---
_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
license: https://creativecommons.org/licenses/by/4.0/
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: '45972'
author:
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Kovács B. Numerical surgery for mean curvature flow of surfaces. SIAM Journal
on Scientific Computing. 2024;46(2):A645--A669. doi:10.1137/22M1531919
apa: Kovács, B. (2024). Numerical surgery for mean curvature flow of surfaces. SIAM
Journal on Scientific Computing, 46(2), A645--A669. https://doi.org/10.1137/22M1531919
bibtex: '@article{Kovács_2024, title={Numerical surgery for mean curvature flow
of surfaces}, volume={46}, DOI={10.1137/22M1531919},
number={2}, journal={SIAM Journal on Scientific Computing}, author={Kovács, Balázs},
year={2024}, pages={A645--A669} }'
chicago: 'Kovács, Balázs. “Numerical Surgery for Mean Curvature Flow of Surfaces.”
SIAM Journal on Scientific Computing 46, no. 2 (2024): A645--A669. https://doi.org/10.1137/22M1531919.'
ieee: 'B. Kovács, “Numerical surgery for mean curvature flow of surfaces,” SIAM
Journal on Scientific Computing, vol. 46, no. 2, pp. A645--A669, 2024, doi:
10.1137/22M1531919.'
mla: Kovács, Balázs. “Numerical Surgery for Mean Curvature Flow of Surfaces.” SIAM
Journal on Scientific Computing, vol. 46, no. 2, 2024, pp. A645--A669, doi:10.1137/22M1531919.
short: B. Kovács, SIAM Journal on Scientific Computing 46 (2024) A645--A669.
date_created: 2023-07-10T12:32:34Z
date_updated: 2024-08-27T07:42:56Z
department:
- _id: '841'
doi: 10.1137/22M1531919
extern: '1'
intvolume: ' 46'
issue: '2'
language:
- iso: eng
page: A645--A669
publication: SIAM Journal on Scientific Computing
status: public
title: Numerical surgery for mean curvature flow of surfaces
type: journal_article
user_id: '100441'
volume: 46
year: '2024'
...
---
_id: '56497'
article_number: '114258'
author:
- first_name: Chiara
full_name: Cappello, Chiara
last_name: Cappello
- first_name: Reza
full_name: Naserasr, Reza
last_name: Naserasr
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
- first_name: Zhouningxin
full_name: Wang, Zhouningxin
last_name: Wang
citation:
ama: Cappello C, Naserasr R, Steffen E, Wang Z. Critically 3-frustrated signed graphs.
Discrete Mathematics. 2024;348(1). doi:10.1016/j.disc.2024.114258
apa: Cappello, C., Naserasr, R., Steffen, E., & Wang, Z. (2024). Critically
3-frustrated signed graphs. Discrete Mathematics, 348(1), Article
114258. https://doi.org/10.1016/j.disc.2024.114258
bibtex: '@article{Cappello_Naserasr_Steffen_Wang_2024, title={Critically 3-frustrated
signed graphs}, volume={348}, DOI={10.1016/j.disc.2024.114258},
number={1114258}, journal={Discrete Mathematics}, publisher={Elsevier BV}, author={Cappello,
Chiara and Naserasr, Reza and Steffen, Eckhard and Wang, Zhouningxin}, year={2024}
}'
chicago: Cappello, Chiara, Reza Naserasr, Eckhard Steffen, and Zhouningxin Wang.
“Critically 3-Frustrated Signed Graphs.” Discrete Mathematics 348, no.
1 (2024). https://doi.org/10.1016/j.disc.2024.114258.
ieee: 'C. Cappello, R. Naserasr, E. Steffen, and Z. Wang, “Critically 3-frustrated
signed graphs,” Discrete Mathematics, vol. 348, no. 1, Art. no. 114258,
2024, doi: 10.1016/j.disc.2024.114258.'
mla: Cappello, Chiara, et al. “Critically 3-Frustrated Signed Graphs.” Discrete
Mathematics, vol. 348, no. 1, 114258, Elsevier BV, 2024, doi:10.1016/j.disc.2024.114258.
short: C. Cappello, R. Naserasr, E. Steffen, Z. Wang, Discrete Mathematics 348 (2024).
date_created: 2024-10-10T12:27:11Z
date_updated: 2024-10-10T12:28:13Z
department:
- _id: '542'
doi: 10.1016/j.disc.2024.114258
intvolume: ' 348'
issue: '1'
language:
- iso: eng
publication: Discrete Mathematics
publication_identifier:
issn:
- 0012-365X
publication_status: published
publisher: Elsevier BV
status: public
title: Critically 3-frustrated signed graphs
type: journal_article
user_id: '15540'
volume: 348
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: '55078'
abstract:
- lang: eng
text: "This paper develops and discusses a residual-based a posteriori error\r\nestimate
and a space--time adaptive algorithm for solving parabolic surface\r\npartial
differential equations on closed stationary surfaces. The full\r\ndiscretization
uses the surface finite element method in space and the backward\r\nEuler method
in time. The proposed error indicator bounds the error quantities\r\nglobally
in space from above and below, and globally in time from above and\r\nlocally
from below. A space--time adaptive algorithm is proposed using the\r\nderived
error indicator. Numerical experiments illustrate and complement the\r\ntheory."
author:
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Michael Frederik Raúl
full_name: Lantelme, Michael Frederik Raúl
id: '102867'
last_name: Lantelme
citation:
ama: Kovács B, Lantelme MFR. A posteriori error estimates for parabolic partial
differential equations on stationary surfaces. arXiv:240702101. Published
online 2024.
apa: Kovács, B., & Lantelme, M. F. R. (2024). A posteriori error estimates for
parabolic partial differential equations on stationary surfaces. In arXiv:2407.02101.
bibtex: '@article{Kovács_Lantelme_2024, title={A posteriori error estimates for
parabolic partial differential equations on stationary surfaces}, journal={arXiv:2407.02101},
author={Kovács, Balázs and Lantelme, Michael Frederik Raúl}, year={2024} }'
chicago: Kovács, Balázs, and Michael Frederik Raúl Lantelme. “A Posteriori Error
Estimates for Parabolic Partial Differential Equations on Stationary Surfaces.”
ArXiv:2407.02101, 2024.
ieee: B. Kovács and M. F. R. Lantelme, “A posteriori error estimates for parabolic
partial differential equations on stationary surfaces,” arXiv:2407.02101.
2024.
mla: Kovács, Balázs, and Michael Frederik Raúl Lantelme. “A Posteriori Error Estimates
for Parabolic Partial Differential Equations on Stationary Surfaces.” ArXiv:2407.02101,
2024.
short: B. Kovács, M.F.R. Lantelme, ArXiv:2407.02101 (2024).
date_created: 2024-07-04T12:53:47Z
date_updated: 2026-02-18T14:45:36Z
department:
- _id: '841'
external_id:
arxiv:
- '2407.02101'
language:
- iso: eng
publication: arXiv:2407.02101
status: public
title: A posteriori error estimates for parabolic partial differential equations on
stationary surfaces
type: preprint
user_id: '100441'
year: '2024'
...
---
_id: '56429'
abstract:
- lang: eng
text: "It is known that the notion of a transitive subgroup of a permutation group\r\n$P$
extends naturally to the subsets of $P$. We study transitive subsets of the\r\nwreath
product $G \\wr S_n$, where $G$ is a finite abelian group. This includes\r\nthe
hyperoctahedral group for $G=C_2$. We give structural characterisations of\r\ntransitive
subsets using the character theory of $G \\wr S_n$ and interpret such\r\nsubsets
as designs in the conjugacy class association scheme of $G \\wr S_n$. In\r\nparticular,
we prove a generalisation of the Livingstone-Wagner theorem and\r\ngive explicit
constructions of transitive sets. Moreover, we establish\r\nconnections to orthogonal
polynomials, namely the Charlier polynomials, and use\r\nthem to study codes and
designs in $C_r \\wr S_n$. Many of our results extend\r\nresults about the symmetric
group $S_n$."
author:
- first_name: Lukas-André Dominik
full_name: Klawuhn, Lukas-André Dominik
id: '91965'
last_name: Klawuhn
orcid: 0009-0009-7736-4885
- first_name: Kai-Uwe
full_name: Schmidt, Kai-Uwe
last_name: Schmidt
citation:
ama: Klawuhn L-AD, Schmidt K-U. Transitivity in wreath products with symmetric groups.
arXiv:240920495. Published online 2024.
apa: Klawuhn, L.-A. D., & Schmidt, K.-U. (2024). Transitivity in wreath products
with symmetric groups. In arXiv:2409.20495.
bibtex: '@article{Klawuhn_Schmidt_2024, title={Transitivity in wreath products with
symmetric groups}, journal={arXiv:2409.20495}, author={Klawuhn, Lukas-André Dominik
and Schmidt, Kai-Uwe}, year={2024} }'
chicago: Klawuhn, Lukas-André Dominik, and Kai-Uwe Schmidt. “Transitivity in Wreath
Products with Symmetric Groups.” ArXiv:2409.20495, 2024.
ieee: L.-A. D. Klawuhn and K.-U. Schmidt, “Transitivity in wreath products with
symmetric groups,” arXiv:2409.20495. 2024.
mla: Klawuhn, Lukas-André Dominik, and Kai-Uwe Schmidt. “Transitivity in Wreath
Products with Symmetric Groups.” ArXiv:2409.20495, 2024.
short: L.-A.D. Klawuhn, K.-U. Schmidt, ArXiv:2409.20495 (2024).
date_created: 2024-10-08T13:14:45Z
date_updated: 2024-11-15T12:34:03Z
department:
- _id: '100'
external_id:
arxiv:
- '2409.20495'
language:
- iso: eng
page: '38'
publication: arXiv:2409.20495
status: public
title: Transitivity in wreath products with symmetric groups
type: preprint
user_id: '91965'
year: '2024'
...
---
_id: '59171'
abstract:
- lang: eng
text: To model dynamical systems on networks with higher-order (non-pairwise) interactions,
we recently introduced a new class of ordinary differential equations (ODEs) on
hypernetworks. Here, we consider one-parameter synchrony breaking bifurcations
in such ODEs. We call a synchrony breaking steady-state branch ‘reluctant’ if
it is tangent to a synchrony space, but does not lie inside it. We prove that
reluctant synchrony breaking is ubiquitous in hypernetwork systems, by constructing
a large class of examples that support it. We also give an explicit formula for
the order of tangency to the synchrony space of a reluctant steady-state branch.
author:
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Eddie
full_name: Nijholt, Eddie
last_name: Nijholt
- first_name: Bob
full_name: Rink, Bob
last_name: Rink
citation:
ama: 'von der Gracht S, Nijholt E, Rink B. Higher-order interactions lead to ‘reluctant’
synchrony breaking. Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences. 2024;480(2301). doi:10.1098/rspa.2023.0945'
apa: 'von der Gracht, S., Nijholt, E., & Rink, B. (2024). Higher-order interactions
lead to ‘reluctant’ synchrony breaking. Proceedings of the Royal Society A:
Mathematical, Physical and Engineering Sciences, 480(2301). https://doi.org/10.1098/rspa.2023.0945'
bibtex: '@article{von der Gracht_Nijholt_Rink_2024, title={Higher-order interactions
lead to ‘reluctant’ synchrony breaking}, volume={480}, DOI={10.1098/rspa.2023.0945},
number={2301}, journal={Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences}, publisher={The Royal Society}, author={von der Gracht,
Sören and Nijholt, Eddie and Rink, Bob}, year={2024} }'
chicago: 'Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Higher-Order Interactions
Lead to ‘Reluctant’ Synchrony Breaking.” Proceedings of the Royal Society A:
Mathematical, Physical and Engineering Sciences 480, no. 2301 (2024). https://doi.org/10.1098/rspa.2023.0945.'
ieee: 'S. von der Gracht, E. Nijholt, and B. Rink, “Higher-order interactions lead
to ‘reluctant’ synchrony breaking,” Proceedings of the Royal Society A: Mathematical,
Physical and Engineering Sciences, vol. 480, no. 2301, 2024, doi: 10.1098/rspa.2023.0945.'
mla: 'von der Gracht, Sören, et al. “Higher-Order Interactions Lead to ‘Reluctant’
Synchrony Breaking.” Proceedings of the Royal Society A: Mathematical, Physical
and Engineering Sciences, vol. 480, no. 2301, The Royal Society, 2024, doi:10.1098/rspa.2023.0945.'
short: 'S. von der Gracht, E. Nijholt, B. Rink, Proceedings of the Royal Society
A: Mathematical, Physical and Engineering Sciences 480 (2024).'
date_created: 2025-03-27T10:15:06Z
date_updated: 2025-03-27T10:19:56Z
ddc:
- '510'
department:
- _id: '101'
doi: 10.1098/rspa.2023.0945
file:
- access_level: open_access
content_type: application/pdf
creator: svdg
date_created: 2025-03-27T10:16:20Z
date_updated: 2025-03-27T10:19:48Z
file_id: '59172'
file_name: higher-order-interactions-lead-to-reluctant-synchrony-breaking.pdf
file_size: 820435
relation: main_file
file_date_updated: 2025-03-27T10:19:48Z
has_accepted_license: '1'
intvolume: ' 480'
issue: '2301'
keyword:
- higher-order interactions
- synchrony breaking
- network dynamics
- coupled cell systems
language:
- iso: eng
oa: '1'
publication: 'Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Sciences'
publication_identifier:
issn:
- 1364-5021
- 1471-2946
publication_status: published
publisher: The Royal Society
status: public
title: Higher-order interactions lead to ‘reluctant’ synchrony breaking
type: journal_article
user_id: '97359'
volume: 480
year: '2024'
...
---
_id: '21199'
abstract:
- lang: eng
text: "As in almost every other branch of science, the major advances in data\r\nscience
and machine learning have also resulted in significant improvements\r\nregarding
the modeling and simulation of nonlinear dynamical systems. It is\r\nnowadays
possible to make accurate medium to long-term predictions of highly\r\ncomplex
systems such as the weather, the dynamics within a nuclear fusion\r\nreactor,
of disease models or the stock market in a very efficient manner. In\r\nmany cases,
predictive methods are advertised to ultimately be useful for\r\ncontrol, as the
control of high-dimensional nonlinear systems is an engineering\r\ngrand challenge
with huge potential in areas such as clean and efficient energy\r\nproduction,
or the development of advanced medical devices. However, the\r\nquestion of how
to use a predictive model for control is often left unanswered\r\ndue to the associated
challenges, namely a significantly higher system\r\ncomplexity, the requirement
of much larger data sets and an increased and often\r\nproblem-specific modeling
effort. To solve these issues, we present a universal\r\nframework (which we call
QuaSiModO:\r\nQuantization-Simulation-Modeling-Optimization) to transform arbitrary\r\npredictive
models into control systems and use them for feedback control. The\r\nadvantages
of our approach are a linear increase in data requirements with\r\nrespect to
the control dimension, performance guarantees that rely exclusively\r\non the
accuracy of the predictive model, and only little prior knowledge\r\nrequirements
in control theory to solve complex control problems. In particular\r\nthe latter
point is of key importance to enable a large number of researchers\r\nand practitioners
to exploit the ever increasing capabilities of predictive\r\nmodels for control
in a straight-forward and systematic fashion."
article_number: '110840'
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Katharina
full_name: Bieker, Katharina
id: '32829'
last_name: Bieker
citation:
ama: Peitz S, Bieker K. On the Universal Transformation of Data-Driven Models to
Control Systems. Automatica. 2023;149. doi:10.1016/j.automatica.2022.110840
apa: Peitz, S., & Bieker, K. (2023). On the Universal Transformation of Data-Driven
Models to Control Systems. Automatica, 149, Article 110840. https://doi.org/10.1016/j.automatica.2022.110840
bibtex: '@article{Peitz_Bieker_2023, title={On the Universal Transformation of Data-Driven
Models to Control Systems}, volume={149}, DOI={10.1016/j.automatica.2022.110840},
number={110840}, journal={Automatica}, publisher={Elsevier}, author={Peitz, Sebastian
and Bieker, Katharina}, year={2023} }'
chicago: Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation
of Data-Driven Models to Control Systems.” Automatica 149 (2023). https://doi.org/10.1016/j.automatica.2022.110840.
ieee: 'S. Peitz and K. Bieker, “On the Universal Transformation of Data-Driven Models
to Control Systems,” Automatica, vol. 149, Art. no. 110840, 2023, doi:
10.1016/j.automatica.2022.110840.'
mla: Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of
Data-Driven Models to Control Systems.” Automatica, vol. 149, 110840, Elsevier,
2023, doi:10.1016/j.automatica.2022.110840.
short: S. Peitz, K. Bieker, Automatica 149 (2023).
date_created: 2021-02-10T07:04:15Z
date_updated: 2023-01-07T12:01:58Z
department:
- _id: '101'
- _id: '655'
doi: 10.1016/j.automatica.2022.110840
intvolume: ' 149'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/S0005109822007075/pdfft?isDTMRedir=true&download=true
oa: '1'
project:
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Automatica
publication_status: published
publisher: Elsevier
status: public
title: On the Universal Transformation of Data-Driven Models to Control Systems
type: journal_article
user_id: '47427'
volume: 149
year: '2023'
...
---
_id: '49326'
abstract:
- lang: eng
text: Many networked systems are governed by non-pairwise interactions between nodes.
The resulting higher-order interaction structure can then be encoded by means
of a hypernetwork. In this paper we consider dynamical systems on hypernetworks
by defining a class of admissible maps for every such hypernetwork. We explain
how to classify robust cluster synchronization patterns on hypernetworks by finding
balanced partitions, and we generalize the concept of a graph fibration to the
hypernetwork context. We also show that robust synchronization patterns are only
fully determined by polynomial admissible maps of high order. This means that,
unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order,
i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork,
for the degree of the polynomial admissible maps that determine robust synchronization
patterns. We also demonstrate that this degree is optimal by investigating a class
of examples. We conclude by demonstrating how this effect may cause remarkable
synchrony breaking bifurcations that occur at high polynomial degree.
author:
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Eddie
full_name: Nijholt, Eddie
last_name: Nijholt
- first_name: Bob
full_name: Rink, Bob
last_name: Rink
citation:
ama: 'von der Gracht S, Nijholt E, Rink B. Hypernetworks: Cluster Synchronization
Is a Higher-Order Effect. SIAM Journal on Applied Mathematics. 2023;83(6):2329-2353.
doi:10.1137/23m1561075'
apa: 'von der Gracht, S., Nijholt, E., & Rink, B. (2023). Hypernetworks: Cluster
Synchronization Is a Higher-Order Effect. SIAM Journal on Applied Mathematics,
83(6), 2329–2353. https://doi.org/10.1137/23m1561075'
bibtex: '@article{von der Gracht_Nijholt_Rink_2023, title={Hypernetworks: Cluster
Synchronization Is a Higher-Order Effect}, volume={83}, DOI={10.1137/23m1561075},
number={6}, journal={SIAM Journal on Applied Mathematics}, publisher={Society
for Industrial & Applied Mathematics (SIAM)}, author={von der Gracht, Sören
and Nijholt, Eddie and Rink, Bob}, year={2023}, pages={2329–2353} }'
chicago: 'Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Hypernetworks: Cluster
Synchronization Is a Higher-Order Effect.” SIAM Journal on Applied Mathematics
83, no. 6 (2023): 2329–53. https://doi.org/10.1137/23m1561075.'
ieee: 'S. von der Gracht, E. Nijholt, and B. Rink, “Hypernetworks: Cluster Synchronization
Is a Higher-Order Effect,” SIAM Journal on Applied Mathematics, vol. 83,
no. 6, pp. 2329–2353, 2023, doi: 10.1137/23m1561075.'
mla: 'von der Gracht, Sören, et al. “Hypernetworks: Cluster Synchronization Is a
Higher-Order Effect.” SIAM Journal on Applied Mathematics, vol. 83, no.
6, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 2329–53,
doi:10.1137/23m1561075.'
short: S. von der Gracht, E. Nijholt, B. Rink, SIAM Journal on Applied Mathematics
83 (2023) 2329–2353.
date_created: 2023-11-29T10:50:05Z
date_updated: 2023-11-29T10:52:23Z
department:
- _id: '101'
doi: 10.1137/23m1561075
external_id:
arxiv:
- '2302.08974'
intvolume: ' 83'
issue: '6'
keyword:
- Applied Mathematics
language:
- iso: eng
page: 2329-2353
publication: SIAM Journal on Applied Mathematics
publication_identifier:
issn:
- 0036-1399
- 1095-712X
publication_status: published
publisher: Society for Industrial & Applied Mathematics (SIAM)
status: public
title: 'Hypernetworks: Cluster Synchronization Is a Higher-Order Effect'
type: journal_article
user_id: '97359'
volume: 83
year: '2023'
...
---
_id: '49372'
author:
- first_name: Jürgen
full_name: Klüners, Jürgen
id: '21202'
last_name: Klüners
- first_name: Jiuya
full_name: Wang, Jiuya
last_name: Wang
citation:
ama: Klüners J, Wang J. Idélic Approach in Enumerating Heisenberg Extensions. La
Matematica. Published online 2023. doi:10.1007/s44007-023-00067-w
apa: Klüners, J., & Wang, J. (2023). Idélic Approach in Enumerating Heisenberg
Extensions. La Matematica. https://doi.org/10.1007/s44007-023-00067-w
bibtex: '@article{Klüners_Wang_2023, title={Idélic Approach in Enumerating Heisenberg
Extensions}, DOI={10.1007/s44007-023-00067-w},
journal={La Matematica}, publisher={Springer Science and Business Media LLC},
author={Klüners, Jürgen and Wang, Jiuya}, year={2023} }'
chicago: Klüners, Jürgen, and Jiuya Wang. “Idélic Approach in Enumerating Heisenberg
Extensions.” La Matematica, 2023. https://doi.org/10.1007/s44007-023-00067-w.
ieee: 'J. Klüners and J. Wang, “Idélic Approach in Enumerating Heisenberg Extensions,”
La Matematica, 2023, doi: 10.1007/s44007-023-00067-w.'
mla: Klüners, Jürgen, and Jiuya Wang. “Idélic Approach in Enumerating Heisenberg
Extensions.” La Matematica, Springer Science and Business Media LLC, 2023,
doi:10.1007/s44007-023-00067-w.
short: J. Klüners, J. Wang, La Matematica (2023).
date_created: 2023-12-01T09:23:59Z
date_updated: 2023-12-06T09:50:43Z
department:
- _id: '102'
doi: 10.1007/s44007-023-00067-w
language:
- iso: eng
publication: La Matematica
publication_identifier:
issn:
- 2730-9657
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Idélic Approach in Enumerating Heisenberg Extensions
type: journal_article
user_id: '21202'
year: '2023'
...
---
_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: '50298'
abstract:
- lang: eng
text: A finite classical polar space of rank $n$ consists of the totally isotropic
subspaces of a finite vector space equipped with a nondegenerate form such that
$n$ is the maximal dimension of such a subspace. A $t$-Steiner system in a finite
classical polar space of rank $n$ is a collection $Y$ of totally isotropic $n$-spaces
such that each totally isotropic $t$-space is contained in exactly one member
of $Y$. Nontrivial examples are known only for $t=1$ and $t=n-1$. We give an almost
complete classification of such $t$-Steiner systems, showing that such objects
can only exist in some corner cases. This classification result arises from a
more general result on packings in polar spaces.
author:
- first_name: Kai-Uwe
full_name: Schmidt, Kai-Uwe
last_name: Schmidt
- first_name: Charlene
full_name: Weiß, Charlene
id: '70420'
last_name: Weiß
citation:
ama: Schmidt K-U, Weiß C. Packings and Steiner systems in polar spaces. Combinatorial
Theory. 2023;3(1). doi:10.5070/c63160424
apa: Schmidt, K.-U., & Weiß, C. (2023). Packings and Steiner systems in polar
spaces. Combinatorial Theory, 3(1). https://doi.org/10.5070/c63160424
bibtex: '@article{Schmidt_Weiß_2023, title={Packings and Steiner systems in polar
spaces}, volume={3}, DOI={10.5070/c63160424},
number={1}, journal={Combinatorial Theory}, author={Schmidt, Kai-Uwe and Weiß,
Charlene}, year={2023} }'
chicago: Schmidt, Kai-Uwe, and Charlene Weiß. “Packings and Steiner Systems in Polar
Spaces.” Combinatorial Theory 3, no. 1 (2023). https://doi.org/10.5070/c63160424.
ieee: 'K.-U. Schmidt and C. Weiß, “Packings and Steiner systems in polar spaces,”
Combinatorial Theory, vol. 3, no. 1, 2023, doi: 10.5070/c63160424.'
mla: Schmidt, Kai-Uwe, and Charlene Weiß. “Packings and Steiner Systems in Polar
Spaces.” Combinatorial Theory, vol. 3, no. 1, 2023, doi:10.5070/c63160424.
short: K.-U. Schmidt, C. Weiß, Combinatorial Theory 3 (2023).
date_created: 2024-01-08T14:33:54Z
date_updated: 2024-01-08T14:39:20Z
department:
- _id: '100'
doi: 10.5070/c63160424
intvolume: ' 3'
issue: '1'
language:
- iso: eng
publication: Combinatorial Theory
publication_status: published
status: public
title: Packings and Steiner systems in polar spaces
type: journal_article
user_id: '70420'
volume: 3
year: '2023'
...
---
_id: '50297'
abstract:
- lang: eng
text: We show that there exist ordered orthogonal arrays, whose sizes deviate from
the Rao bound by a factor that is polynomial in the parameters of the ordered
orthogonal array. The proof is nonconstructive and based on a probabilistic method
due to Kuperberg, Lovett and Peled.
author:
- first_name: Kai‐Uwe
full_name: Schmidt, Kai‐Uwe
last_name: Schmidt
- first_name: Charlene
full_name: Weiß, Charlene
id: '70420'
last_name: Weiß
citation:
ama: Schmidt K, Weiß C. Existence of small ordered orthogonal arrays. Journal
of Combinatorial Designs. 2023;31(9):422-431. doi:10.1002/jcd.21903
apa: Schmidt, K., & Weiß, C. (2023). Existence of small ordered orthogonal arrays.
Journal of Combinatorial Designs, 31(9), 422–431. https://doi.org/10.1002/jcd.21903
bibtex: '@article{Schmidt_Weiß_2023, title={Existence of small ordered orthogonal
arrays}, volume={31}, DOI={10.1002/jcd.21903},
number={9}, journal={Journal of Combinatorial Designs}, publisher={Wiley}, author={Schmidt,
Kai‐Uwe and Weiß, Charlene}, year={2023}, pages={422–431} }'
chicago: 'Schmidt, Kai‐Uwe, and Charlene Weiß. “Existence of Small Ordered Orthogonal
Arrays.” Journal of Combinatorial Designs 31, no. 9 (2023): 422–31. https://doi.org/10.1002/jcd.21903.'
ieee: 'K. Schmidt and C. Weiß, “Existence of small ordered orthogonal arrays,” Journal
of Combinatorial Designs, vol. 31, no. 9, pp. 422–431, 2023, doi: 10.1002/jcd.21903.'
mla: Schmidt, Kai‐Uwe, and Charlene Weiß. “Existence of Small Ordered Orthogonal
Arrays.” Journal of Combinatorial Designs, vol. 31, no. 9, Wiley, 2023,
pp. 422–31, doi:10.1002/jcd.21903.
short: K. Schmidt, C. Weiß, Journal of Combinatorial Designs 31 (2023) 422–431.
date_created: 2024-01-08T14:25:28Z
date_updated: 2024-01-08T14:38:53Z
department:
- _id: '100'
doi: 10.1002/jcd.21903
intvolume: ' 31'
issue: '9'
language:
- iso: eng
page: 422-431
publication: Journal of Combinatorial Designs
publication_status: published
publisher: Wiley
status: public
title: Existence of small ordered orthogonal arrays
type: journal_article
user_id: '70420'
volume: 31
year: '2023'
...
---
_id: '50300'
abstract:
- lang: eng
text: Digital communications relies heavily on the usage of different types of codes.
Prominent codes nowadays are rank-metric codes and subspace codes - the q-analogs
of binary codes and binary codes with constant weight. All these codes can be
viewed as subsets of classical association schemes. A central coding-theoretic
problem is to derive upper bounds for the size of codes. This thesis investigates
Delsartes powerful linear program whose optimum is precisely such a bound for
codes in association schemes. The linear programs for binary codes and binary
constant-weight codes have been extensively studied since the 1970s, but their
optimum is still unknown. We determine in a unified way the optimum of the linear
program in several ordinary q-analogs as well as in their affine counterparts.
In particular, bounds and constructions for codes in polar spaces are established,
where the bounds are sharp up to a constant factor in many cases. Moreover, based
on these results, an almost complete classification of Steiner systems in polar
spaces is provided by showing that they could only exist in some corner cases.
author:
- first_name: Charlene
full_name: Weiß, Charlene
id: '70420'
last_name: Weiß
citation:
ama: Weiß C. Linear Programming Bounds in Classical Association Schemes.;
2023. doi:10.17619/UNIPB/1-1672
apa: Weiß, C. (2023). Linear programming bounds in classical association schemes.
https://doi.org/10.17619/UNIPB/1-1672
bibtex: '@book{Weiß_2023, title={Linear programming bounds in classical association
schemes}, DOI={10.17619/UNIPB/1-1672},
author={Weiß, Charlene}, year={2023} }'
chicago: Weiß, Charlene. Linear Programming Bounds in Classical Association Schemes,
2023. https://doi.org/10.17619/UNIPB/1-1672.
ieee: C. Weiß, Linear programming bounds in classical association schemes.
2023.
mla: Weiß, Charlene. Linear Programming Bounds in Classical Association Schemes.
2023, doi:10.17619/UNIPB/1-1672.
short: C. Weiß, Linear Programming Bounds in Classical Association Schemes, 2023.
date_created: 2024-01-08T14:42:12Z
date_updated: 2024-01-08T14:46:14Z
department:
- _id: '100'
doi: 10.17619/UNIPB/1-1672
language:
- iso: eng
status: public
title: Linear programming bounds in classical association schemes
type: dissertation
user_id: '70420'
year: '2023'
...
---
_id: '51351'
author:
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
- first_name: Isaak Hieronymus
full_name: Wolf, Isaak Hieronymus
id: '88145'
last_name: Wolf
citation:
ama: Steffen E, Wolf IH. Bounds for the chromatic index of signed multigraphs. Discrete
Applied Mathematics. 2023;337:185-189. doi:10.1016/j.dam.2023.05.008
apa: Steffen, E., & Wolf, I. H. (2023). Bounds for the chromatic index of signed
multigraphs. Discrete Applied Mathematics, 337, 185–189. https://doi.org/10.1016/j.dam.2023.05.008
bibtex: '@article{Steffen_Wolf_2023, title={Bounds for the chromatic index of signed
multigraphs}, volume={337}, DOI={10.1016/j.dam.2023.05.008},
journal={Discrete Applied Mathematics}, publisher={Elsevier BV}, author={Steffen,
Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={185–189} }'
chicago: 'Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic
Index of Signed Multigraphs.” Discrete Applied Mathematics 337 (2023):
185–89. https://doi.org/10.1016/j.dam.2023.05.008.'
ieee: 'E. Steffen and I. H. Wolf, “Bounds for the chromatic index of signed multigraphs,”
Discrete Applied Mathematics, vol. 337, pp. 185–189, 2023, doi: 10.1016/j.dam.2023.05.008.'
mla: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Bounds for the Chromatic Index
of Signed Multigraphs.” Discrete Applied Mathematics, vol. 337, Elsevier
BV, 2023, pp. 185–89, doi:10.1016/j.dam.2023.05.008.
short: E. Steffen, I.H. Wolf, Discrete Applied Mathematics 337 (2023) 185–189.
date_created: 2024-02-14T17:33:29Z
date_updated: 2024-02-14T17:33:59Z
department:
- _id: '542'
doi: 10.1016/j.dam.2023.05.008
intvolume: ' 337'
keyword:
- Applied Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
page: 185-189
publication: Discrete Applied Mathematics
publication_identifier:
issn:
- 0166-218X
publication_status: published
publisher: Elsevier BV
status: public
title: Bounds for the chromatic index of signed multigraphs
type: journal_article
user_id: '15540'
volume: 337
year: '2023'
...
---
_id: '45190'
author:
- first_name: Chiara
full_name: Cappello, Chiara
id: '72874'
last_name: Cappello
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
citation:
ama: 'Cappello C, Steffen E. Graph-Theoretical Models for the Analysis and Design
of Socio-Technical Networks. In: The Digital Twin of Humans. Springer International
Publishing; 2023:93--110. doi:10.1007/978-3-031-26104-6_5'
apa: Cappello, C., & Steffen, E. (2023). Graph-Theoretical Models for the Analysis
and Design of Socio-Technical Networks. In The Digital Twin of Humans (pp.
93--110). Springer International Publishing. https://doi.org/10.1007/978-3-031-26104-6_5
bibtex: '@inbook{Cappello_Steffen_2023, place={Cham}, title={Graph-Theoretical Models
for the Analysis and Design of Socio-Technical Networks}, DOI={10.1007/978-3-031-26104-6_5},
booktitle={The Digital Twin of Humans}, publisher={Springer International Publishing},
author={Cappello, Chiara and Steffen, Eckhard}, year={2023}, pages={93--110} }'
chicago: 'Cappello, Chiara, and Eckhard Steffen. “Graph-Theoretical Models for the
Analysis and Design of Socio-Technical Networks.” In The Digital Twin of Humans,
93--110. Cham: Springer International Publishing, 2023. https://doi.org/10.1007/978-3-031-26104-6_5.'
ieee: 'C. Cappello and E. Steffen, “Graph-Theoretical Models for the Analysis and
Design of Socio-Technical Networks,” in The Digital Twin of Humans, Cham:
Springer International Publishing, 2023, pp. 93--110.'
mla: Cappello, Chiara, and Eckhard Steffen. “Graph-Theoretical Models for the Analysis
and Design of Socio-Technical Networks.” The Digital Twin of Humans, Springer
International Publishing, 2023, pp. 93--110, doi:10.1007/978-3-031-26104-6_5.
short: 'C. Cappello, E. Steffen, in: The Digital Twin of Humans, Springer International
Publishing, Cham, 2023, pp. 93--110.'
date_created: 2023-05-22T10:22:21Z
date_updated: 2024-02-16T07:42:38Z
department:
- _id: '542'
doi: 10.1007/978-3-031-26104-6_5
language:
- iso: eng
page: 93--110
place: Cham
publication: The Digital Twin of Humans
publication_identifier:
isbn:
- '9783031261039'
- '9783031261046'
publication_status: published
publisher: Springer International Publishing
status: public
title: Graph-Theoretical Models for the Analysis and Design of Socio-Technical Networks
type: book_chapter
user_id: '15540'
year: '2023'
...
---
_id: '51357'
article_number: '113457'
author:
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
- first_name: Isaak Hieronymus
full_name: Wolf, Isaak Hieronymus
id: '88145'
last_name: Wolf
citation:
ama: Steffen E, Wolf IH. Rotation r-graphs. Discrete Mathematics. Published
online 2023. doi:10.1016/j.disc.2023.113457
apa: Steffen, E., & Wolf, I. H. (2023). Rotation r-graphs. Discrete Mathematics,
Article 113457. https://doi.org/10.1016/j.disc.2023.113457
bibtex: '@article{Steffen_Wolf_2023, title={Rotation r-graphs}, DOI={10.1016/j.disc.2023.113457},
number={113457}, journal={Discrete Mathematics}, publisher={Elsevier BV}, author={Steffen,
Eckhard and Wolf, Isaak Hieronymus}, year={2023} }'
chicago: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” Discrete
Mathematics, 2023. https://doi.org/10.1016/j.disc.2023.113457.
ieee: 'E. Steffen and I. H. Wolf, “Rotation r-graphs,” Discrete Mathematics,
Art. no. 113457, 2023, doi: 10.1016/j.disc.2023.113457.'
mla: Steffen, Eckhard, and Isaak Hieronymus Wolf. “Rotation R-Graphs.” Discrete
Mathematics, 113457, Elsevier BV, 2023, doi:10.1016/j.disc.2023.113457.
short: E. Steffen, I.H. Wolf, Discrete Mathematics (2023).
date_created: 2024-02-16T08:44:50Z
date_updated: 2024-02-16T08:45:10Z
department:
- _id: '542'
doi: 10.1016/j.disc.2023.113457
keyword:
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science
language:
- iso: eng
publication: Discrete Mathematics
publication_identifier:
issn:
- 0012-365X
publication_status: published
publisher: Elsevier BV
status: public
title: Rotation r-graphs
type: journal_article
user_id: '15540'
year: '2023'
...
---
_id: '46578'
abstract:
- lang: eng
text: 'Multiobjective optimization plays an increasingly important role in modern
applications, where several criteria are often of equal importance. The task in
multiobjective optimization and multiobjective optimal control is therefore to
compute the set of optimal compromises (the Pareto set) between the conflicting
objectives. The advances in algorithms and the increasing interest in Pareto-optimal
solutions have led to a wide range of new applications related to optimal and
feedback control - potentially with non-smoothness both on the level of the objectives
or in the system dynamics. This results in new challenges such as dealing with
expensive models (e.g., governed by partial differential equations (PDEs)) and
developing dedicated algorithms handling the non-smoothness. Since in contrast
to single-objective optimization, the Pareto set generally consists of an infinite
number of solutions, the computational effort can quickly become challenging,
which is particularly problematic when the objectives are costly to evaluate or
when a solution has to be presented very quickly. This article gives an overview
of recent developments in the field of multiobjective optimization of non-smooth
PDE-constrained problems. In particular we report on the advances achieved within
Project 2 "Multiobjective Optimization of Non-Smooth PDE-Constrained Problems
- Switches, State Constraints and Model Order Reduction" of the DFG Priority Programm
1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation
and Hierarchical Optimization".'
author:
- first_name: Marco
full_name: Bernreuther, Marco
last_name: Bernreuther
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Georg
full_name: Müller, Georg
last_name: Müller
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Stefan
full_name: Volkwein, Stefan
last_name: Volkwein
citation:
ama: Bernreuther M, Dellnitz M, Gebken B, et al. Multiobjective Optimization of
Non-Smooth PDE-Constrained Problems. arXiv:230801113. Published online
2023.
apa: Bernreuther, M., Dellnitz, M., Gebken, B., Müller, G., Peitz, S., Sonntag,
K., & Volkwein, S. (2023). Multiobjective Optimization of Non-Smooth PDE-Constrained
Problems. In arXiv:2308.01113.
bibtex: '@article{Bernreuther_Dellnitz_Gebken_Müller_Peitz_Sonntag_Volkwein_2023,
title={Multiobjective Optimization of Non-Smooth PDE-Constrained Problems}, journal={arXiv:2308.01113},
author={Bernreuther, Marco and Dellnitz, Michael and Gebken, Bennet and Müller,
Georg and Peitz, Sebastian and Sonntag, Konstantin and Volkwein, Stefan}, year={2023}
}'
chicago: Bernreuther, Marco, Michael Dellnitz, Bennet Gebken, Georg Müller, Sebastian
Peitz, Konstantin Sonntag, and Stefan Volkwein. “Multiobjective Optimization of
Non-Smooth PDE-Constrained Problems.” ArXiv:2308.01113, 2023.
ieee: M. Bernreuther et al., “Multiobjective Optimization of Non-Smooth PDE-Constrained
Problems,” arXiv:2308.01113. 2023.
mla: Bernreuther, Marco, et al. “Multiobjective Optimization of Non-Smooth PDE-Constrained
Problems.” ArXiv:2308.01113, 2023.
short: M. Bernreuther, M. Dellnitz, B. Gebken, G. Müller, S. Peitz, K. Sonntag,
S. Volkwein, ArXiv:2308.01113 (2023).
date_created: 2023-08-21T05:50:12Z
date_updated: 2024-02-21T12:22:20Z
department:
- _id: '655'
- _id: '101'
external_id:
arxiv:
- '2308.01113'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2308.01113
oa: '1'
publication: arXiv:2308.01113
status: public
title: Multiobjective Optimization of Non-Smooth PDE-Constrained Problems
type: preprint
user_id: '47427'
year: '2023'
...
---
_id: '45191'
alternative_title:
- An Interdisciplinary Concept of Digital Working Environments in Industry 4.0
citation:
ama: Gräßler I, Maier GW, Steffen E, Roesmann D, eds. The Digital Twin of Humans.
Springer International Publishing; 2023. doi:10.1007/978-3-031-26104-6
apa: Gräßler, I., Maier, G. W., Steffen, E., & Roesmann, D. (Eds.). (2023).
The Digital Twin of Humans. Springer International Publishing. https://doi.org/10.1007/978-3-031-26104-6
bibtex: '@book{Gräßler_Maier_Steffen_Roesmann_2023, place={Cham}, title={The Digital
Twin of Humans}, DOI={10.1007/978-3-031-26104-6},
publisher={Springer International Publishing}, year={2023} }'
chicago: 'Gräßler, Iris, Günter W. Maier, Eckhard Steffen, and Daniel Roesmann,
eds. The Digital Twin of Humans. Cham: Springer International Publishing,
2023. https://doi.org/10.1007/978-3-031-26104-6.'
ieee: 'I. Gräßler, G. W. Maier, E. Steffen, and D. Roesmann, Eds., The Digital
Twin of Humans. Cham: Springer International Publishing, 2023.'
mla: Gräßler, Iris, et al., editors. The Digital Twin of Humans. Springer
International Publishing, 2023, doi:10.1007/978-3-031-26104-6.
short: I. Gräßler, G.W. Maier, E. Steffen, D. Roesmann, eds., The Digital Twin of
Humans, Springer International Publishing, Cham, 2023.
date_created: 2023-05-22T10:24:10Z
date_updated: 2024-03-25T09:07:55Z
department:
- _id: '542'
- _id: '152'
doi: 10.1007/978-3-031-26104-6
editor:
- first_name: Iris
full_name: Gräßler, Iris
id: '47565'
last_name: Gräßler
orcid: 0000-0001-5765-971X
- first_name: Günter W.
full_name: Maier, Günter W.
last_name: Maier
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
- first_name: Daniel
full_name: Roesmann, Daniel
id: '54680'
last_name: Roesmann
language:
- iso: eng
place: Cham
publication_identifier:
isbn:
- '9783031261039'
- '9783031261046'
publication_status: published
publisher: Springer International Publishing
quality_controlled: '1'
status: public
title: The Digital Twin of Humans
type: book_editor
user_id: '5905'
year: '2023'
...