---
_id: '32097'
author:
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Yannick
full_name: Guedes Bonthonneau, Yannick
last_name: Guedes Bonthonneau
- first_name: Colin
full_name: Guillarmou, Colin
last_name: Guillarmou
citation:
ama: Weich T, Guedes Bonthonneau Y, Guillarmou C. SRB Measures of Anosov Actions.
Journal of Differential Geometry (to appear) -- arXiv:210312127. Published
online 2024.
apa: Weich, T., Guedes Bonthonneau, Y., & Guillarmou, C. (2024). SRB Measures
of Anosov Actions. Journal of Differential Geometry (to Appear) -- ArXiv:2103.12127.
bibtex: '@article{Weich_Guedes Bonthonneau_Guillarmou_2024, title={SRB Measures
of Anosov Actions}, journal={Journal of Differential Geometry (to appear) --
arXiv:2103.12127}, author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou,
Colin}, year={2024} }'
chicago: Weich, Tobias, Yannick Guedes Bonthonneau, and Colin Guillarmou. “SRB Measures
of Anosov Actions.” Journal of Differential Geometry (to Appear) -- ArXiv:2103.12127,
2024.
ieee: T. Weich, Y. Guedes Bonthonneau, and C. Guillarmou, “SRB Measures of Anosov
Actions,” Journal of Differential Geometry (to appear) -- arXiv:2103.12127,
2024.
mla: Weich, Tobias, et al. “SRB Measures of Anosov Actions.” Journal of Differential
Geometry (to Appear) -- ArXiv:2103.12127, 2024.
short: T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, Journal of Differential Geometry
(to Appear) -- ArXiv:2103.12127 (2024).
date_created: 2022-06-22T09:56:23Z
date_updated: 2023-12-21T09:47:22Z
ddc:
- '510'
department:
- _id: '10'
- _id: '623'
- _id: '548'
external_id:
arxiv:
- https://arxiv.org/abs/2103.12127
file:
- access_level: open_access
content_type: application/pdf
creator: weich
date_created: 2022-06-22T09:56:08Z
date_updated: 2022-06-22T09:56:08Z
file_id: '32098'
file_name: 2103.12127.pdf
file_size: 745870
relation: main_file
file_date_updated: 2022-06-22T09:56:08Z
has_accepted_license: '1'
language:
- iso: eng
oa: '1'
publication: Journal of Differential Geometry (to appear) -- arXiv:2103.12127
status: public
title: SRB Measures of Anosov Actions
type: journal_article
user_id: '49178'
year: '2024'
...
---
_id: '46469'
abstract:
- lang: eng
text: 'We show how to learn discrete field theories from observational data of fields
on a space-time lattice. For this, we train a neural network model of a discrete
Lagrangian density such that the discrete Euler--Lagrange equations are consistent
with the given training data. We, thus, obtain a structure-preserving machine
learning architecture. Lagrangian densities are not uniquely defined by the solutions
of a field theory. We introduce a technique to derive regularisers for the training
process which optimise numerical regularity of the discrete field theory. Minimisation
of the regularisers guarantees that close to the training data the discrete field
theory behaves robust and efficient when used in numerical simulations. Further,
we show how to identify structurally simple solutions of the underlying continuous
field theory such as travelling waves. This is possible even when travelling waves
are not present in the training data. This is compared to data-driven model order
reduction based approaches, which struggle to identify suitable latent spaces
containing structurally simple solutions when these are not present in the training
data. Ideas are demonstrated on examples based on the wave equation and the Schrödinger
equation. '
article_number: '013104'
article_type: original
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: Offen C, Ober-Blöbaum S. Learning of discrete models of variational PDEs from
data. Chaos. 2024;34(1). doi:10.1063/5.0172287
apa: Offen, C., & Ober-Blöbaum, S. (2024). Learning of discrete models of variational
PDEs from data. Chaos, 34(1), Article 013104. https://doi.org/10.1063/5.0172287
bibtex: '@article{Offen_Ober-Blöbaum_2024, title={Learning of discrete models of
variational PDEs from data}, volume={34}, DOI={10.1063/5.0172287},
number={1013104}, journal={Chaos}, publisher={AIP Publishing}, author={Offen,
Christian and Ober-Blöbaum, Sina}, year={2024} }'
chicago: Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of
Variational PDEs from Data.” Chaos 34, no. 1 (2024). https://doi.org/10.1063/5.0172287.
ieee: 'C. Offen and S. Ober-Blöbaum, “Learning of discrete models of variational
PDEs from data,” Chaos, vol. 34, no. 1, Art. no. 013104, 2024, doi: 10.1063/5.0172287.'
mla: Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational
PDEs from Data.” Chaos, vol. 34, no. 1, 013104, AIP Publishing, 2024, doi:10.1063/5.0172287.
short: C. Offen, S. Ober-Blöbaum, Chaos 34 (2024).
date_created: 2023-08-10T08:24:48Z
date_updated: 2024-01-09T11:29:06Z
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'
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: '50554'
author:
- first_name: Susanne
full_name: Prediger, Susanne
last_name: Prediger
- first_name: Lena
full_name: Wessel, Lena
id: '85190'
last_name: Wessel
citation:
ama: 'Prediger S, Wessel L. 31 Sprachbildung im berufsbezogenen Mathematikunterricht.
In: Efing C, Kalkavan-Aydin Z, eds. Berufs-und Fachsprache Deutsch in Wissenschaft
und Praxis. Vol Band 3. DaZ-Handbücher. DE GRUYTER; 2024:363-372.'
apa: 'Prediger, S., & Wessel, L. (2024). 31 Sprachbildung im berufsbezogenen
Mathematikunterricht. In C. Efing & Z. Kalkavan-Aydin (Eds.), Berufs-und
Fachsprache Deutsch in Wissenschaft und Praxis: Vol. Band 3 (pp. 363–372).
DE GRUYTER.'
bibtex: '@inbook{Prediger_Wessel_2024, place={Berlin}, series={DaZ-Handbücher},
title={31 Sprachbildung im berufsbezogenen Mathematikunterricht.}, volume={Band
3}, booktitle={Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis}, publisher={DE
GRUYTER}, author={Prediger, Susanne and Wessel, Lena}, editor={Efing, Christian
and Kalkavan-Aydin, Zeynep}, year={2024}, pages={363–372}, collection={DaZ-Handbücher}
}'
chicago: 'Prediger, Susanne, and Lena Wessel. “31 Sprachbildung im berufsbezogenen
Mathematikunterricht.” In Berufs-und Fachsprache Deutsch in Wissenschaft und
Praxis, edited by Christian Efing and Zeynep Kalkavan-Aydin, Band 3:363–72.
DaZ-Handbücher. Berlin: DE GRUYTER, 2024.'
ieee: 'S. Prediger and L. Wessel, “31 Sprachbildung im berufsbezogenen Mathematikunterricht.,”
in Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, vol. Band
3, C. Efing and Z. Kalkavan-Aydin, Eds. Berlin: DE GRUYTER, 2024, pp. 363–372.'
mla: Prediger, Susanne, and Lena Wessel. “31 Sprachbildung im berufsbezogenen Mathematikunterricht.”
Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis, edited by Christian
Efing and Zeynep Kalkavan-Aydin, vol. Band 3, DE GRUYTER, 2024, pp. 363–72.
short: 'S. Prediger, L. Wessel, in: C. Efing, Z. Kalkavan-Aydin (Eds.), Berufs-und
Fachsprache Deutsch in Wissenschaft und Praxis, DE GRUYTER, Berlin, 2024, pp.
363–372.'
date_created: 2024-01-17T10:58:04Z
date_updated: 2024-01-17T11:07:21Z
department:
- _id: '34'
- _id: '10'
- _id: '643'
editor:
- first_name: Christian
full_name: Efing, Christian
last_name: Efing
- first_name: Zeynep
full_name: Kalkavan-Aydin, Zeynep
last_name: Kalkavan-Aydin
language:
- iso: ger
main_file_link:
- open_access: '1'
url: https://www.degruyter.com/document/doi/10.1515/9783110745504/pdf?licenseType=restricted#page=381
oa: '1'
page: 363-372
place: Berlin
publication: Berufs-und Fachsprache Deutsch in Wissenschaft und Praxis
publication_identifier:
isbn:
- 978-3-11-074544-3
publication_status: published
publisher: DE GRUYTER
series_title: DaZ-Handbücher
status: public
title: 31 Sprachbildung im berufsbezogenen Mathematikunterricht.
type: book_chapter
user_id: '37888'
volume: Band 3
year: '2024'
...
---
_id: '51208'
abstract:
- lang: eng
text: AbstractApproximation of subdifferentials
is one of the main tasks when computing descent directions for nonsmooth optimization
problems. In this article, we propose a bisection method for weakly lower semismooth
functions which is able to compute new subgradients that improve a given approximation
in case a direction with insufficient descent was computed. Combined with a recently
proposed deterministic gradient sampling approach, this yields a deterministic
and provably convergent way to approximate subdifferentials for computing descent
directions.
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
citation:
ama: Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth
optimization. Computational Optimization and Applications. Published online
2024. doi:10.1007/s10589-024-00552-0
apa: Gebken, B. (2024). A note on the convergence of deterministic gradient sampling
in nonsmooth optimization. Computational Optimization and Applications.
https://doi.org/10.1007/s10589-024-00552-0
bibtex: '@article{Gebken_2024, title={A note on the convergence of deterministic
gradient sampling in nonsmooth optimization}, DOI={10.1007/s10589-024-00552-0},
journal={Computational Optimization and Applications}, publisher={Springer Science
and Business Media LLC}, author={Gebken, Bennet}, year={2024} }'
chicago: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
in Nonsmooth Optimization.” Computational Optimization and Applications,
2024. https://doi.org/10.1007/s10589-024-00552-0.
ieee: 'B. Gebken, “A note on the convergence of deterministic gradient sampling
in nonsmooth optimization,” Computational Optimization and Applications,
2024, doi: 10.1007/s10589-024-00552-0.'
mla: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
in Nonsmooth Optimization.” Computational Optimization and Applications,
Springer Science and Business Media LLC, 2024, doi:10.1007/s10589-024-00552-0.
short: B. Gebken, Computational Optimization and Applications (2024).
date_created: 2024-02-07T07:23:23Z
date_updated: 2024-02-08T08:05:54Z
department:
- _id: '101'
doi: 10.1007/s10589-024-00552-0
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
language:
- iso: eng
publication: Computational Optimization and Applications
publication_identifier:
issn:
- 0926-6003
- 1573-2894
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A note on the convergence of deterministic gradient sampling in nonsmooth optimization
type: journal_article
user_id: '32643'
year: '2024'
...
---
_id: '51204'
abstract:
- lang: eng
text: "Given a real semisimple connected Lie group $G$ and a discrete torsion-free\r\nsubgroup
$\\Gamma < G$ we prove a precise connection between growth rates of the\r\ngroup
$\\Gamma$, polyhedral bounds on the joint spectrum of the ring of\r\ninvariant
differential operators, and the decay of matrix coefficients. In\r\nparticular,
this allows us to completely characterize temperedness of\r\n$L^2(\\Gamma\\backslash
G)$ in this general setting."
author:
- first_name: Christopher
full_name: Lutsko, Christopher
last_name: Lutsko
- first_name: Tobias
full_name: Weich, Tobias
last_name: Weich
- first_name: Lasse Lennart
full_name: Wolf, Lasse Lennart
id: '45027'
last_name: Wolf
citation:
ama: Lutsko C, Weich T, Wolf LL. Polyhedral bounds on the joint spectrum and temperedness
of locally symmetric spaces. arXiv:240202530. Published online 2024.
apa: Lutsko, C., Weich, T., & Wolf, L. L. (2024). Polyhedral bounds on the joint
spectrum and temperedness of locally symmetric spaces. In arXiv:2402.02530.
bibtex: '@article{Lutsko_Weich_Wolf_2024, title={Polyhedral bounds on the joint
spectrum and temperedness of locally symmetric spaces}, journal={arXiv:2402.02530},
author={Lutsko, Christopher and Weich, Tobias and Wolf, Lasse Lennart}, year={2024}
}'
chicago: Lutsko, Christopher, Tobias Weich, and Lasse Lennart Wolf. “Polyhedral
Bounds on the Joint Spectrum and Temperedness of Locally Symmetric Spaces.” ArXiv:2402.02530,
2024.
ieee: C. Lutsko, T. Weich, and L. L. Wolf, “Polyhedral bounds on the joint spectrum
and temperedness of locally symmetric spaces,” arXiv:2402.02530. 2024.
mla: Lutsko, Christopher, et al. “Polyhedral Bounds on the Joint Spectrum and Temperedness
of Locally Symmetric Spaces.” ArXiv:2402.02530, 2024.
short: C. Lutsko, T. Weich, L.L. Wolf, ArXiv:2402.02530 (2024).
date_created: 2024-02-06T20:35:36Z
date_updated: 2024-02-11T19:56:35Z
department:
- _id: '10'
- _id: '623'
- _id: '548'
external_id:
arxiv:
- '2402.02530'
language:
- iso: eng
publication: arXiv:2402.02530
status: public
title: Polyhedral bounds on the joint spectrum and temperedness of locally symmetric
spaces
type: preprint
user_id: '49178'
year: '2024'
...
---
_id: '51374'
article_number: '110319'
author:
- first_name: David
full_name: Hasler, David
last_name: Hasler
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Oliver
full_name: Siebert, Oliver
last_name: Siebert
citation:
ama: Hasler D, Hinrichs B, Siebert O. Non-Fock ground states in the translation-invariant
Nelson model revisited non-perturbatively. Journal of Functional Analysis.
2024;286(7). doi:10.1016/j.jfa.2024.110319
apa: Hasler, D., Hinrichs, B., & Siebert, O. (2024). Non-Fock ground states
in the translation-invariant Nelson model revisited non-perturbatively. Journal
of Functional Analysis, 286(7), Article 110319. https://doi.org/10.1016/j.jfa.2024.110319
bibtex: '@article{Hasler_Hinrichs_Siebert_2024, title={Non-Fock ground states in
the translation-invariant Nelson model revisited non-perturbatively}, volume={286},
DOI={10.1016/j.jfa.2024.110319},
number={7110319}, journal={Journal of Functional Analysis}, publisher={Elsevier
BV}, author={Hasler, David and Hinrichs, Benjamin and Siebert, Oliver}, year={2024}
}'
chicago: Hasler, David, Benjamin Hinrichs, and Oliver Siebert. “Non-Fock Ground
States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively.”
Journal of Functional Analysis 286, no. 7 (2024). https://doi.org/10.1016/j.jfa.2024.110319.
ieee: 'D. Hasler, B. Hinrichs, and O. Siebert, “Non-Fock ground states in the translation-invariant
Nelson model revisited non-perturbatively,” Journal of Functional Analysis,
vol. 286, no. 7, Art. no. 110319, 2024, doi: 10.1016/j.jfa.2024.110319.'
mla: Hasler, David, et al. “Non-Fock Ground States in the Translation-Invariant
Nelson Model Revisited Non-Perturbatively.” Journal of Functional Analysis,
vol. 286, no. 7, 110319, Elsevier BV, 2024, doi:10.1016/j.jfa.2024.110319.
short: D. Hasler, B. Hinrichs, O. Siebert, Journal of Functional Analysis 286 (2024).
date_created: 2024-02-18T12:31:28Z
date_updated: 2024-02-18T12:32:23Z
department:
- _id: '799'
doi: 10.1016/j.jfa.2024.110319
extern: '1'
external_id:
arxiv:
- '2302.06998'
intvolume: ' 286'
issue: '7'
keyword:
- Analysis
language:
- iso: eng
publication: Journal of Functional Analysis
publication_identifier:
issn:
- 0022-1236
publication_status: published
publisher: Elsevier BV
status: public
title: Non-Fock ground states in the translation-invariant Nelson model revisited
non-perturbatively
type: journal_article
user_id: '99427'
volume: 286
year: '2024'
...
---
_id: '32101'
author:
- first_name: Tobias
full_name: Weich, Tobias
id: '49178'
last_name: Weich
orcid: 0000-0002-9648-6919
- first_name: Yannick
full_name: Guedes Bonthonneau, Yannick
last_name: Guedes Bonthonneau
- first_name: Colin
full_name: Guillarmou, Colin
last_name: Guillarmou
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
citation:
ama: Weich T, Guedes Bonthonneau Y, Guillarmou C, Hilgert J. Ruelle-Taylor resonaces
of Anosov actions. J Europ Math Soc. Published online 2024:1-36.
apa: Weich, T., Guedes Bonthonneau, Y., Guillarmou, C., & Hilgert, J. (2024).
Ruelle-Taylor resonaces of Anosov actions. J. Europ. Math. Soc., 1–36.
bibtex: '@article{Weich_Guedes Bonthonneau_Guillarmou_Hilgert_2024, title={Ruelle-Taylor
resonaces of Anosov actions}, journal={J. Europ. Math. Soc.}, author={Weich, Tobias
and Guedes Bonthonneau, Yannick and Guillarmou, Colin and Hilgert, Joachim}, year={2024},
pages={1–36} }'
chicago: Weich, Tobias, Yannick Guedes Bonthonneau, Colin Guillarmou, and Joachim
Hilgert. “Ruelle-Taylor Resonaces of Anosov Actions.” J. Europ. Math. Soc.,
2024, 1–36.
ieee: T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, and J. Hilgert, “Ruelle-Taylor
resonaces of Anosov actions,” J. Europ. Math. Soc., pp. 1–36, 2024.
mla: Weich, Tobias, et al. “Ruelle-Taylor Resonaces of Anosov Actions.” J. Europ.
Math. Soc., 2024, pp. 1–36.
short: T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, J. Hilgert, J. Europ. Math.
Soc. (2024) 1–36.
date_created: 2022-06-22T09:56:51Z
date_updated: 2024-02-19T06:25:13Z
ddc:
- '510'
department:
- _id: '10'
- _id: '623'
- _id: '548'
- _id: '91'
file:
- access_level: open_access
content_type: application/pdf
creator: weich
date_created: 2022-06-22T09:56:47Z
date_updated: 2022-06-22T09:56:47Z
file_id: '32102'
file_name: 2007.14275.pdf
file_size: 796410
relation: main_file
file_date_updated: 2022-06-22T09:56:47Z
has_accepted_license: '1'
language:
- iso: eng
oa: '1'
page: 1-36
publication: J. Europ. Math. Soc.
publication_status: published
status: public
title: Ruelle-Taylor resonaces of Anosov actions
type: journal_article
user_id: '49063'
year: '2024'
...
---
_id: '51501'
author:
- first_name: Joachim
full_name: Hilgert, Joachim
id: '220'
last_name: Hilgert
citation:
ama: Hilgert J. Quantum-Classical Correspondences for Locally Symmetric Spaces.
Published online 2024.
apa: Hilgert, J. (2024). Quantum-Classical Correspondences for Locally Symmetric
Spaces.
bibtex: '@article{Hilgert_2024, title={Quantum-Classical Correspondences for Locally
Symmetric Spaces}, author={Hilgert, Joachim}, year={2024} }'
chicago: Hilgert, Joachim. “Quantum-Classical Correspondences for Locally Symmetric
Spaces,” 2024.
ieee: J. Hilgert, “Quantum-Classical Correspondences for Locally Symmetric Spaces.”
2024.
mla: Hilgert, Joachim. Quantum-Classical Correspondences for Locally Symmetric
Spaces. 2024.
short: J. Hilgert, (2024).
date_created: 2024-02-19T10:31:51Z
date_updated: 2024-02-19T10:32:07Z
department:
- _id: '91'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2303.00578.pdf
oa: '1'
publication_status: published
status: public
title: Quantum-Classical Correspondences for Locally Symmetric Spaces
type: preprint
user_id: '49063'
year: '2024'
...
---
_id: '46019'
abstract:
- lang: eng
text: We derive efficient algorithms to compute weakly Pareto optimal solutions
for smooth, convex and unconstrained multiobjective optimization problems in general
Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical
system in the multiobjective setting, which trajectories converge weakly to Pareto
optimal solutions. Discretization of this system yields an inertial multiobjective
algorithm which generates sequences that converge weakly to Pareto optimal solutions.
We employ Nesterov acceleration to define an algorithm with an improved convergence
rate compared to the plain multiobjective steepest descent method (Algorithm 1).
A further improvement in terms of efficiency is achieved by avoiding the solution
of a quadratic subproblem to compute a common step direction for all objective
functions, which is usually required in first-order methods. Using a different
discretization of our inertial gradient-like dynamical system, we obtain an accelerated
multiobjective gradient method that does not require the solution of a subproblem
in each step (Algorithm 2). While this algorithm does not converge in general,
it yields good results on test problems while being faster than standard steepest
descent.
author:
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Sonntag K, Peitz S. Fast Multiobjective Gradient Methods with Nesterov Acceleration
via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications.
Published online 2024. doi:10.1007/s10957-024-02389-3
apa: Sonntag, K., & Peitz, S. (2024). Fast Multiobjective Gradient Methods with
Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization
Theory and Applications. https://doi.org/10.1007/s10957-024-02389-3
bibtex: '@article{Sonntag_Peitz_2024, title={Fast Multiobjective Gradient Methods
with Nesterov Acceleration via Inertial Gradient-Like Systems}, DOI={10.1007/s10957-024-02389-3},
journal={Journal of Optimization Theory and Applications}, publisher={Springer},
author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024} }'
chicago: Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient
Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal
of Optimization Theory and Applications, 2024. https://doi.org/10.1007/s10957-024-02389-3.
ieee: 'K. Sonntag and S. Peitz, “Fast Multiobjective Gradient Methods with Nesterov
Acceleration via Inertial Gradient-Like Systems,” Journal of Optimization Theory
and Applications, 2024, doi: 10.1007/s10957-024-02389-3.'
mla: Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods
with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal of
Optimization Theory and Applications, Springer, 2024, doi:10.1007/s10957-024-02389-3.
short: K. Sonntag, S. Peitz, Journal of Optimization Theory and Applications (2024).
date_created: 2023-07-12T06:35:58Z
date_updated: 2024-02-21T10:13:33Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s10957-024-02389-3
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf
oa: '1'
publication: Journal of Optimization Theory and Applications
publication_status: published
publisher: Springer
status: public
title: Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial
Gradient-Like Systems
type: journal_article
user_id: '56399'
year: '2024'
...
---
_id: '51334'
abstract:
- lang: eng
text: The efficient optimization method for locally Lipschitz continuous multiobjective
optimization problems from [1] is extended from finite-dimensional problems to
general Hilbert spaces. The method iteratively computes Pareto critical points,
where in each iteration, an approximation of the subdifferential is computed in
an efficient manner and then used to compute a common descent direction for all
objective functions. To prove convergence, we present some new optimality results
for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these,
we can show that every accumulation point of the sequence generated by our algorithm
is Pareto critical under common assumptions. Computational efficiency for finding
Pareto critical points is numerically demonstrated for multiobjective optimal
control of an obstacle problem.
author:
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- 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: Stefan
full_name: Volkwein, Stefan
last_name: Volkwein
citation:
ama: Sonntag K, Gebken B, Müller G, Peitz S, Volkwein S. A Descent Method for Nonsmooth
Multiobjective Optimization in Hilbert Spaces. arXiv:240206376. Published
online 2024.
apa: Sonntag, K., Gebken, B., Müller, G., Peitz, S., & Volkwein, S. (2024).
A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.
In arXiv:2402.06376.
bibtex: '@article{Sonntag_Gebken_Müller_Peitz_Volkwein_2024, title={A Descent Method
for Nonsmooth Multiobjective Optimization in Hilbert Spaces}, journal={arXiv:2402.06376},
author={Sonntag, Konstantin and Gebken, Bennet and Müller, Georg and Peitz, Sebastian
and Volkwein, Stefan}, year={2024} }'
chicago: Sonntag, Konstantin, Bennet Gebken, Georg Müller, Sebastian Peitz, and
Stefan Volkwein. “A Descent Method for Nonsmooth Multiobjective Optimization in
Hilbert Spaces.” ArXiv:2402.06376, 2024.
ieee: K. Sonntag, B. Gebken, G. Müller, S. Peitz, and S. Volkwein, “A Descent Method
for Nonsmooth Multiobjective Optimization in Hilbert Spaces,” arXiv:2402.06376.
2024.
mla: Sonntag, Konstantin, et al. “A Descent Method for Nonsmooth Multiobjective
Optimization in Hilbert Spaces.” ArXiv:2402.06376, 2024.
short: K. Sonntag, B. Gebken, G. Müller, S. Peitz, S. Volkwein, ArXiv:2402.06376
(2024).
date_created: 2024-02-13T09:35:26Z
date_updated: 2024-02-21T10:21:03Z
department:
- _id: '101'
- _id: '655'
external_id:
arxiv:
- "\t2402.06376"
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2402.06376
oa: '1'
publication: arXiv:2402.06376
status: public
title: A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces
type: preprint
user_id: '56399'
year: '2024'
...
---
_id: '51841'
abstract:
- lang: ger
text: 'athematische Kompetenzen digital zu fördern und digitale Kompetenzen mathematisch
zu fördern – dies ist eine Forderung der neuen Bildungsstandards mit Blick auf
eine Bildung in der digitalen Welt. Gerade das Potenzial digitaler Medien für
das fachliche Lernen wurde in vielen Studien bestätigt. Eine sinnvoll gestaltete
Einbettung digitaler Medien bietet die Chance, allen fünf Prinzipien eines guten
Unterrichts gerecht zu werden: Verstehensorientierung, Durchgängigkeit, kognitive
Aktivierung, Lernendenorientierung & Adaptivität und Kommunikationsförderung.
Die flächendeckende Nutzung digitaler Medien etabliert sich bislang nur zögerlich.
Aber wie können wir Lehrkräfte stärken, digitale Medien sinnvoll einzusetzen?
Wir möchten hier die Bandbreite der Möglichkeiten an Beispielen verdeutlichen,
ihren Einsatz motivieren und Wege für einen guten Unterricht aufzeigen.'
article_type: original
author:
- first_name: Bärbel
full_name: Barzel, Bärbel
last_name: Barzel
- first_name: Gilbert
full_name: Greefrath, Gilbert
last_name: Greefrath
- first_name: Mareike
full_name: Nagel, Mareike
last_name: Nagel
- first_name: Max
full_name: Hoffmann, Max
id: '32202'
last_name: Hoffmann
orcid: 0000-0002-6964-7123
citation:
ama: Barzel B, Greefrath G, Nagel M, Hoffmann M. Digitalisierung als Chance für
alle Prinzipien guten Unterrichts. mathematik lehren. 2024;242:42-47.
apa: Barzel, B., Greefrath, G., Nagel, M., & Hoffmann, M. (2024). Digitalisierung
als Chance für alle Prinzipien guten Unterrichts. mathematik lehren, 242,
42–47.
bibtex: '@article{Barzel_Greefrath_Nagel_Hoffmann_2024, title={Digitalisierung als
Chance für alle Prinzipien guten Unterrichts}, volume={242}, journal={mathematik
lehren}, author={Barzel, Bärbel and Greefrath, Gilbert and Nagel, Mareike and
Hoffmann, Max}, year={2024}, pages={42–47} }'
chicago: 'Barzel, Bärbel, Gilbert Greefrath, Mareike Nagel, and Max Hoffmann. “Digitalisierung
als Chance für alle Prinzipien guten Unterrichts.” mathematik lehren 242
(2024): 42–47.'
ieee: B. Barzel, G. Greefrath, M. Nagel, and M. Hoffmann, “Digitalisierung als Chance
für alle Prinzipien guten Unterrichts,” mathematik lehren, vol. 242, pp.
42–47, 2024.
mla: Barzel, Bärbel, et al. “Digitalisierung als Chance für alle Prinzipien guten
Unterrichts.” mathematik lehren, vol. 242, 2024, pp. 42–47.
short: B. Barzel, G. Greefrath, M. Nagel, M. Hoffmann, mathematik lehren 242 (2024)
42–47.
date_created: 2024-02-25T20:58:51Z
date_updated: 2024-02-25T21:01:03Z
ddc:
- '510'
- '370'
department:
- _id: '97'
- _id: '643'
file:
- access_level: closed
content_type: application/pdf
creator: maxh
date_created: 2024-02-25T20:55:29Z
date_updated: 2024-02-25T20:55:29Z
file_id: '51842'
file_name: Barzel_etal_2024_DigitalisierungalsChancefrallePrinzipiengut.pdf
file_size: 1410541
relation: main_file
success: 1
file_date_updated: 2024-02-25T20:55:29Z
has_accepted_license: '1'
intvolume: ' 242'
language:
- iso: ger
main_file_link:
- open_access: '1'
url: https://www.friedrich-verlag.de/shop/mwdownloads/download/link/id/114555/
oa: '1'
page: 42 - 47
publication: mathematik lehren
publication_status: published
status: public
title: Digitalisierung als Chance für alle Prinzipien guten Unterrichts
type: journal_article
user_id: '32202'
volume: 242
year: '2024'
...
---
_id: '52342'
abstract:
- lang: eng
text: 'We introduce the concept of a k-token signed graph and study some of its
combinatorial and algebraic properties. We prove that two switching isomorphic
signed graphs have switching isomorphic token graphs. Moreover, we show that the
Laplacian spectrum of a balanced signed graph is contained in the Laplacian spectra
of its k-token signed graph. Besides, we introduce and study the unbalance level
of a signed graph, which is a new parameter that measures how far a signed graph
is from being balanced. Moreover, we study the relation between the frustration
index and the unbalance level of signed graphs and their token signed graphs. '
author:
- first_name: C.
full_name: Dalfó, C.
last_name: Dalfó
- first_name: M. A.
full_name: Fiol, M. A.
last_name: Fiol
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
citation:
ama: Dalfó C, Fiol MA, Steffen E. On token signed graphs. arXiv:240302924.
Published online 2024.
apa: Dalfó, C., Fiol, M. A., & Steffen, E. (2024). On token signed graphs. In
arXiv:2403.02924.
bibtex: '@article{Dalfó_Fiol_Steffen_2024, title={On token signed graphs}, journal={arXiv:2403.02924},
author={Dalfó, C. and Fiol, M. A. and Steffen, Eckhard}, year={2024} }'
chicago: Dalfó, C., M. A. Fiol, and Eckhard Steffen. “On Token Signed Graphs.” ArXiv:2403.02924,
2024.
ieee: C. Dalfó, M. A. Fiol, and E. Steffen, “On token signed graphs,” arXiv:2403.02924.
2024.
mla: Dalfó, C., et al. “On Token Signed Graphs.” ArXiv:2403.02924, 2024.
short: C. Dalfó, M.A. Fiol, E. Steffen, ArXiv:2403.02924 (2024).
date_created: 2024-03-07T08:48:39Z
date_updated: 2024-03-07T08:50:33Z
department:
- _id: '542'
external_id:
arxiv:
- '2403.02924'
language:
- iso: eng
publication: arXiv:2403.02924
status: public
title: On token signed graphs
type: preprint
user_id: '15540'
year: '2024'
...
---
_id: '52691'
abstract:
- lang: eng
text: "We prove Feynman-Kac formulas for the semigroups generated by selfadjoint\r\noperators
in a class containing Fr\\\"ohlich Hamiltonians known from solid state\r\nphysics.
The latter model multi-polarons, i.e., a fixed number of quantum\r\nmechanical
electrons moving in a polarizable crystal and interacting with the\r\nquantized
phonon field generated by the crystal's vibrational modes. Both the\r\nelectrons
and phonons can be confined to suitable open subsets of Euclidean\r\nspace. We
also include possibly very singular magnetic vector potentials and\r\nelectrostatic
potentials. Our Feynman-Kac formulas comprise Fock space\r\noperator-valued multiplicative
functionals and can be applied to every vector\r\nin the underlying Hilbert space.
In comparison to the renormalized Nelson\r\nmodel, for which analogous Feynman-Kac
formulas are known, the analysis of the\r\ncreation and annihilation terms in
the multiplicative functionals requires\r\nnovel ideas to overcome difficulties
caused by the phonon dispersion relation\r\nbeing constant. Getting these terms
under control and generalizing other\r\nconstruction steps so as to cover confined
systems are the main achievements of\r\nthis article."
author:
- first_name: Benjamin
full_name: Hinrichs, Benjamin
id: '99427'
last_name: Hinrichs
orcid: 0000-0001-9074-1205
- first_name: Oliver
full_name: Matte, Oliver
last_name: Matte
citation:
ama: Hinrichs B, Matte O. Feynman-Kac formulas for semigroups generated by multi-polaron
Hamiltonians in magnetic fields and on general domains. arXiv:240312147.
Published online 2024.
apa: Hinrichs, B., & Matte, O. (2024). Feynman-Kac formulas for semigroups generated
by multi-polaron Hamiltonians in magnetic fields and on general domains. In arXiv:2403.12147.
bibtex: '@article{Hinrichs_Matte_2024, title={Feynman-Kac formulas for semigroups
generated by multi-polaron Hamiltonians in magnetic fields and on general domains},
journal={arXiv:2403.12147}, author={Hinrichs, Benjamin and Matte, Oliver}, year={2024}
}'
chicago: Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formulas for Semigroups
Generated by Multi-Polaron Hamiltonians in Magnetic Fields and on General Domains.”
ArXiv:2403.12147, 2024.
ieee: B. Hinrichs and O. Matte, “Feynman-Kac formulas for semigroups generated by
multi-polaron Hamiltonians in magnetic fields and on general domains,” arXiv:2403.12147.
2024.
mla: Hinrichs, Benjamin, and Oliver Matte. “Feynman-Kac Formulas for Semigroups
Generated by Multi-Polaron Hamiltonians in Magnetic Fields and on General Domains.”
ArXiv:2403.12147, 2024.
short: B. Hinrichs, O. Matte, ArXiv:2403.12147 (2024).
date_created: 2024-03-20T14:56:05Z
date_updated: 2024-03-20T14:56:50Z
department:
- _id: '799'
external_id:
arxiv:
- '2403.12147'
language:
- iso: eng
publication: arXiv:2403.12147
status: public
title: Feynman-Kac formulas for semigroups generated by multi-polaron Hamiltonians
in magnetic fields and on general domains
type: preprint
user_id: '99427'
year: '2024'
...
---
_id: '52726'
abstract:
- lang: eng
text: Heteroclinic structures organize global features of dynamical systems. We
analyse whether heteroclinic structures can arise in network dynamics with higher-order
interactions which describe the nonlinear interactions between three or more units.
We find that while commonly analysed model equations such as network dynamics
on undirected hypergraphs may be useful to describe local dynamics such as cluster
synchronization, they give rise to obstructions that allow to design of heteroclinic
structures in phase space. By contrast, directed hypergraphs break the homogeneity
and lead to vector fields that support heteroclinic structures.
article_type: original
author:
- first_name: Christian
full_name: Bick, Christian
last_name: Bick
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
citation:
ama: Bick C, von der Gracht S. Heteroclinic dynamics in network dynamical systems
with higher-order interactions. Journal of Complex Networks. 2024;12(2).
doi:10.1093/comnet/cnae009
apa: Bick, C., & von der Gracht, S. (2024). Heteroclinic dynamics in network
dynamical systems with higher-order interactions. Journal of Complex Networks,
12(2). https://doi.org/10.1093/comnet/cnae009
bibtex: '@article{Bick_von der Gracht_2024, title={Heteroclinic dynamics in network
dynamical systems with higher-order interactions}, volume={12}, DOI={10.1093/comnet/cnae009},
number={2}, journal={Journal of Complex Networks}, publisher={Oxford University
Press (OUP)}, author={Bick, Christian and von der Gracht, Sören}, year={2024}
}'
chicago: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network
Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks
12, no. 2 (2024). https://doi.org/10.1093/comnet/cnae009.
ieee: 'C. Bick and S. von der Gracht, “Heteroclinic dynamics in network dynamical
systems with higher-order interactions,” Journal of Complex Networks, vol.
12, no. 2, 2024, doi: 10.1093/comnet/cnae009.'
mla: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network
Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks,
vol. 12, no. 2, Oxford University Press (OUP), 2024, doi:10.1093/comnet/cnae009.
short: C. Bick, S. von der Gracht, Journal of Complex Networks 12 (2024).
date_created: 2024-03-22T09:04:57Z
date_updated: 2024-03-22T09:11:53Z
ddc:
- '510'
department:
- _id: '101'
doi: 10.1093/comnet/cnae009
external_id:
arxiv:
- '2309.02006'
file:
- access_level: closed
content_type: application/pdf
creator: svdg
date_created: 2024-03-22T09:06:07Z
date_updated: 2024-03-22T09:06:07Z
file_id: '52728'
file_name: heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf
file_size: 649155
relation: main_file
success: 1
file_date_updated: 2024-03-22T09:06:07Z
has_accepted_license: '1'
intvolume: ' 12'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
- Management Science and Operations Research
- Computer Networks and Communications
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf
oa: '1'
publication: Journal of Complex Networks
publication_identifier:
issn:
- 2051-1329
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Heteroclinic dynamics in network dynamical systems with higher-order interactions
type: journal_article
user_id: '97359'
volume: 12
year: '2024'
...
---
_id: '49905'
abstract:
- lang: eng
text: "For 0 ≤ t ≤ r let m(t, r) be the maximum number s such that every t-edge-connected
r-graph has s pairwise disjoint perfect matchings. There are only a few values
of m(t, r) known, for instance m(3, 3) = m(4, r) = 1, and m(t, r) ≤ r − 2 for
all t \x03 = 5,\r\nand m(t, r) ≤ r − 3 if r is even. We prove that m(2l, r) ≤
3l − 6 for every l ≥ 3 and r ≥ 2l."
author:
- first_name: Yulai
full_name: Ma, Yulai
id: '92748'
last_name: Ma
- first_name: Davide
full_name: Mattiolo, Davide
last_name: Mattiolo
- 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: Ma Y, Mattiolo D, Steffen E, Wolf IH. Edge-Connectivity and Pairwise Disjoint
Perfect Matchings in Regular Graphs. Combinatorica. 2024;44:429-440. doi:10.1007/s00493-023-00078-9
apa: Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2024). Edge-Connectivity
and Pairwise Disjoint Perfect Matchings in Regular Graphs. Combinatorica,
44, 429–440. https://doi.org/10.1007/s00493-023-00078-9
bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2024, title={Edge-Connectivity and Pairwise
Disjoint Perfect Matchings in Regular Graphs}, volume={44}, DOI={10.1007/s00493-023-00078-9},
journal={Combinatorica}, publisher={Springer Science and Business Media LLC},
author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus},
year={2024}, pages={429–440} }'
chicago: 'Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf.
“Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.”
Combinatorica 44 (2024): 429–40. https://doi.org/10.1007/s00493-023-00078-9.'
ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Edge-Connectivity and Pairwise
Disjoint Perfect Matchings in Regular Graphs,” Combinatorica, vol. 44,
pp. 429–440, 2024, doi: 10.1007/s00493-023-00078-9.'
mla: Ma, Yulai, et al. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings
in Regular Graphs.” Combinatorica, vol. 44, Springer Science and Business
Media LLC, 2024, pp. 429–40, doi:10.1007/s00493-023-00078-9.
short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 44 (2024) 429–440.
date_created: 2023-12-20T10:31:27Z
date_updated: 2024-03-22T12:11:35Z
department:
- _id: '542'
doi: 10.1007/s00493-023-00078-9
intvolume: ' 44'
keyword:
- Computational Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
page: 429-440
publication: Combinatorica
publication_identifier:
issn:
- 0209-9683
- 1439-6912
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs
type: journal_article
user_id: '15540'
volume: 44
year: '2024'
...
---
_id: '53101'
abstract:
- lang: eng
text: In this work, we consider optimal control problems for mechanical systems
with fixed initial and free final state and a quadratic Lagrange term. Specifically,
the dynamics is described by a second order ODE containing an affine control term.
Classically, Pontryagin's maximum principle gives necessary optimality conditions
for the optimal control problem. For smooth problems, alternatively, a variational
approach based on an augmented objective can be followed. Here, we propose a new
Lagrangian approach leading to equivalent necessary optimality conditions in the
form of Euler-Lagrange equations. Thus, the differential geometric structure (similar
to classical Lagrangian dynamics) can be exploited in the framework of optimal
control problems. In particular, the formulation enables the symplectic discretisation
of the optimal control problem via variational integrators in a straightforward
way.
article_type: original
author:
- first_name: Sigrid
full_name: Leyendecker, Sigrid
last_name: Leyendecker
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Rodrigo T. Sato Martín de
full_name: Almagro, Rodrigo T. Sato Martín de
last_name: Almagro
- first_name: Flóra Orsolya
full_name: Szemenyei, Flóra Orsolya
last_name: Szemenyei
citation:
ama: Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Almagro RTSM de, Szemenyei FO.
A new Lagrangian approach to control affine systems with a quadratic Lagrange
term. Journal of Computational Dynamics. 2024;0(0):0-0. doi:10.3934/jcd.2024017
apa: Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., Almagro, R. T. S. M. de,
& Szemenyei, F. O. (2024). A new Lagrangian approach to control affine systems
with a quadratic Lagrange term. Journal of Computational Dynamics, 0(0),
0–0. https://doi.org/10.3934/jcd.2024017
bibtex: '@article{Leyendecker_Maslovskaya_Ober-Blöbaum_Almagro_Szemenyei_2024, title={A
new Lagrangian approach to control affine systems with a quadratic Lagrange term},
volume={0}, DOI={10.3934/jcd.2024017},
number={0}, journal={Journal of Computational Dynamics}, publisher={American Institute
of Mathematical Sciences (AIMS)}, author={Leyendecker, Sigrid and Maslovskaya,
Sofya and Ober-Blöbaum, Sina and Almagro, Rodrigo T. Sato Martín de and Szemenyei,
Flóra Orsolya}, year={2024}, pages={0–0} }'
chicago: 'Leyendecker, Sigrid, Sofya Maslovskaya, Sina Ober-Blöbaum, Rodrigo T.
Sato Martín de Almagro, and Flóra Orsolya Szemenyei. “A New Lagrangian Approach
to Control Affine Systems with a Quadratic Lagrange Term.” Journal of Computational
Dynamics 0, no. 0 (2024): 0–0. https://doi.org/10.3934/jcd.2024017.'
ieee: 'S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R. T. S. M. de Almagro,
and F. O. Szemenyei, “A new Lagrangian approach to control affine systems with
a quadratic Lagrange term,” Journal of Computational Dynamics, vol. 0,
no. 0, pp. 0–0, 2024, doi: 10.3934/jcd.2024017.'
mla: Leyendecker, Sigrid, et al. “A New Lagrangian Approach to Control Affine Systems
with a Quadratic Lagrange Term.” Journal of Computational Dynamics, vol.
0, no. 0, American Institute of Mathematical Sciences (AIMS), 2024, pp. 0–0, doi:10.3934/jcd.2024017.
short: S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T.S.M. de Almagro, F.O.
Szemenyei, Journal of Computational Dynamics 0 (2024) 0–0.
date_created: 2024-03-28T15:58:02Z
date_updated: 2024-03-28T16:07:34Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.3934/jcd.2024017
has_accepted_license: '1'
issue: '0'
keyword:
- Optimal control problem
- Lagrangian system
- Hamiltonian system
- Variations
- Pontryagin's maximum principle.
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.aimsciences.org/article/doi/10.3934/jcd.2024017
oa: '1'
page: 0-0
publication: Journal of Computational Dynamics
publication_identifier:
issn:
- 2158-2491
- 2158-2505
publication_status: published
publisher: American Institute of Mathematical Sciences (AIMS)
status: public
title: A new Lagrangian approach to control affine systems with a quadratic Lagrange
term
type: journal_article
user_id: '87909'
volume: '0'
year: '2024'
...
---
_id: '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: '35697'
author:
- first_name: Laura
full_name: Ostsieker, Laura
last_name: Ostsieker
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
citation:
ama: 'Ostsieker L, Biehler R. Supporting Students in Developing Adequate Concept
Images and Definitions at University: The Case of the Convergence of Sequences.
In: Practice-Oriented Research in Tertiary Mathematics Education. Springer
International Publishing; 2023:181-201. doi:10.1007/978-3-031-14175-1_9'
apa: 'Ostsieker, L., & Biehler, R. (2023). Supporting Students in Developing
Adequate Concept Images and Definitions at University: The Case of the Convergence
of Sequences. In Practice-Oriented Research in Tertiary Mathematics Education
(pp. 181–201). Springer International Publishing. https://doi.org/10.1007/978-3-031-14175-1_9'
bibtex: '@inbook{Ostsieker_Biehler_2023, place={Cham}, title={Supporting Students
in Developing Adequate Concept Images and Definitions at University: The Case
of the Convergence of Sequences}, DOI={10.1007/978-3-031-14175-1_9},
booktitle={Practice-Oriented Research in Tertiary Mathematics Education}, publisher={Springer
International Publishing}, author={Ostsieker, Laura and Biehler, Rolf}, year={2023},
pages={181–201} }'
chicago: 'Ostsieker, Laura, and Rolf Biehler. “Supporting Students in Developing
Adequate Concept Images and Definitions at University: The Case of the Convergence
of Sequences.” In Practice-Oriented Research in Tertiary Mathematics Education,
181–201. Cham: Springer International Publishing, 2023. https://doi.org/10.1007/978-3-031-14175-1_9.'
ieee: 'L. Ostsieker and R. Biehler, “Supporting Students in Developing Adequate
Concept Images and Definitions at University: The Case of the Convergence of Sequences,”
in Practice-Oriented Research in Tertiary Mathematics Education, Cham:
Springer International Publishing, 2023, pp. 181–201.'
mla: 'Ostsieker, Laura, and Rolf Biehler. “Supporting Students in Developing Adequate
Concept Images and Definitions at University: The Case of the Convergence of Sequences.”
Practice-Oriented Research in Tertiary Mathematics Education, Springer
International Publishing, 2023, pp. 181–201, doi:10.1007/978-3-031-14175-1_9.'
short: 'L. Ostsieker, R. Biehler, in: Practice-Oriented Research in Tertiary Mathematics
Education, Springer International Publishing, Cham, 2023, pp. 181–201.'
date_created: 2023-01-10T09:03:11Z
date_updated: 2023-01-11T08:19:24Z
department:
- _id: '34'
- _id: '10'
- _id: '97'
- _id: '363'
doi: 10.1007/978-3-031-14175-1_9
language:
- iso: eng
page: 181-201
place: Cham
publication: Practice-Oriented Research in Tertiary Mathematics Education
publication_identifier:
isbn:
- '9783031141744'
- '9783031141751'
issn:
- 1869-4918
- 1869-4926
publication_status: published
publisher: Springer International Publishing
status: public
title: 'Supporting Students in Developing Adequate Concept Images and Definitions
at University: The Case of the Convergence of Sequences'
type: book_chapter
user_id: '37888'
year: '2023'
...
---
_id: '35678'
author:
- first_name: Jörg
full_name: Kortemeyer, Jörg
last_name: Kortemeyer
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
citation:
ama: 'Kortemeyer J, Biehler R. Analyzing the Interface Between Mathematics and Engineering
in Basic Engineering Courses. In: Practice-Oriented Research in Tertiary Mathematics
Education. Springer International Publishing; 2023:669-692. doi:10.1007/978-3-031-14175-1_32'
apa: Kortemeyer, J., & Biehler, R. (2023). Analyzing the Interface Between Mathematics
and Engineering in Basic Engineering Courses. In Practice-Oriented Research
in Tertiary Mathematics Education (pp. 669–692). Springer International Publishing.
https://doi.org/10.1007/978-3-031-14175-1_32
bibtex: '@inbook{Kortemeyer_Biehler_2023, place={Cham}, title={Analyzing the Interface
Between Mathematics and Engineering in Basic Engineering Courses}, DOI={10.1007/978-3-031-14175-1_32},
booktitle={Practice-Oriented Research in Tertiary Mathematics Education}, publisher={Springer
International Publishing}, author={Kortemeyer, Jörg and Biehler, Rolf}, year={2023},
pages={669–692} }'
chicago: 'Kortemeyer, Jörg, and Rolf Biehler. “Analyzing the Interface Between Mathematics
and Engineering in Basic Engineering Courses.” In Practice-Oriented Research
in Tertiary Mathematics Education, 669–92. Cham: Springer International Publishing,
2023. https://doi.org/10.1007/978-3-031-14175-1_32.'
ieee: 'J. Kortemeyer and R. Biehler, “Analyzing the Interface Between Mathematics
and Engineering in Basic Engineering Courses,” in Practice-Oriented Research
in Tertiary Mathematics Education, Cham: Springer International Publishing,
2023, pp. 669–692.'
mla: Kortemeyer, Jörg, and Rolf Biehler. “Analyzing the Interface Between Mathematics
and Engineering in Basic Engineering Courses.” Practice-Oriented Research in
Tertiary Mathematics Education, Springer International Publishing, 2023, pp.
669–92, doi:10.1007/978-3-031-14175-1_32.
short: 'J. Kortemeyer, R. Biehler, in: Practice-Oriented Research in Tertiary Mathematics
Education, Springer International Publishing, Cham, 2023, pp. 669–692.'
date_created: 2023-01-10T08:53:44Z
date_updated: 2023-01-11T08:20:40Z
department:
- _id: '34'
- _id: '10'
- _id: '97'
- _id: '363'
doi: 10.1007/978-3-031-14175-1_32
language:
- iso: eng
page: 669-692
place: Cham
publication: Practice-Oriented Research in Tertiary Mathematics Education
publication_identifier:
isbn:
- '9783031141744'
- '9783031141751'
issn:
- 1869-4918
- 1869-4926
publication_status: published
publisher: Springer International Publishing
status: public
title: Analyzing the Interface Between Mathematics and Engineering in Basic Engineering
Courses
type: book_chapter
user_id: '37888'
year: '2023'
...
---
_id: '35669'
author:
- first_name: Rolf
full_name: Biehler, Rolf
id: '16274'
last_name: Biehler
- first_name: Michael
full_name: Liebendörfer, Michael
last_name: Liebendörfer
- first_name: Ghislaine
full_name: Gueudet, Ghislaine
last_name: Gueudet
- first_name: Chris
full_name: Rasmussen, Chris
last_name: Rasmussen
- first_name: Carl
full_name: Winsløw, Carl
last_name: Winsløw
citation:
ama: 'Biehler R, Liebendörfer M, Gueudet G, Rasmussen C, Winsløw C. Practice-Oriented
Research in Tertiary Mathematics Education – An Introduction. In: Practice-Oriented
Research in Tertiary Mathematics Education. Springer International Publishing;
2023. doi:10.1007/978-3-031-14175-1_1'
apa: Biehler, R., Liebendörfer, M., Gueudet, G., Rasmussen, C., & Winsløw, C.
(2023). Practice-Oriented Research in Tertiary Mathematics Education – An Introduction.
In Practice-Oriented Research in Tertiary Mathematics Education. Springer
International Publishing. https://doi.org/10.1007/978-3-031-14175-1_1
bibtex: '@inbook{Biehler_Liebendörfer_Gueudet_Rasmussen_Winsløw_2023, place={Cham},
title={Practice-Oriented Research in Tertiary Mathematics Education – An Introduction},
DOI={10.1007/978-3-031-14175-1_1},
booktitle={Practice-Oriented Research in Tertiary Mathematics Education}, publisher={Springer
International Publishing}, author={Biehler, Rolf and Liebendörfer, Michael and
Gueudet, Ghislaine and Rasmussen, Chris and Winsløw, Carl}, year={2023} }'
chicago: 'Biehler, Rolf, Michael Liebendörfer, Ghislaine Gueudet, Chris Rasmussen,
and Carl Winsløw. “Practice-Oriented Research in Tertiary Mathematics Education
– An Introduction.” In Practice-Oriented Research in Tertiary Mathematics Education.
Cham: Springer International Publishing, 2023. https://doi.org/10.1007/978-3-031-14175-1_1.'
ieee: 'R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, and C. Winsløw, “Practice-Oriented
Research in Tertiary Mathematics Education – An Introduction,” in Practice-Oriented
Research in Tertiary Mathematics Education, Cham: Springer International Publishing,
2023.'
mla: Biehler, Rolf, et al. “Practice-Oriented Research in Tertiary Mathematics Education
– An Introduction.” Practice-Oriented Research in Tertiary Mathematics Education,
Springer International Publishing, 2023, doi:10.1007/978-3-031-14175-1_1.
short: 'R. Biehler, M. Liebendörfer, G. Gueudet, C. Rasmussen, C. Winsløw, in: Practice-Oriented
Research in Tertiary Mathematics Education, Springer International Publishing,
Cham, 2023.'
date_created: 2023-01-10T08:46:17Z
date_updated: 2023-01-11T08:38:52Z
department:
- _id: '34'
- _id: '10'
- _id: '97'
- _id: '363'
doi: 10.1007/978-3-031-14175-1_1
language:
- iso: eng
place: Cham
publication: Practice-Oriented Research in Tertiary Mathematics Education
publication_identifier:
isbn:
- '9783031141744'
- '9783031141751'
issn:
- 1869-4918
- 1869-4926
publication_status: published
publisher: Springer International Publishing
status: public
title: Practice-Oriented Research in Tertiary Mathematics Education – An Introduction
type: book_chapter
user_id: '37888'
year: '2023'
...