title: 'Learning ODE Models with Qualitative Structure Using Gaussian Processes '
type: conference
user_id: '15694'
year: '2021'
...