---
_id: '45854'
abstract:
- lang: eng
text: In a previous paper the authors developed an algorithm to classify certain
quaternary quadratic lattices over totally real fields. The present article applies
this algorithm to the classification of binary Hermitian lattices over totally
imaginary fields. We use it in particular to classify the 48-dimensional extremal
even unimodular lattices over the integers that admit a semilarge automorphism.
author:
- first_name: Markus
full_name: Kirschmer, Markus
id: '82258'
last_name: Kirschmer
- first_name: Gabriele
full_name: Nebe, Gabriele
last_name: Nebe
citation:
ama: Kirschmer M, Nebe G. Binary Hermitian Lattices over Number Fields. Experimental
Mathematics. 2022;31(1):280-301. doi:10.1080/10586458.2019.1618756
apa: Kirschmer, M., & Nebe, G. (2022). Binary Hermitian Lattices over Number
Fields. Experimental Mathematics, 31(1), 280–301. https://doi.org/10.1080/10586458.2019.1618756
bibtex: '@article{Kirschmer_Nebe_2022, title={Binary Hermitian Lattices over Number
Fields}, volume={31}, DOI={10.1080/10586458.2019.1618756},
number={1}, journal={Experimental Mathematics}, publisher={Informa UK Limited},
author={Kirschmer, Markus and Nebe, Gabriele}, year={2022}, pages={280–301} }'
chicago: 'Kirschmer, Markus, and Gabriele Nebe. “Binary Hermitian Lattices over
Number Fields.” Experimental Mathematics 31, no. 1 (2022): 280–301. https://doi.org/10.1080/10586458.2019.1618756.'
ieee: 'M. Kirschmer and G. Nebe, “Binary Hermitian Lattices over Number Fields,”
Experimental Mathematics, vol. 31, no. 1, pp. 280–301, 2022, doi: 10.1080/10586458.2019.1618756.'
mla: Kirschmer, Markus, and Gabriele Nebe. “Binary Hermitian Lattices over Number
Fields.” Experimental Mathematics, vol. 31, no. 1, Informa UK Limited,
2022, pp. 280–301, doi:10.1080/10586458.2019.1618756.
short: M. Kirschmer, G. Nebe, Experimental Mathematics 31 (2022) 280–301.
date_created: 2023-07-04T08:28:04Z
date_updated: 2023-07-04T08:29:22Z
department:
- _id: '102'
doi: 10.1080/10586458.2019.1618756
intvolume: ' 31'
issue: '1'
keyword:
- General Mathematics
language:
- iso: eng
page: 280-301
publication: Experimental Mathematics
publication_identifier:
issn:
- 1058-6458
- 1944-950X
publication_status: published
publisher: Informa UK Limited
status: public
title: Binary Hermitian Lattices over Number Fields
type: journal_article
user_id: '93826'
volume: 31
year: '2022'
...
---
_id: '19941'
abstract:
- lang: eng
text: "In backward error analysis, an approximate solution to an equation is compared
to the exact solution to a nearby ‘modified’ equation. In numerical ordinary differential
equations, the two agree up to any power of the step size. If the differential
equation has a geometric property then the modified equation may share it. In
this way, known properties of differential equations can be applied to the approximation.
But for partial differential equations, the known modified equations are of higher
order, limiting applicability of the theory. Therefore, we study symmetric solutions
of discretized\r\npartial differential equations that arise from a discrete variational
principle. These symmetric solutions obey infinite-dimensional functional equations.
We show that these equations admit second-order modified equations which are Hamiltonian
and also possess first-order Lagrangians in modified coordinates. The modified
equation and its associated structures are computed explicitly for the case of
rotating travelling waves in the nonlinear wave equation."
article_type: original
author:
- first_name: Robert I
full_name: McLachlan, Robert I
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
citation:
ama: McLachlan RI, Offen C. Backward error analysis for variational discretisations
of partial differential equations. Journal of Geometric Mechanics. 2022;14(3):447-471.
doi:10.3934/jgm.2022014
apa: McLachlan, R. I., & Offen, C. (2022). Backward error analysis for variational
discretisations of partial differential equations. Journal of Geometric Mechanics,
14(3), 447–471. https://doi.org/10.3934/jgm.2022014
bibtex: '@article{McLachlan_Offen_2022, title={Backward error analysis for variational
discretisations of partial differential equations}, volume={14}, DOI={10.3934/jgm.2022014},
number={3}, journal={Journal of Geometric Mechanics}, publisher={AIMS}, author={McLachlan,
Robert I and Offen, Christian}, year={2022}, pages={447–471} }'
chicago: 'McLachlan, Robert I, and Christian Offen. “Backward Error Analysis for
Variational Discretisations of Partial Differential Equations.” Journal of
Geometric Mechanics 14, no. 3 (2022): 447–71. https://doi.org/10.3934/jgm.2022014.'
ieee: 'R. I. McLachlan and C. Offen, “Backward error analysis for variational discretisations
of partial differential equations,” Journal of Geometric Mechanics, vol.
14, no. 3, pp. 447–471, 2022, doi: 10.3934/jgm.2022014.'
mla: McLachlan, Robert I., and Christian Offen. “Backward Error Analysis for Variational
Discretisations of Partial Differential Equations.” Journal of Geometric Mechanics,
vol. 14, no. 3, AIMS, 2022, pp. 447–71, doi:10.3934/jgm.2022014.
short: R.I. McLachlan, C. Offen, Journal of Geometric Mechanics 14 (2022) 447–471.
date_created: 2020-10-06T16:33:19Z
date_updated: 2023-08-10T08:44:55Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.3934/jgm.2022014
external_id:
arxiv:
- '2006.14172'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2022-06-13T09:11:38Z
date_updated: 2022-06-13T09:11:38Z
description: |-
In backward error analysis, an approximate solution to an equa-
tion is compared to the exact solution to a nearby ‘modified’ equation. In
numerical ordinary differential equations, the two agree up to any power of
the step size. If the differential equation has a geometric property then the
modified equation may share it. In this way, known properties of differential
equations can be applied to the approximation. But for partial differential
equations, the known modified equations are of higher order, limiting appli-
cability of the theory. Therefore, we study symmetric solutions of discretized
partial differential equations that arise from a discrete variational principle.
These symmetric solutions obey infinite-dimensional functional equations. We
show that these equations admit second-order modified equations which are
Hamiltonian and also possess first-order Lagrangians in modified coordinates.
The modified equation and its associated structures are computed explicitly
for the case of rotating travelling waves in the nonlinear wave equation.
file_id: '31859'
file_name: 2_BlendedBEASymmPDE.pdf
file_size: 1507248
relation: main_file
title: Backward error analysis for variational discretisations of PDEs
file_date_updated: 2022-06-13T09:11:38Z
has_accepted_license: '1'
intvolume: ' 14'
issue: '3'
language:
- iso: eng
oa: '1'
page: 447 - 471
publication: Journal of Geometric Mechanics
publication_status: published
publisher: AIMS
related_material:
link:
- relation: software
url: https://github.com/Christian-Offen/multisymplectic
status: public
title: Backward error analysis for variational discretisations of partial differential
equations
type: journal_article
user_id: '85279'
volume: 14
year: '2022'
...
---
_id: '23382'
abstract:
- lang: eng
text: Hamiltonian systems are differential equations which describe systems in classical
mechanics, plasma physics, and sampling problems. They exhibit many structural
properties, such as a lack of attractors and the presence of conservation laws.
To predict Hamiltonian dynamics based on discrete trajectory observations, incorporation
of prior knowledge about Hamiltonian structure greatly improves predictions. This
is typically done by learning the system's Hamiltonian and then integrating the
Hamiltonian vector field with a symplectic integrator. For this, however, Hamiltonian
data needs to be approximated based on the trajectory observations. Moreover,
the numerical integrator introduces an additional discretisation error. In this
paper, we show that an inverse modified Hamiltonian structure adapted to the geometric
integrator can be learned directly from observations. A separate approximation
step for the Hamiltonian data avoided. The inverse modified data compensates for
the discretisation error such that the discretisation error is eliminated. The
technique is developed for Gaussian Processes.
article_type: original
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Offen C, Ober-Blöbaum S. Symplectic integration of learned Hamiltonian systems.
Chaos: An Interdisciplinary Journal of Nonlinear Science. 2022;32(1). doi:10.1063/5.0065913'
apa: 'Offen, C., & Ober-Blöbaum, S. (2022). Symplectic integration of learned
Hamiltonian systems. Chaos: An Interdisciplinary Journal of Nonlinear Science,
32(1). https://doi.org/10.1063/5.0065913'
bibtex: '@article{Offen_Ober-Blöbaum_2022, title={Symplectic integration of learned
Hamiltonian systems}, volume={32(1)}, DOI={10.1063/5.0065913},
journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP},
author={Offen, Christian and Ober-Blöbaum, Sina}, year={2022} }'
chicago: 'Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned
Hamiltonian Systems.” Chaos: An Interdisciplinary Journal of Nonlinear Science
32(1) (2022). https://doi.org/10.1063/5.0065913.'
ieee: 'C. Offen and S. Ober-Blöbaum, “Symplectic integration of learned Hamiltonian
systems,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.
32(1), 2022, doi: 10.1063/5.0065913.'
mla: 'Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned
Hamiltonian Systems.” Chaos: An Interdisciplinary Journal of Nonlinear Science,
vol. 32(1), AIP, 2022, doi:10.1063/5.0065913.'
short: 'C. Offen, S. Ober-Blöbaum, Chaos: An Interdisciplinary Journal of Nonlinear
Science 32(1) (2022).'
date_created: 2021-08-11T08:24:02Z
date_updated: 2023-08-10T08:48:14Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1063/5.0065913
external_id:
arxiv:
- '2108.02492'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2021-12-13T14:56:15Z
date_updated: 2021-12-13T14:56:15Z
file_id: '28734'
file_name: SymplecticShadowIntegration_AIP.pdf
file_size: 2285059
relation: main_file
file_date_updated: 2021-12-13T14:56:15Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://aip.scitation.org/doi/abs/10.1063/5.0065913
oa: '1'
publication: 'Chaos: An Interdisciplinary Journal of Nonlinear Science'
publication_status: published
publisher: AIP
quality_controlled: '1'
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Christian-Offen/symplectic-shadow-integration
status: public
title: Symplectic integration of learned Hamiltonian systems
type: journal_article
user_id: '85279'
volume: 32(1)
year: '2022'
...
---
_id: '24169'
article_number: '133018'
author:
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Patrick
full_name: Gelß, Patrick
last_name: Gelß
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
citation:
ama: 'Nüske F, Gelß P, Klus S, Clementi C. Tensor-based computation of metastable
and coherent sets. Physica D: Nonlinear Phenomena. Published online 2021.
doi:10.1016/j.physd.2021.133018'
apa: 'Nüske, F., Gelß, P., Klus, S., & Clementi, C. (2021). Tensor-based computation
of metastable and coherent sets. Physica D: Nonlinear Phenomena, Article
133018. https://doi.org/10.1016/j.physd.2021.133018'
bibtex: '@article{Nüske_Gelß_Klus_Clementi_2021, title={Tensor-based computation
of metastable and coherent sets}, DOI={10.1016/j.physd.2021.133018},
number={133018}, journal={Physica D: Nonlinear Phenomena}, author={Nüske, Feliks
and Gelß, Patrick and Klus, Stefan and Clementi, Cecilia}, year={2021} }'
chicago: 'Nüske, Feliks, Patrick Gelß, Stefan Klus, and Cecilia Clementi. “Tensor-Based
Computation of Metastable and Coherent Sets.” Physica D: Nonlinear Phenomena,
2021. https://doi.org/10.1016/j.physd.2021.133018.'
ieee: 'F. Nüske, P. Gelß, S. Klus, and C. Clementi, “Tensor-based computation of
metastable and coherent sets,” Physica D: Nonlinear Phenomena, Art. no.
133018, 2021, doi: 10.1016/j.physd.2021.133018.'
mla: 'Nüske, Feliks, et al. “Tensor-Based Computation of Metastable and Coherent
Sets.” Physica D: Nonlinear Phenomena, 133018, 2021, doi:10.1016/j.physd.2021.133018.'
short: 'F. Nüske, P. Gelß, S. Klus, C. Clementi, Physica D: Nonlinear Phenomena
(2021).'
date_created: 2021-09-12T08:51:24Z
date_updated: 2022-01-06T06:56:08Z
department:
- _id: '101'
doi: 10.1016/j.physd.2021.133018
language:
- iso: eng
publication: 'Physica D: Nonlinear Phenomena'
publication_identifier:
issn:
- 0167-2789
publication_status: published
status: public
title: Tensor-based computation of metastable and coherent sets
type: journal_article
user_id: '81513'
year: '2021'
...
---
_id: '24170'
article_number: '045016'
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Patrick
full_name: Gelß, Patrick
last_name: Gelß
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Frank
full_name: Noé, Frank
last_name: Noé
citation:
ama: 'Klus S, Gelß P, Nüske F, Noé F. Symmetric and antisymmetric kernels for machine
learning problems in quantum physics and chemistry. Machine Learning: Science
and Technology. Published online 2021. doi:10.1088/2632-2153/ac14ad'
apa: 'Klus, S., Gelß, P., Nüske, F., & Noé, F. (2021). Symmetric and antisymmetric
kernels for machine learning problems in quantum physics and chemistry. Machine
Learning: Science and Technology, Article 045016. https://doi.org/10.1088/2632-2153/ac14ad'
bibtex: '@article{Klus_Gelß_Nüske_Noé_2021, title={Symmetric and antisymmetric kernels
for machine learning problems in quantum physics and chemistry}, DOI={10.1088/2632-2153/ac14ad},
number={045016}, journal={Machine Learning: Science and Technology}, author={Klus,
Stefan and Gelß, Patrick and Nüske, Feliks and Noé, Frank}, year={2021} }'
chicago: 'Klus, Stefan, Patrick Gelß, Feliks Nüske, and Frank Noé. “Symmetric and
Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry.”
Machine Learning: Science and Technology, 2021. https://doi.org/10.1088/2632-2153/ac14ad.'
ieee: 'S. Klus, P. Gelß, F. Nüske, and F. Noé, “Symmetric and antisymmetric kernels
for machine learning problems in quantum physics and chemistry,” Machine Learning:
Science and Technology, Art. no. 045016, 2021, doi: 10.1088/2632-2153/ac14ad.'
mla: 'Klus, Stefan, et al. “Symmetric and Antisymmetric Kernels for Machine Learning
Problems in Quantum Physics and Chemistry.” Machine Learning: Science and Technology,
045016, 2021, doi:10.1088/2632-2153/ac14ad.'
short: 'S. Klus, P. Gelß, F. Nüske, F. Noé, Machine Learning: Science and Technology
(2021).'
date_created: 2021-09-12T08:52:57Z
date_updated: 2022-01-06T06:56:08Z
department:
- _id: '101'
doi: 10.1088/2632-2153/ac14ad
language:
- iso: eng
publication: 'Machine Learning: Science and Technology'
publication_identifier:
issn:
- 2632-2153
publication_status: published
status: public
title: Symmetric and antisymmetric kernels for machine learning problems in quantum
physics and chemistry
type: journal_article
user_id: '81513'
year: '2021'
...
---
_id: '21195'
author:
- first_name: Christian
full_name: Goelz, Christian
last_name: Goelz
- first_name: Karin
full_name: Mora, Karin
last_name: Mora
- first_name: Julia Kristin
full_name: Stroehlein, Julia Kristin
last_name: Stroehlein
- first_name: Franziska Katharina
full_name: Haase, Franziska Katharina
last_name: Haase
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Claus
full_name: Reinsberger, Claus
last_name: Reinsberger
- first_name: Solveig
full_name: Vieluf, Solveig
last_name: Vieluf
citation:
ama: Goelz C, Mora K, Stroehlein JK, et al. Electrophysiological signatures of dedifferentiation
differ between fit and less fit older adults. Cognitive Neurodynamics.
2021. doi:10.1007/s11571-020-09656-9
apa: Goelz, C., Mora, K., Stroehlein, J. K., Haase, F. K., Dellnitz, M., Reinsberger,
C., & Vieluf, S. (2021). Electrophysiological signatures of dedifferentiation
differ between fit and less fit older adults. Cognitive Neurodynamics.
https://doi.org/10.1007/s11571-020-09656-9
bibtex: '@article{Goelz_Mora_Stroehlein_Haase_Dellnitz_Reinsberger_Vieluf_2021,
title={Electrophysiological signatures of dedifferentiation differ between fit
and less fit older adults}, DOI={10.1007/s11571-020-09656-9},
journal={Cognitive Neurodynamics}, author={Goelz, Christian and Mora, Karin and
Stroehlein, Julia Kristin and Haase, Franziska Katharina and Dellnitz, Michael
and Reinsberger, Claus and Vieluf, Solveig}, year={2021} }'
chicago: Goelz, Christian, Karin Mora, Julia Kristin Stroehlein, Franziska Katharina
Haase, Michael Dellnitz, Claus Reinsberger, and Solveig Vieluf. “Electrophysiological
Signatures of Dedifferentiation Differ between Fit and Less Fit Older Adults.”
Cognitive Neurodynamics, 2021. https://doi.org/10.1007/s11571-020-09656-9.
ieee: C. Goelz et al., “Electrophysiological signatures of dedifferentiation
differ between fit and less fit older adults,” Cognitive Neurodynamics,
2021.
mla: Goelz, Christian, et al. “Electrophysiological Signatures of Dedifferentiation
Differ between Fit and Less Fit Older Adults.” Cognitive Neurodynamics,
2021, doi:10.1007/s11571-020-09656-9.
short: C. Goelz, K. Mora, J.K. Stroehlein, F.K. Haase, M. Dellnitz, C. Reinsberger,
S. Vieluf, Cognitive Neurodynamics (2021).
date_created: 2021-02-08T13:16:07Z
date_updated: 2022-01-06T06:54:49Z
department:
- _id: '101'
doi: 10.1007/s11571-020-09656-9
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/content/pdf/10.1007/s11571-020-09656-9.pdf
publication: Cognitive Neurodynamics
status: public
title: Electrophysiological signatures of dedifferentiation differ between fit and
less fit older adults
type: journal_article
user_id: '32643'
year: '2021'
...
---
_id: '21337'
abstract:
- lang: eng
text: "We present a flexible trust region descend algorithm for unconstrained and\r\nconvexly
constrained multiobjective optimization problems. It is targeted at\r\nheterogeneous
and expensive problems, i.e., problems that have at least one\r\nobjective function
that is computationally expensive. The method is\r\nderivative-free in the sense
that neither need derivative information be\r\navailable for the expensive objectives
nor are gradients approximated using\r\nrepeated function evaluations as is the
case in finite-difference methods.\r\nInstead, a multiobjective trust region approach
is used that works similarly to\r\nits well-known scalar pendants. Local surrogate
models constructed from\r\nevaluation data of the true objective functions are
employed to compute\r\npossible descent directions. In contrast to existing multiobjective
trust\r\nregion algorithms, these surrogates are not polynomial but carefully\r\nconstructed
radial basis function networks. This has the important advantage\r\nthat the number
of data points scales linearly with the parameter space\r\ndimension. The local
models qualify as fully linear and the corresponding\r\ngeneral scalar framework
is adapted for problems with multiple objectives.\r\nConvergence to Pareto critical
points is proven and numerical examples\r\nillustrate our findings."
article_number: '31'
author:
- first_name: Manuel Bastian
full_name: Berkemeier, Manuel Bastian
id: '51701'
last_name: Berkemeier
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Berkemeier MB, Peitz S. Derivative-Free Multiobjective Trust Region Descent
Method Using Radial Basis Function Surrogate Models. Mathematical and Computational
Applications. 2021;26(2). doi:10.3390/mca26020031
apa: Berkemeier, M. B., & Peitz, S. (2021). Derivative-Free Multiobjective Trust
Region Descent Method Using Radial Basis Function Surrogate Models. Mathematical
and Computational Applications, 26(2). https://doi.org/10.3390/mca26020031
bibtex: '@article{Berkemeier_Peitz_2021, title={Derivative-Free Multiobjective Trust
Region Descent Method Using Radial Basis Function Surrogate Models}, volume={26},
DOI={10.3390/mca26020031}, number={231},
journal={Mathematical and Computational Applications}, author={Berkemeier, Manuel
Bastian and Peitz, Sebastian}, year={2021} }'
chicago: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective
Trust Region Descent Method Using Radial Basis Function Surrogate Models.” Mathematical
and Computational Applications 26, no. 2 (2021). https://doi.org/10.3390/mca26020031.
ieee: M. B. Berkemeier and S. Peitz, “Derivative-Free Multiobjective Trust Region
Descent Method Using Radial Basis Function Surrogate Models,” Mathematical
and Computational Applications, vol. 26, no. 2, 2021.
mla: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective
Trust Region Descent Method Using Radial Basis Function Surrogate Models.” Mathematical
and Computational Applications, vol. 26, no. 2, 31, 2021, doi:10.3390/mca26020031.
short: M.B. Berkemeier, S. Peitz, Mathematical and Computational Applications 26
(2021).
date_created: 2021-03-01T10:46:48Z
date_updated: 2022-01-06T06:54:55Z
department:
- _id: '101'
- _id: '655'
doi: 10.3390/mca26020031
intvolume: ' 26'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.mdpi.com/2297-8747/26/2/31/pdf
oa: '1'
publication: Mathematical and Computational Applications
publication_identifier:
eissn:
- 2297-8747
publication_status: published
status: public
title: Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis
Function Surrogate Models
type: journal_article
user_id: '47427'
volume: 26
year: '2021'
...
---
_id: '21820'
abstract:
- lang: eng
text: The reduction of high-dimensional systems to effective models on a
smaller set of variables is an essential task in many areas of science. For stochastic
dynamics governed by diffusion processes, a general procedure to find effective
equations is the conditioning approach. In this paper, we are interested in the
spectrum of the generator of the resulting effective dynamics, and how it compares
to the spectrum of the full generator. We prove a new relative error bound in
terms of the eigenfunction approximation error for reversible systems. We also
present numerical examples indicating that, if Kramers–Moyal (KM) type approximations
are used to compute the spectrum of the reduced generator, it seems largely insensitive
to the time window used for the KM estimators. We analyze the implications of
these observations for systems driven by underdamped Langevin dynamics, and show
how meaningful effective dynamics can be defined in this setting.
article_number: '134'
author:
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Péter
full_name: Koltai, Péter
last_name: Koltai
- first_name: Lorenzo
full_name: Boninsegna, Lorenzo
last_name: Boninsegna
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
citation:
ama: Nüske F, Koltai P, Boninsegna L, Clementi C. Spectral Properties of Effective
Dynamics from Conditional Expectations. Entropy. 2021. doi:10.3390/e23020134
apa: Nüske, F., Koltai, P., Boninsegna, L., & Clementi, C. (2021). Spectral
Properties of Effective Dynamics from Conditional Expectations. Entropy.
https://doi.org/10.3390/e23020134
bibtex: '@article{Nüske_Koltai_Boninsegna_Clementi_2021, title={Spectral Properties
of Effective Dynamics from Conditional Expectations}, DOI={10.3390/e23020134},
number={134}, journal={Entropy}, author={Nüske, Feliks and Koltai, Péter and Boninsegna,
Lorenzo and Clementi, Cecilia}, year={2021} }'
chicago: Nüske, Feliks, Péter Koltai, Lorenzo Boninsegna, and Cecilia Clementi.
“Spectral Properties of Effective Dynamics from Conditional Expectations.” Entropy,
2021. https://doi.org/10.3390/e23020134.
ieee: F. Nüske, P. Koltai, L. Boninsegna, and C. Clementi, “Spectral Properties
of Effective Dynamics from Conditional Expectations,” Entropy, 2021.
mla: Nüske, Feliks, et al. “Spectral Properties of Effective Dynamics from Conditional
Expectations.” Entropy, 134, 2021, doi:10.3390/e23020134.
short: F. Nüske, P. Koltai, L. Boninsegna, C. Clementi, Entropy (2021).
date_created: 2021-04-28T18:07:56Z
date_updated: 2022-01-06T06:55:16Z
department:
- _id: '101'
doi: 10.3390/e23020134
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.mdpi.com/1099-4300/23/2/134
oa: '1'
publication: Entropy
publication_identifier:
issn:
- 1099-4300
publication_status: published
status: public
title: Spectral Properties of Effective Dynamics from Conditional Expectations
type: journal_article
user_id: '81513'
year: '2021'
...
---
_id: '16867'
abstract:
- lang: eng
text: "In this article, we present an efficient descent method for locally Lipschitz\r\ncontinuous
multiobjective optimization problems (MOPs). The method is realized\r\nby combining
a theoretical result regarding the computation of descent\r\ndirections for nonsmooth
MOPs with a practical method to approximate the\r\nsubdifferentials of the objective
functions. We show convergence to points\r\nwhich satisfy a necessary condition
for Pareto optimality. Using a set of test\r\nproblems, we compare our method
to the multiobjective proximal bundle method by\r\nM\\\"akel\\\"a. The results
indicate that our method is competitive while being\r\neasier to implement. While
the number of objective function evaluations is\r\nlarger, the overall number
of subgradient evaluations is lower. Finally, we\r\nshow that our method can be
combined with a subdivision algorithm to compute\r\nentire Pareto sets of nonsmooth
MOPs."
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Gebken B, Peitz S. An efficient descent method for locally Lipschitz multiobjective
optimization problems. Journal of Optimization Theory and Applications.
2021;188:696-723. doi:10.1007/s10957-020-01803-w
apa: Gebken, B., & Peitz, S. (2021). An efficient descent method for locally
Lipschitz multiobjective optimization problems. Journal of Optimization Theory
and Applications, 188, 696–723. https://doi.org/10.1007/s10957-020-01803-w
bibtex: '@article{Gebken_Peitz_2021, title={An efficient descent method for locally
Lipschitz multiobjective optimization problems}, volume={188}, DOI={10.1007/s10957-020-01803-w},
journal={Journal of Optimization Theory and Applications}, author={Gebken, Bennet
and Peitz, Sebastian}, year={2021}, pages={696–723} }'
chicago: 'Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for
Locally Lipschitz Multiobjective Optimization Problems.” Journal of Optimization
Theory and Applications 188 (2021): 696–723. https://doi.org/10.1007/s10957-020-01803-w.'
ieee: B. Gebken and S. Peitz, “An efficient descent method for locally Lipschitz
multiobjective optimization problems,” Journal of Optimization Theory and Applications,
vol. 188, pp. 696–723, 2021.
mla: Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally
Lipschitz Multiobjective Optimization Problems.” Journal of Optimization Theory
and Applications, vol. 188, 2021, pp. 696–723, doi:10.1007/s10957-020-01803-w.
short: B. Gebken, S. Peitz, Journal of Optimization Theory and Applications 188
(2021) 696–723.
date_created: 2020-04-27T09:11:22Z
date_updated: 2022-01-06T06:52:57Z
department:
- _id: '101'
doi: 10.1007/s10957-020-01803-w
intvolume: ' 188'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s10957-020-01803-w.pdf
oa: '1'
page: 696-723
publication: Journal of Optimization Theory and Applications
publication_status: published
status: public
title: An efficient descent method for locally Lipschitz multiobjective optimization
problems
type: journal_article
user_id: '47427'
volume: 188
year: '2021'
...
---
_id: '16295'
abstract:
- lang: eng
text: It is a challenging task to identify the objectives on which a certain decision
was based, in particular if several, potentially conflicting criteria are equally
important and a continuous set of optimal compromise decisions exists. This task
can be understood as the inverse problem of multiobjective optimization, where
the goal is to find the objective function vector of a given Pareto set. To this
end, we present a method to construct the objective function vector of an unconstrained
multiobjective optimization problem (MOP) such that the Pareto critical set contains
a given set of data points with prescribed KKT multipliers. If such an MOP can
not be found, then the method instead produces an MOP whose Pareto critical set
is at least close to the data points. The key idea is to consider the objective
function vector in the multiobjective KKT conditions as variable and then search
for the objectives that minimize the Euclidean norm of the resulting system of
equations. By expressing the objectives in a finite-dimensional basis, we transform
this problem into a homogeneous, linear system of equations that can be solved
efficiently. Potential applications of this approach include the identification
of objectives (both from clean and noisy data) and the construction of surrogate
models for expensive MOPs.
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
citation:
ama: 'Gebken B, Peitz S. Inverse multiobjective optimization: Inferring decision
criteria from data. Journal of Global Optimization. 2021;80:3-29. doi:10.1007/s10898-020-00983-z'
apa: 'Gebken, B., & Peitz, S. (2021). Inverse multiobjective optimization: Inferring
decision criteria from data. Journal of Global Optimization, 80,
3–29. https://doi.org/10.1007/s10898-020-00983-z'
bibtex: '@article{Gebken_Peitz_2021, title={Inverse multiobjective optimization:
Inferring decision criteria from data}, volume={80}, DOI={10.1007/s10898-020-00983-z},
journal={Journal of Global Optimization}, publisher={Springer}, author={Gebken,
Bennet and Peitz, Sebastian}, year={2021}, pages={3–29} }'
chicago: 'Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization:
Inferring Decision Criteria from Data.” Journal of Global Optimization
80 (2021): 3–29. https://doi.org/10.1007/s10898-020-00983-z.'
ieee: 'B. Gebken and S. Peitz, “Inverse multiobjective optimization: Inferring decision
criteria from data,” Journal of Global Optimization, vol. 80, pp. 3–29,
2021.'
mla: 'Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization:
Inferring Decision Criteria from Data.” Journal of Global Optimization,
vol. 80, Springer, 2021, pp. 3–29, doi:10.1007/s10898-020-00983-z.'
short: B. Gebken, S. Peitz, Journal of Global Optimization 80 (2021) 3–29.
date_created: 2020-03-13T12:45:05Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1007/s10898-020-00983-z
intvolume: ' 80'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s10898-020-00983-z.pdf
oa: '1'
page: 3-29
publication: Journal of Global Optimization
publisher: Springer
status: public
title: 'Inverse multiobjective optimization: Inferring decision criteria from data'
type: journal_article
user_id: '47427'
volume: 80
year: '2021'
...
---
_id: '32057'
abstract:
- lang: ger
text: Ein zentraler Aspekt bei der Untersuchung dynamischer Systeme ist die Analyse
ihrer invarianten Mengen wie des globalen Attraktors und (in)stabiler Mannigfaltigkeiten.
Insbesondere wenn das zugrunde liegende System von einem Parameter abhängt, ist
es entscheidend, sie im Bezug auf diesen Parameter effizient zu verfolgen. Für
die Berechnung invarianter Mengen stützen wir uns für ihre Approximation auf numerische
Algorithmen. Typischerweise können diese Methoden jedoch nur auf endlich-dimensionale
dynamische Systeme angewendet werden. In dieser Arbeit präsentieren wir daher
einen numerischen Rahmen für die globale dynamische Analyse unendlich-dimensionaler
Systeme. Wir werden Einbettungstechniken verwenden, um das core dynamical system
(CDS) zu definieren, welches ein dynamisch äquivalentes endlich-dimensionales
System ist.Das CDS wird dann verwendet, um eingebettete invariante Mengen, also
eins-zu-eins Bilder, mittels Mengen-orientierten numerischen Methoden zu approximieren.
Bei der Konstruktion des CDS ist es entscheidend, eine geeignete Beobachtungsabbildung
auszuwählen und die geeignete inverse Abbildung zu entwerfen. Dazu werden wir
geeignete numerische Implementierungen des CDS für DDEs und PDEs vorstellen. Für
eine nachfolgende geometrische Analyse der eingebetteten invarianten Menge betrachten
wir eine Lerntechnik namens diffusion maps, die ihre intrinsische Geometrie enthüllt
sowie ihre Dimension schätzt. Schließlich wenden wir unsere entwickelten numerischen
Methoden an einigen bekannten unendlich-dimensionale dynamischen Systeme an, wie
die Mackey-Glass-Gleichung, die Kuramoto-Sivashinsky-Gleichung und die Navier-Stokes-Gleichung.
- lang: eng
text: One central aspect in the study of dynamical systems is the analysis of its
invariant sets such as the global attractor and (un)stable manifolds. In particular,
when the underlying system depends on a parameter it is crucial to efficiently
track those set with respect to this parameter. For the computation of invariant
sets we rely on numerical algorithms for their approximation but typically those
tools can only be applied to finite-dimensional dynamical systems. Thus, in thesis
we present a numerical framework for the global dynamical analysis of infinite-dimensional
systems. We will use embedding techniques for the definition of the core dynamical
system (CDS) which is a dynamically equivalent finite-dimensional system. The
CDS is then used for the approximation of related embedded invariant sets, i.e,
one-to-one images, by set-oriented numerical methods. For the construction of
the CDS it is crucial to choose an appropriate observation map and to design its
corresponding inverse. Therefore, we will present suitable numerical realizations
of the CDS for DDEs and PDEs. For a subsequent geometric analysis of the embedded
invariant set we will consider a manifold learning technique called diffusion
maps which reveals its intrinsic geometry and estimates its dimension. Finally,
we apply our develop numerical tools on some well-known infinite-dimensional dynamical
systems such as the Mackey-Glass equation, the Kuramoto-Sivashinsky equation and
the Navier-Stokes equation.
author:
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
citation:
ama: Gerlach R. The Computation and Analysis of Invariant Sets of Infinite-Dimensional
Systems.; 2021. doi:10.17619/UNIPB/1-1278
apa: Gerlach, R. (2021). The Computation and Analysis of Invariant Sets of Infinite-Dimensional
Systems. https://doi.org/10.17619/UNIPB/1-1278
bibtex: '@book{Gerlach_2021, title={The Computation and Analysis of Invariant Sets
of Infinite-Dimensional Systems}, DOI={10.17619/UNIPB/1-1278},
author={Gerlach, Raphael}, year={2021} }'
chicago: Gerlach, Raphael. The Computation and Analysis of Invariant Sets of
Infinite-Dimensional Systems, 2021. https://doi.org/10.17619/UNIPB/1-1278.
ieee: R. Gerlach, The Computation and Analysis of Invariant Sets of Infinite-Dimensional
Systems. 2021.
mla: Gerlach, Raphael. The Computation and Analysis of Invariant Sets of Infinite-Dimensional
Systems. 2021, doi:10.17619/UNIPB/1-1278.
short: R. Gerlach, The Computation and Analysis of Invariant Sets of Infinite-Dimensional
Systems, 2021.
date_created: 2022-06-20T09:54:24Z
date_updated: 2022-06-20T13:40:30Z
department:
- _id: '101'
doi: 10.17619/UNIPB/1-1278
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://digital.ub.uni-paderborn.de/hs/download/pdf/6214949
oa: '1'
status: public
supervisor:
- first_name: Michael
full_name: Dellnitz , Michael
last_name: 'Dellnitz '
- first_name: Péter
full_name: Koltai, Péter
last_name: Koltai
title: The Computation and Analysis of Invariant Sets of Infinite-Dimensional Systems
type: dissertation
user_id: '32643'
year: '2021'
...
---
_id: '34042'
author:
- first_name: Jiaao
full_name: Li, Jiaao
last_name: Li
- first_name: Yulai
full_name: Ma, Yulai
id: '92748'
last_name: Ma
- first_name: Zhengke
full_name: Miao, Zhengke
last_name: Miao
- first_name: Yongtang
full_name: Shi, Yongtang
last_name: Shi
- first_name: Weifan
full_name: Wang, Weifan
last_name: Wang
- first_name: Cun-Quan
full_name: Zhang, Cun-Quan
last_name: Zhang
citation:
ama: Li J, Ma Y, Miao Z, Shi Y, Wang W, Zhang C-Q. Nowhere-zero 3-flows in toroidal
graphs. Journal of Combinatorial Theory, Series B. 2021;153:61-80. doi:10.1016/j.jctb.2021.11.001
apa: Li, J., Ma, Y., Miao, Z., Shi, Y., Wang, W., & Zhang, C.-Q. (2021). Nowhere-zero
3-flows in toroidal graphs. Journal of Combinatorial Theory, Series B,
153, 61–80. https://doi.org/10.1016/j.jctb.2021.11.001
bibtex: '@article{Li_Ma_Miao_Shi_Wang_Zhang_2021, title={Nowhere-zero 3-flows in
toroidal graphs}, volume={153}, DOI={10.1016/j.jctb.2021.11.001},
journal={Journal of Combinatorial Theory, Series B}, publisher={Elsevier BV},
author={Li, Jiaao and Ma, Yulai and Miao, Zhengke and Shi, Yongtang and Wang,
Weifan and Zhang, Cun-Quan}, year={2021}, pages={61–80} }'
chicago: 'Li, Jiaao, Yulai Ma, Zhengke Miao, Yongtang Shi, Weifan Wang, and Cun-Quan
Zhang. “Nowhere-Zero 3-Flows in Toroidal Graphs.” Journal of Combinatorial
Theory, Series B 153 (2021): 61–80. https://doi.org/10.1016/j.jctb.2021.11.001.'
ieee: 'J. Li, Y. Ma, Z. Miao, Y. Shi, W. Wang, and C.-Q. Zhang, “Nowhere-zero 3-flows
in toroidal graphs,” Journal of Combinatorial Theory, Series B, vol. 153,
pp. 61–80, 2021, doi: 10.1016/j.jctb.2021.11.001.'
mla: Li, Jiaao, et al. “Nowhere-Zero 3-Flows in Toroidal Graphs.” Journal of
Combinatorial Theory, Series B, vol. 153, Elsevier BV, 2021, pp. 61–80, doi:10.1016/j.jctb.2021.11.001.
short: J. Li, Y. Ma, Z. Miao, Y. Shi, W. Wang, C.-Q. Zhang, Journal of Combinatorial
Theory, Series B 153 (2021) 61–80.
date_created: 2022-11-09T08:43:55Z
date_updated: 2022-11-09T08:44:37Z
department:
- _id: '542'
doi: 10.1016/j.jctb.2021.11.001
intvolume: ' 153'
keyword:
- Computational Theory and Mathematics
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science
language:
- iso: eng
page: 61-80
publication: Journal of Combinatorial Theory, Series B
publication_identifier:
issn:
- 0095-8956
publication_status: published
publisher: Elsevier BV
status: public
title: Nowhere-zero 3-flows in toroidal graphs
type: journal_article
user_id: '15540'
volume: 153
year: '2021'
...
---
_id: '29421'
author:
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: M.
full_name: Vermeeren, M.
last_name: Vermeeren
citation:
ama: 'Ober-Blöbaum S, Vermeeren M. Superconvergence of galerkin variational integrators.
In: IFAC-PapersOnLine, ed. 7th IIFAC Workshop on Lagrangian and Hamiltonian
Methods for Nonlinear Control LHMNC. Vol 54(19). ; 2021:327-333.'
apa: 'Ober-Blöbaum, S., & Vermeeren, M. (2021). Superconvergence of galerkin
variational integrators. In IFAC-PapersOnLine (Ed.), 7th IIFAC Workshop on
Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC: Vol. 54(19)
(pp. 327–333).'
bibtex: '@inproceedings{Ober-Blöbaum_Vermeeren_2021, title={Superconvergence of
galerkin variational integrators}, volume={54(19)}, booktitle={7th IIFAC Workshop
on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC}, author={Ober-Blöbaum,
Sina and Vermeeren, M.}, editor={IFAC-PapersOnLine}, year={2021}, pages={327–333}
}'
chicago: Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational
Integrators.” In 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for
Nonlinear Control LHMNC, edited by IFAC-PapersOnLine, 54(19):327–33, 2021.
ieee: S. Ober-Blöbaum and M. Vermeeren, “Superconvergence of galerkin variational
integrators,” in 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for
Nonlinear Control LHMNC, 2021, vol. 54(19), pp. 327–333.
mla: Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational
Integrators.” 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for
Nonlinear Control LHMNC, edited by IFAC-PapersOnLine, vol. 54(19), 2021, pp.
327–33.
short: 'S. Ober-Blöbaum, M. Vermeeren, in: IFAC-PapersOnLine (Ed.), 7th IIFAC Workshop
on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC, 2021, pp. 327–333.'
corporate_editor:
- IFAC-PapersOnLine
date_created: 2022-01-18T14:27:56Z
date_updated: 2022-01-21T13:36:53Z
department:
- _id: '636'
language:
- iso: eng
page: 327-333
publication: 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear
Control LHMNC
status: public
title: Superconvergence of galerkin variational integrators
type: conference
user_id: '15694'
volume: 54(19)
year: '2021'
...
---
_id: '16294'
abstract:
- lang: eng
text: "Model predictive control is a prominent approach to construct a feedback\r\ncontrol
loop for dynamical systems. Due to real-time constraints, the major\r\nchallenge
in MPC is to solve model-based optimal control problems in a very\r\nshort amount
of time. For linear-quadratic problems, Bemporad et al. have\r\nproposed an explicit
formulation where the underlying optimization problems are\r\nsolved a priori
in an offline phase. In this article, we present an extension\r\nof this concept
in two significant ways. We consider nonlinear problems and -\r\nmore importantly
- problems with multiple conflicting objective functions. In\r\nthe offline phase,
we build a library of Pareto optimal solutions from which we\r\nthen obtain a
valid compromise solution in the online phase according to a\r\ndecision maker's
preference. Since the standard multi-parametric programming\r\napproach is no
longer valid in this situation, we instead use interpolation\r\nbetween different
entries of the library. To reduce the number of problems that\r\nhave to be solved
in the offline phase, we exploit symmetries in the dynamical\r\nsystem and the
corresponding multiobjective optimal control problem. The\r\nresults are verified
using two different examples from autonomous driving."
author:
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
citation:
ama: Ober-Blöbaum S, Peitz S. Explicit multiobjective model predictive control for
nonlinear systems with symmetries. International Journal of Robust and Nonlinear
Control. 2021;31(2):380-403. doi:10.1002/rnc.5281
apa: Ober-Blöbaum, S., & Peitz, S. (2021). Explicit multiobjective model predictive
control for nonlinear systems with symmetries. International Journal of Robust
and Nonlinear Control, 31(2), 380–403. https://doi.org/10.1002/rnc.5281
bibtex: '@article{Ober-Blöbaum_Peitz_2021, title={Explicit multiobjective model
predictive control for nonlinear systems with symmetries}, volume={31(2)}, DOI={10.1002/rnc.5281}, journal={International
Journal of Robust and Nonlinear Control}, author={Ober-Blöbaum, Sina and Peitz,
Sebastian}, year={2021}, pages={380–403} }'
chicago: 'Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model
Predictive Control for Nonlinear Systems with Symmetries.” International Journal
of Robust and Nonlinear Control 31(2) (2021): 380–403. https://doi.org/10.1002/rnc.5281.'
ieee: 'S. Ober-Blöbaum and S. Peitz, “Explicit multiobjective model predictive control
for nonlinear systems with symmetries,” International Journal of Robust and
Nonlinear Control, vol. 31(2), pp. 380–403, 2021, doi: 10.1002/rnc.5281.'
mla: Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive
Control for Nonlinear Systems with Symmetries.” International Journal of Robust
and Nonlinear Control, vol. 31(2), 2021, pp. 380–403, doi:10.1002/rnc.5281.
short: S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear
Control 31(2) (2021) 380–403.
date_created: 2020-03-13T12:44:36Z
date_updated: 2022-01-24T13:27:50Z
department:
- _id: '101'
doi: 10.1002/rnc.5281
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://onlinelibrary.wiley.com/doi/epdf/10.1002/rnc.5281
oa: '1'
page: 380-403
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: International Journal of Robust and Nonlinear Control
status: public
title: Explicit multiobjective model predictive control for nonlinear systems with
symmetries
type: journal_article
user_id: '15694'
volume: 31(2)
year: '2021'
...
---
_id: '29543'
article_number: '109804'
author:
- first_name: Walid
full_name: Djema, Walid
last_name: Djema
- first_name: Laetitia
full_name: Giraldi, Laetitia
last_name: Giraldi
- first_name: Sofya
full_name: Maslovskaya, Sofya
id: '87909'
last_name: Maslovskaya
- first_name: Olivier
full_name: Bernard, Olivier
last_name: Bernard
citation:
ama: Djema W, Giraldi L, Maslovskaya S, Bernard O. Turnpike features in optimal
selection of species represented by quota models. Automatica. 2021;132.
doi:10.1016/j.automatica.2021.109804
apa: Djema, W., Giraldi, L., Maslovskaya, S., & Bernard, O. (2021). Turnpike
features in optimal selection of species represented by quota models. Automatica,
132, Article 109804. https://doi.org/10.1016/j.automatica.2021.109804
bibtex: '@article{Djema_Giraldi_Maslovskaya_Bernard_2021, title={Turnpike features
in optimal selection of species represented by quota models}, volume={132}, DOI={10.1016/j.automatica.2021.109804},
number={109804}, journal={Automatica}, publisher={Elsevier BV}, author={Djema,
Walid and Giraldi, Laetitia and Maslovskaya, Sofya and Bernard, Olivier}, year={2021}
}'
chicago: Djema, Walid, Laetitia Giraldi, Sofya Maslovskaya, and Olivier Bernard.
“Turnpike Features in Optimal Selection of Species Represented by Quota Models.”
Automatica 132 (2021). https://doi.org/10.1016/j.automatica.2021.109804.
ieee: 'W. Djema, L. Giraldi, S. Maslovskaya, and O. Bernard, “Turnpike features
in optimal selection of species represented by quota models,” Automatica,
vol. 132, Art. no. 109804, 2021, doi: 10.1016/j.automatica.2021.109804.'
mla: Djema, Walid, et al. “Turnpike Features in Optimal Selection of Species Represented
by Quota Models.” Automatica, vol. 132, 109804, Elsevier BV, 2021, doi:10.1016/j.automatica.2021.109804.
short: W. Djema, L. Giraldi, S. Maslovskaya, O. Bernard, Automatica 132 (2021).
date_created: 2022-01-26T13:13:06Z
date_updated: 2022-01-26T13:15:33Z
department:
- _id: '636'
doi: 10.1016/j.automatica.2021.109804
intvolume: ' 132'
keyword:
- Electrical and Electronic Engineering
- Control and Systems Engineering
language:
- iso: eng
publication: Automatica
publication_identifier:
issn:
- 0005-1098
publication_status: published
publisher: Elsevier BV
status: public
title: Turnpike features in optimal selection of species represented by quota models
type: journal_article
user_id: '87909'
volume: 132
year: '2021'
...
---
_id: '32810'
article_number: '103451'
author:
- first_name: Jiaao
full_name: Li, Jiaao
last_name: Li
- first_name: Yulai
full_name: Ma, Yulai
id: '92748'
last_name: Ma
- first_name: Yongtang
full_name: Shi, Yongtang
last_name: Shi
- first_name: Weifan
full_name: Wang, Weifan
last_name: Wang
- first_name: Yezhou
full_name: Wu, Yezhou
last_name: Wu
citation:
ama: Li J, Ma Y, Shi Y, Wang W, Wu Y. On 3-flow-critical graphs. European Journal
of Combinatorics. 2021;100. doi:10.1016/j.ejc.2021.103451
apa: Li, J., Ma, Y., Shi, Y., Wang, W., & Wu, Y. (2021). On 3-flow-critical
graphs. European Journal of Combinatorics, 100, Article 103451.
https://doi.org/10.1016/j.ejc.2021.103451
bibtex: '@article{Li_Ma_Shi_Wang_Wu_2021, title={On 3-flow-critical graphs}, volume={100},
DOI={10.1016/j.ejc.2021.103451},
number={103451}, journal={European Journal of Combinatorics}, publisher={Elsevier
BV}, author={Li, Jiaao and Ma, Yulai and Shi, Yongtang and Wang, Weifan and Wu,
Yezhou}, year={2021} }'
chicago: Li, Jiaao, Yulai Ma, Yongtang Shi, Weifan Wang, and Yezhou Wu. “On 3-Flow-Critical
Graphs.” European Journal of Combinatorics 100 (2021). https://doi.org/10.1016/j.ejc.2021.103451.
ieee: 'J. Li, Y. Ma, Y. Shi, W. Wang, and Y. Wu, “On 3-flow-critical graphs,” European
Journal of Combinatorics, vol. 100, Art. no. 103451, 2021, doi: 10.1016/j.ejc.2021.103451.'
mla: Li, Jiaao, et al. “On 3-Flow-Critical Graphs.” European Journal of Combinatorics,
vol. 100, 103451, Elsevier BV, 2021, doi:10.1016/j.ejc.2021.103451.
short: J. Li, Y. Ma, Y. Shi, W. Wang, Y. Wu, European Journal of Combinatorics 100
(2021).
date_created: 2022-08-15T09:35:02Z
date_updated: 2022-08-15T09:35:32Z
department:
- _id: '542'
doi: 10.1016/j.ejc.2021.103451
intvolume: ' 100'
keyword:
- Discrete Mathematics and Combinatorics
language:
- iso: eng
publication: European Journal of Combinatorics
publication_identifier:
issn:
- 0195-6698
publication_status: published
publisher: Elsevier BV
status: public
title: On 3-flow-critical graphs
type: journal_article
user_id: '15540'
volume: 100
year: '2021'
...
---
_id: '22894'
abstract:
- lang: eng
text: "The first order optimality conditions of optimal control problems (OCPs)
can\r\nbe regarded as boundary value problems for Hamiltonian systems. Variational
or\r\nsymplectic discretisation methods are classically known for their excellent\r\nlong
term behaviour. As boundary value problems are posed on intervals of\r\nfixed,
moderate length, it is not immediately clear whether methods can profit\r\nfrom
structure preservation in this context. When parameters are present,\r\nsolutions
can undergo bifurcations, for instance, two solutions can merge and\r\nannihilate
one another as parameters are varied. We will show that generic\r\nbifurcations
of an OCP are preserved under discretisation when the OCP is\r\neither directly
discretised to a discrete OCP (direct method) or translated\r\ninto a Hamiltonian
boundary value problem using first order necessary\r\nconditions of optimality
which is then solved using a symplectic integrator\r\n(indirect method). Moreover,
certain bifurcations break when a non-symplectic\r\nscheme is used. The general
phenomenon is illustrated on the example of a cut\r\nlocus of an ellipsoid."
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: Offen C, Ober-Blöbaum S. Bifurcation preserving discretisations of optimal
control problems. 2021;54(19):334-339. doi:https://doi.org/10.1016/j.ifacol.2021.11.099
apa: 'Offen, C., & Ober-Blöbaum, S. (2021). Bifurcation preserving discretisations
of optimal control problems: Vol. 54(19) (pp. 334–339). https://doi.org/10.1016/j.ifacol.2021.11.099'
bibtex: '@article{Offen_Ober-Blöbaum_2021, series={IFAC-PapersOnLine}, title={Bifurcation
preserving discretisations of optimal control problems}, volume={54(19)}, DOI={https://doi.org/10.1016/j.ifacol.2021.11.099},
author={Offen, Christian and Ober-Blöbaum, Sina}, year={2021}, pages={334–339},
collection={IFAC-PapersOnLine} }'
chicago: Offen, Christian, and Sina Ober-Blöbaum. “Bifurcation Preserving Discretisations
of Optimal Control Problems.” IFAC-PapersOnLine, 2021. https://doi.org/10.1016/j.ifacol.2021.11.099.
ieee: 'C. Offen and S. Ober-Blöbaum, “Bifurcation preserving discretisations of
optimal control problems,” vol. 54(19). pp. 334–339, 2021, doi: https://doi.org/10.1016/j.ifacol.2021.11.099.'
mla: Offen, Christian, and Sina Ober-Blöbaum. Bifurcation Preserving Discretisations
of Optimal Control Problems. 2021, pp. 334–39, doi:https://doi.org/10.1016/j.ifacol.2021.11.099.
short: C. Offen, S. Ober-Blöbaum, 54(19) (2021) 334–339.
conference:
end_date: 2021-10-13
location: Berlin, Germany
name: 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control,
LHMNC 2021
start_date: 2021-10-11
date_created: 2021-07-29T09:38:32Z
date_updated: 2023-11-29T10:19:41Z
ddc:
- '510'
department:
- _id: '636'
doi: https://doi.org/10.1016/j.ifacol.2021.11.099
external_id:
arxiv:
- '2107.13853'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2021-07-29T09:37:49Z
date_updated: 2021-07-29T09:37:49Z
file_id: '22895'
file_name: ifacconf.pdf
file_size: 3125220
relation: main_file
file_date_updated: 2021-07-29T09:37:49Z
has_accepted_license: '1'
keyword:
- optimal control
- catastrophe theory
- bifurcations
- variational methods
- symplectic integrators
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/S2405896321021236
oa: '1'
page: 334-339
publication_identifier:
issn:
- 2405-8963
publication_status: published
quality_controlled: '1'
related_material:
link:
- description: GitHub/Zenodo
relation: software
url: https://doi.org/10.5281/zenodo.4562664
series_title: IFAC-PapersOnLine
status: public
title: Bifurcation preserving discretisations of optimal control problems
type: conference
user_id: '15694'
volume: 54(19)
year: '2021'
...
---
_id: '21572'
author:
- first_name: Steffen
full_name: Ridderbusch, Steffen
last_name: Ridderbusch
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Paul
full_name: Goulart, Paul
last_name: Goulart
citation:
ama: 'Ridderbusch S, Offen C, Ober-Blöbaum S, Goulart P. Learning ODE Models with
Qualitative Structure Using Gaussian Processes . In: 2021 60th IEEE Conference
on Decision and Control (CDC). IEEE; 2021:2896. doi:10.1109/CDC45484.2021.9683426'
apa: Ridderbusch, S., Offen, C., Ober-Blöbaum, S., & Goulart, P. (2021). Learning
ODE Models with Qualitative Structure Using Gaussian Processes . 2021 60th
IEEE Conference on Decision and Control (CDC), 2896. https://doi.org/10.1109/CDC45484.2021.9683426
bibtex: '@inproceedings{Ridderbusch_Offen_Ober-Blöbaum_Goulart_2021, title={Learning
ODE Models with Qualitative Structure Using Gaussian Processes }, DOI={10.1109/CDC45484.2021.9683426},
booktitle={2021 60th IEEE Conference on Decision and Control (CDC)}, publisher={IEEE},
author={Ridderbusch, Steffen and Offen, Christian and Ober-Blöbaum, Sina and Goulart,
Paul}, year={2021}, pages={2896} }'
chicago: Ridderbusch, Steffen, Christian Offen, Sina Ober-Blöbaum, and Paul Goulart.
“Learning ODE Models with Qualitative Structure Using Gaussian Processes .” In
2021 60th IEEE Conference on Decision and Control (CDC), 2896. IEEE, 2021.
https://doi.org/10.1109/CDC45484.2021.9683426.
ieee: 'S. Ridderbusch, C. Offen, S. Ober-Blöbaum, and P. Goulart, “Learning ODE
Models with Qualitative Structure Using Gaussian Processes ,” in 2021 60th
IEEE Conference on Decision and Control (CDC), Austin, TX, USA, 2021, p. 2896,
doi: 10.1109/CDC45484.2021.9683426.'
mla: Ridderbusch, Steffen, et al. “Learning ODE Models with Qualitative Structure
Using Gaussian Processes .” 2021 60th IEEE Conference on Decision and Control
(CDC), IEEE, 2021, p. 2896, doi:10.1109/CDC45484.2021.9683426.
short: 'S. Ridderbusch, C. Offen, S. Ober-Blöbaum, P. Goulart, in: 2021 60th IEEE
Conference on Decision and Control (CDC), IEEE, 2021, p. 2896.'
conference:
end_date: 2021-12-17
location: Austin, TX, USA
name: 60th IEEE Conference on Decision and Control (CDC)
start_date: 2021-12-14
date_created: 2021-03-30T10:27:44Z
date_updated: 2023-11-29T10:24:55Z
department:
- _id: '636'
doi: 10.1109/CDC45484.2021.9683426
external_id:
arxiv:
- '2011.05364'
language:
- iso: eng
page: '2896'
publication: 2021 60th IEEE Conference on Decision and Control (CDC)
publication_identifier:
eisbn:
- 978-1-6654-3659-5
publication_status: published
publisher: IEEE
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Crown421/StructureGPs-paper
status: public
title: 'Learning ODE Models with Qualitative Structure Using Gaussian Processes '
type: conference
user_id: '15694'
year: '2021'
...
---
_id: '21592'
abstract:
- lang: eng
text: We propose a reachability approach for infinite and finite horizon multi-objective
optimization problems for low-thrust spacecraft trajectory design. The main advantage
of the proposed method is that the Pareto front can be efficiently constructed
from the zero level set of the solution to a Hamilton-Jacobi-Bellman equation.
We demonstrate the proposed method by applying it to a low-thrust spacecraft trajectory
design problem. By deriving the analytic expression for the Hamiltonian and the
optimal control policy, we are able to efficiently compute the backward reachable
set and reconstruct the optimal trajectories. Furthermore, we show that any reconstructed
trajectory will be guaranteed to be weakly Pareto optimal. The proposed method
can be used as a benchmark for future research of applying reachability analysis
to low-thrust spacecraft trajectory design.
author:
- first_name: Nikolaus
full_name: Vertovec, Nikolaus
id: '87056'
last_name: Vertovec
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Kostas
full_name: Margellos, Kostas
last_name: Margellos
citation:
ama: 'Vertovec N, Ober-Blöbaum S, Margellos K. Multi-objective minimum time optimal
control for low-thrust trajectory design. In: ; :1975-1980.'
apa: Vertovec, N., Ober-Blöbaum, S., & Margellos, K. (n.d.). Multi-objective
minimum time optimal control for low-thrust trajectory design. 1975–1980.
bibtex: '@inproceedings{Vertovec_Ober-Blöbaum_Margellos, title={Multi-objective
minimum time optimal control for low-thrust trajectory design}, author={Vertovec,
Nikolaus and Ober-Blöbaum, Sina and Margellos, Kostas}, pages={1975–1980} }'
chicago: Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Multi-Objective
Minimum Time Optimal Control for Low-Thrust Trajectory Design,” 1975–80, n.d.
ieee: N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Multi-objective minimum time
optimal control for low-thrust trajectory design,” Rotterdam, the Netherlands,
pp. 1975–1980.
mla: Vertovec, Nikolaus, et al. Multi-Objective Minimum Time Optimal Control
for Low-Thrust Trajectory Design. pp. 1975–80.
short: 'N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: n.d., pp. 1975–1980.'
conference:
end_date: 2021-07-02
location: Rotterdam, the Netherlands
name: 2021 European Control Conference (ECC)
start_date: 2021-06-29
date_created: 2021-04-03T03:00:35Z
date_updated: 2023-11-29T10:26:49Z
department:
- _id: '636'
external_id:
arxiv:
- '2103.08813'
language:
- iso: eng
page: 1975-1980
publication_status: accepted
status: public
title: Multi-objective minimum time optimal control for low-thrust trajectory design
type: conference
user_id: '15694'
year: '2021'
...
---
_id: '29868'
author:
- first_name: F.
full_name: Jiménez, F.
last_name: Jiménez
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Jiménez F, Ober-Blöbaum S. Fractional Damping Through Restricted Calculus
of Variations. In: Nichtlineare Sci 31. Vol 46. J Nonlinear Sci . ; 2021.'
apa: Jiménez, F., & Ober-Blöbaum, S. (2021). Fractional Damping Through Restricted
Calculus of Variations. Nichtlineare Sci 31, 46.
bibtex: '@inproceedings{Jiménez_Ober-Blöbaum_2021, series={J Nonlinear Sci }, title={Fractional
Damping Through Restricted Calculus of Variations}, volume={46}, booktitle={Nichtlineare
Sci 31}, author={Jiménez, F. and Ober-Blöbaum, Sina}, year={2021}, collection={J
Nonlinear Sci } }'
chicago: Jiménez, F., and Sina Ober-Blöbaum. “Fractional Damping Through Restricted
Calculus of Variations.” In Nichtlineare Sci 31, Vol. 46. J Nonlinear Sci
, 2021.
ieee: F. Jiménez and S. Ober-Blöbaum, “Fractional Damping Through Restricted Calculus
of Variations,” in Nichtlineare Sci 31, 2021, vol. 46.
mla: Jiménez, F., and Sina Ober-Blöbaum. “Fractional Damping Through Restricted
Calculus of Variations.” Nichtlineare Sci 31, vol. 46, 2021.
short: 'F. Jiménez, S. Ober-Blöbaum, in: Nichtlineare Sci 31, 2021.'
date_created: 2022-02-17T07:28:47Z
date_updated: 2023-11-29T10:23:46Z
department:
- _id: '636'
intvolume: ' 46'
language:
- iso: eng
publication: Nichtlineare Sci 31
series_title: 'J Nonlinear Sci '
status: public
title: Fractional Damping Through Restricted Calculus of Variations
type: conference
user_id: '15694'
volume: 46
year: '2021'
...