---
_id: '16296'
abstract:
- lang: eng
text: "Multiobjective optimization plays an increasingly important role in modern\r\napplications,
where several objectives are often of equal importance. The task\r\nin multiobjective
optimization and multiobjective optimal control is therefore\r\nto compute the
set of optimal compromises (the Pareto set) between the\r\nconflicting objectives.
Since the Pareto set generally consists of an infinite\r\nnumber of solutions,
the computational effort can quickly become challenging\r\nwhich is particularly
problematic when the objectives are costly to evaluate as\r\nis the case for models
governed by partial differential equations (PDEs). To\r\ndecrease the numerical
effort to an affordable amount, surrogate models can be\r\nused to replace the
expensive PDE evaluations. Existing multiobjective\r\noptimization methods using
model reduction are limited either to low parameter\r\ndimensions or to few (ideally
two) objectives. In this article, we present a\r\ncombination of the reduced basis
model reduction method with a continuation\r\napproach using inexact gradients.
The resulting approach can handle an\r\narbitrary number of objectives while yielding
a significant reduction in\r\ncomputing time."
author:
- first_name: Stefan
full_name: Banholzer, Stefan
last_name: Banholzer
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Stefan
full_name: Volkwein, Stefan
last_name: Volkwein
citation:
ama: 'Banholzer S, Gebken B, Dellnitz M, Peitz S, Volkwein S. ROM-Based Multiobjective
Optimization of Elliptic PDEs via Numerical Continuation. In: Michael H, Roland
H, Christian K, Michael U, Stefan U, eds. Non-Smooth and Complementarity-Based
Distributed Parameter Systems. Springer; 2022:43-76. doi:10.1007/978-3-030-79393-7_3'
apa: Banholzer, S., Gebken, B., Dellnitz, M., Peitz, S., & Volkwein, S. (2022).
ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation.
In H. Michael, H. Roland, K. Christian, U. Michael, & U. Stefan (Eds.), Non-Smooth
and Complementarity-Based Distributed Parameter Systems (pp. 43–76). Springer.
https://doi.org/10.1007/978-3-030-79393-7_3
bibtex: '@inbook{Banholzer_Gebken_Dellnitz_Peitz_Volkwein_2022, place={Cham}, title={ROM-Based
Multiobjective Optimization of Elliptic PDEs via Numerical Continuation}, DOI={10.1007/978-3-030-79393-7_3},
booktitle={Non-Smooth and Complementarity-Based Distributed Parameter Systems},
publisher={Springer}, author={Banholzer, Stefan and Gebken, Bennet and Dellnitz,
Michael and Peitz, Sebastian and Volkwein, Stefan}, editor={Michael, Hintermüller
and Roland, Herzog and Christian, Kanzow and Michael, Ulbrich and Stefan, Ulbrich},
year={2022}, pages={43–76} }'
chicago: 'Banholzer, Stefan, Bennet Gebken, Michael Dellnitz, Sebastian Peitz, and
Stefan Volkwein. “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical
Continuation.” In Non-Smooth and Complementarity-Based Distributed Parameter
Systems, edited by Hintermüller Michael, Herzog Roland, Kanzow Christian,
Ulbrich Michael, and Ulbrich Stefan, 43–76. Cham: Springer, 2022. https://doi.org/10.1007/978-3-030-79393-7_3.'
ieee: 'S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, and S. Volkwein, “ROM-Based
Multiobjective Optimization of Elliptic PDEs via Numerical Continuation,” in Non-Smooth
and Complementarity-Based Distributed Parameter Systems, H. Michael, H. Roland,
K. Christian, U. Michael, and U. Stefan, Eds. Cham: Springer, 2022, pp. 43–76.'
mla: Banholzer, Stefan, et al. “ROM-Based Multiobjective Optimization of Elliptic
PDEs via Numerical Continuation.” Non-Smooth and Complementarity-Based Distributed
Parameter Systems, edited by Hintermüller Michael et al., Springer, 2022,
pp. 43–76, doi:10.1007/978-3-030-79393-7_3.
short: 'S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, S. Volkwein, in: H. Michael,
H. Roland, K. Christian, U. Michael, U. Stefan (Eds.), Non-Smooth and Complementarity-Based
Distributed Parameter Systems, Springer, Cham, 2022, pp. 43–76.'
date_created: 2020-03-13T12:45:31Z
date_updated: 2022-03-14T13:04:51Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/978-3-030-79393-7_3
editor:
- first_name: Hintermüller
full_name: Michael, Hintermüller
last_name: Michael
- first_name: Herzog
full_name: Roland, Herzog
last_name: Roland
- first_name: Kanzow
full_name: Christian, Kanzow
last_name: Christian
- first_name: Ulbrich
full_name: Michael, Ulbrich
last_name: Michael
- first_name: Ulbrich
full_name: Stefan, Ulbrich
last_name: Stefan
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/1906.09075.pdf
oa: '1'
page: 43-76
place: Cham
publication: Non-Smooth and Complementarity-Based Distributed Parameter Systems
publication_identifier:
isbn:
- 978-3-030-79392-0
publisher: Springer
status: public
title: ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation
type: book_chapter
user_id: '47427'
year: '2022'
...
---
_id: '30294'
abstract:
- lang: eng
text: With the ever increasing capabilities of sensors and controllers, autonomous
driving is quickly becoming a reality. This disruptive change in the automotive
industry poses major challenges for manufacturers as well as suppliers as entirely
new design and testing strategies have to be developed to remain competitive.
Most importantly, the complexity of autonomously driving vehicles in a complex,
uncertain, and safety-critical environment requires new testing procedures to
cover the almost infinite range of potential scenarios.
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Sebastian
full_name: Bannenberg, Sebastian
last_name: Bannenberg
citation:
ama: 'Peitz S, Dellnitz M, Bannenberg S. Efficient Virtual Design and Testing of
Autonomous Vehicles. In: Bock HG, Küfer K-H, Maas P, Milde A, Schulz V, eds. German
Success Stories in Industrial Mathematics. Vol 35. Mathematics in Industry.
Springer International Publishing; 2022. doi:10.1007/978-3-030-81455-7_23'
apa: Peitz, S., Dellnitz, M., & Bannenberg, S. (2022). Efficient Virtual Design
and Testing of Autonomous Vehicles. In H. G. Bock, K.-H. Küfer, P. Maas, A. Milde,
& V. Schulz (Eds.), German Success Stories in Industrial Mathematics
(Vol. 35). Springer International Publishing. https://doi.org/10.1007/978-3-030-81455-7_23
bibtex: '@inbook{Peitz_Dellnitz_Bannenberg_2022, place={Cham}, series={Mathematics
in Industry}, title={Efficient Virtual Design and Testing of Autonomous Vehicles},
volume={35}, DOI={10.1007/978-3-030-81455-7_23},
booktitle={German Success Stories in Industrial Mathematics}, publisher={Springer
International Publishing}, author={Peitz, Sebastian and Dellnitz, Michael and
Bannenberg, Sebastian}, editor={Bock, H. G. and Küfer, K.-H. and Maas, P. and
Milde, A. and Schulz, V.}, year={2022}, collection={Mathematics in Industry} }'
chicago: 'Peitz, Sebastian, Michael Dellnitz, and Sebastian Bannenberg. “Efficient
Virtual Design and Testing of Autonomous Vehicles.” In German Success Stories
in Industrial Mathematics, edited by H. G. Bock, K.-H. Küfer, P. Maas, A.
Milde, and V. Schulz, Vol. 35. Mathematics in Industry. Cham: Springer International
Publishing, 2022. https://doi.org/10.1007/978-3-030-81455-7_23.'
ieee: 'S. Peitz, M. Dellnitz, and S. Bannenberg, “Efficient Virtual Design and Testing
of Autonomous Vehicles,” in German Success Stories in Industrial Mathematics,
vol. 35, H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, and V. Schulz, Eds. Cham:
Springer International Publishing, 2022.'
mla: Peitz, Sebastian, et al. “Efficient Virtual Design and Testing of Autonomous
Vehicles.” German Success Stories in Industrial Mathematics, edited by
H. G. Bock et al., vol. 35, Springer International Publishing, 2022, doi:10.1007/978-3-030-81455-7_23.
short: 'S. Peitz, M. Dellnitz, S. Bannenberg, in: H.G. Bock, K.-H. Küfer, P. Maas,
A. Milde, V. Schulz (Eds.), German Success Stories in Industrial Mathematics,
Springer International Publishing, Cham, 2022.'
date_created: 2022-03-14T07:32:41Z
date_updated: 2022-03-14T07:42:01Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/978-3-030-81455-7_23
editor:
- first_name: H. G.
full_name: Bock, H. G.
last_name: Bock
- first_name: K.-H.
full_name: Küfer, K.-H.
last_name: Küfer
- first_name: P.
full_name: Maas, P.
last_name: Maas
- first_name: A.
full_name: Milde, A.
last_name: Milde
- first_name: V.
full_name: Schulz, V.
last_name: Schulz
intvolume: ' 35'
language:
- iso: eng
place: Cham
publication: German Success Stories in Industrial Mathematics
publication_identifier:
isbn:
- '9783030814540'
- '9783030814557'
issn:
- 1612-3956
- 2198-3283
publication_status: published
publisher: Springer International Publishing
series_title: Mathematics in Industry
status: public
title: Efficient Virtual Design and Testing of Autonomous Vehicles
type: book_chapter
user_id: '47427'
volume: 35
year: '2022'
...
---
_id: '29673'
abstract:
- lang: eng
text: Koopman operator theory has been successfully applied to problems from various
research areas such as fluid dynamics, molecular dynamics, climate science, engineering,
and biology. Applications include detecting metastable or coherent sets, coarse-graining,
system identification, and control. There is an intricate connection between dynamical
systems driven by stochastic differential equations and quantum mechanics. In
this paper, we compare the ground-state transformation and Nelson's stochastic
mechanics and demonstrate how data-driven methods developed for the approximation
of the Koopman operator can be used to analyze quantum physics problems. Moreover,
we exploit the relationship between Schrödinger operators and stochastic control
problems to show that modern data-driven methods for stochastic control can be
used to solve the stationary or imaginary-time Schrödinger equation. Our findings
open up a new avenue towards solving Schrödinger's equation using recently developed
tools from data science.
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: 'Klus S, Nüske F, Peitz S. Koopman analysis of quantum systems. Journal
of Physics A: Mathematical and Theoretical. 2022;55(31):314002. doi:10.1088/1751-8121/ac7d22'
apa: 'Klus, S., Nüske, F., & Peitz, S. (2022). Koopman analysis of quantum systems.
Journal of Physics A: Mathematical and Theoretical, 55(31), 314002.
https://doi.org/10.1088/1751-8121/ac7d22'
bibtex: '@article{Klus_Nüske_Peitz_2022, title={Koopman analysis of quantum systems},
volume={55}, DOI={10.1088/1751-8121/ac7d22},
number={31}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP
Publishing Ltd.}, author={Klus, Stefan and Nüske, Feliks and Peitz, Sebastian},
year={2022}, pages={314002} }'
chicago: 'Klus, Stefan, Feliks Nüske, and Sebastian Peitz. “Koopman Analysis of
Quantum Systems.” Journal of Physics A: Mathematical and Theoretical 55,
no. 31 (2022): 314002. https://doi.org/10.1088/1751-8121/ac7d22.'
ieee: 'S. Klus, F. Nüske, and S. Peitz, “Koopman analysis of quantum systems,” Journal
of Physics A: Mathematical and Theoretical, vol. 55, no. 31, p. 314002, 2022,
doi: 10.1088/1751-8121/ac7d22.'
mla: 'Klus, Stefan, et al. “Koopman Analysis of Quantum Systems.” Journal of
Physics A: Mathematical and Theoretical, vol. 55, no. 31, IOP Publishing Ltd.,
2022, p. 314002, doi:10.1088/1751-8121/ac7d22.'
short: 'S. Klus, F. Nüske, S. Peitz, Journal of Physics A: Mathematical and Theoretical
55 (2022) 314002.'
date_created: 2022-01-31T09:49:40Z
date_updated: 2022-07-18T14:26:41Z
department:
- _id: '655'
- _id: '101'
doi: 10.1088/1751-8121/ac7d22
external_id:
arxiv:
- '2201.12062'
intvolume: ' 55'
issue: '31'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://iopscience.iop.org/article/10.1088/1751-8121/ac7d22/pdf
oa: '1'
page: '314002'
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_status: published
publisher: IOP Publishing Ltd.
status: public
title: Koopman analysis of quantum systems
type: journal_article
user_id: '47427'
volume: 55
year: '2022'
...
---
_id: '34618'
abstract:
- lang: eng
text: "In this article, we show how second-order derivative information can be\r\nincorporated
into gradient sampling methods for nonsmooth optimization. The\r\nsecond-order
information we consider is essentially the set of coefficients of\r\nall second-order
Taylor expansions of the objective in a closed ball around a\r\ngiven point. Based
on this concept, we define a model of the objective as the\r\nmaximum of these
Taylor expansions. Iteratively minimizing this model\r\n(constrained to the closed
ball) results in a simple descent method, for which\r\nwe prove convergence to
minimal points in case the objective is convex. To\r\nobtain an implementable
method, we construct an approximation scheme for the\r\nsecond-order information
based on sampling objective values, gradients and\r\nHessian matrices at finitely
many points. Using a set of test problems, we\r\ncompare the resulting method
to five other available solvers. Considering the\r\nnumber of function evaluations,
the results suggest that the method we propose\r\nis superior to the standard
gradient sampling method, and competitive compared\r\nto other methods."
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
citation:
ama: Gebken B. Using second-order information in gradient sampling methods for
nonsmooth optimization. arXiv:221004579. Published online 2022.
apa: Gebken, B. (2022). Using second-order information in gradient sampling methods
for nonsmooth optimization. In arXiv:2210.04579.
bibtex: '@article{Gebken_2022, title={Using second-order information in gradient
sampling methods for nonsmooth optimization}, journal={arXiv:2210.04579}, author={Gebken,
Bennet}, year={2022} }'
chicago: Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods
for Nonsmooth Optimization.” ArXiv:2210.04579, 2022.
ieee: B. Gebken, “Using second-order information in gradient sampling methods for
nonsmooth optimization,” arXiv:2210.04579. 2022.
mla: Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods
for Nonsmooth Optimization.” ArXiv:2210.04579, 2022.
short: B. Gebken, ArXiv:2210.04579 (2022).
date_created: 2022-12-20T15:25:17Z
date_updated: 2022-12-20T15:28:54Z
department:
- _id: '101'
external_id:
arxiv:
- '2210.04579'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2210.04579
oa: '1'
publication: arXiv:2210.04579
status: public
title: Using second-order information in gradient sampling methods for nonsmooth
optimization
type: preprint
user_id: '32643'
year: '2022'
...
---
_id: '31556'
abstract:
- lang: ger
text: Mehrzieloptimierung behandelt Probleme, bei denen mehrere skalare Zielfunktionen
simultan optimiert werden sollen. Ein Punkt ist in diesem Fall optimal, wenn es
keinen anderen Punkt gibt, der mindestens genauso gut ist in allen Zielfunktionen
und besser in mindestens einer Zielfunktion. Ein notwendiges Optimalitätskriterium
lässt sich über Ableitungsinformationen erster Ordnung der Zielfunktionen herleiten.
Die Menge der Punkte, die dieses notwendige Kriterium erfüllen, wird als Pareto-kritische
Menge bezeichnet. Diese Arbeit enthält neue Resultate über Pareto-kritische Mengen
für glatte und nicht-glatte Mehrzieloptimierungsprobleme, sowohl was deren Berechnung
betrifft als auch deren Struktur. Im glatten Fall erfolgt die Berechnung über
ein Fortsetzungsverfahren, im nichtglatten Fall über ein Abstiegsverfahren. Anschließend
wird die Struktur des Randes der Pareto-kritischen Menge analysiert, welcher aus
Pareto-kritischen Mengen kleinerer Subprobleme besteht. Schlussendlich werden
inverse Probleme betrachtet, bei denen zu einer gegebenen Datenmenge ein Zielfunktionsvektor
gefunden werden soll, für den die Datenpunkte kritisch sind.
- lang: eng
text: Multiobjective optimization is concerned with the simultaneous optimization
of multiple scalar-valued functions. In this case, a point is optimal if there
is no other point that is at least as good in all objectives and better in at
least one objective. A necessary condition for optimality can be derived based
on first-order information of the objectives. The set of points that satisfy this
necessary condition is called the Pareto critical set. This thesis presents new
results about Pareto critical sets for smooth and nonsmooth multiobjective optimization
problems, both in terms of their efficient computation and structural properties.
In the smooth case they are computed via a continuation method and in the nonsmooth
case via a descent method. Afterwards, the structure of the boundary of the Pareto
critical set is analyzed, which consists of Pareto critical sets of smaller subproblems.
Finally, inverse problems are considered, where a data set is given and an objective
vector is sought for which the data points are critical.
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
citation:
ama: Gebken B. Computation and Analysis of Pareto Critical Sets in Smooth and
Nonsmooth Multiobjective Optimization.; 2022. doi:10.17619/UNIPB/1-1327
apa: Gebken, B. (2022). Computation and analysis of Pareto critical sets in smooth
and nonsmooth multiobjective optimization. https://doi.org/10.17619/UNIPB/1-1327
bibtex: '@book{Gebken_2022, title={Computation and analysis of Pareto critical sets
in smooth and nonsmooth multiobjective optimization}, DOI={10.17619/UNIPB/1-1327},
author={Gebken, Bennet}, year={2022} }'
chicago: Gebken, Bennet. Computation and Analysis of Pareto Critical Sets in
Smooth and Nonsmooth Multiobjective Optimization, 2022. https://doi.org/10.17619/UNIPB/1-1327.
ieee: B. Gebken, Computation and analysis of Pareto critical sets in smooth and
nonsmooth multiobjective optimization. 2022.
mla: Gebken, Bennet. Computation and Analysis of Pareto Critical Sets in Smooth
and Nonsmooth Multiobjective Optimization. 2022, doi:10.17619/UNIPB/1-1327.
short: B. Gebken, Computation and Analysis of Pareto Critical Sets in Smooth and
Nonsmooth Multiobjective Optimization, 2022.
date_created: 2022-06-01T06:48:08Z
date_updated: 2022-06-01T07:13:09Z
department:
- _id: '101'
doi: 10.17619/UNIPB/1-1327
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://digital.ub.uni-paderborn.de/hs/download/pdf/6531779
oa: '1'
status: public
supervisor:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
title: Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective
optimization
type: dissertation
user_id: '32643'
year: '2022'
...
---
_id: '33150'
abstract:
- lang: eng
text: In this article, we build on previous work to present an optimization algorithm
for nonlinearly constrained multi-objective optimization problems. The algorithm
combines a surrogate-assisted derivative-free trust-region approach with the filter
method known from single-objective optimization. Instead of the true objective
and constraint functions, so-called fully linear models are employed and we show
how to deal with the gradient inexactness in the composite step setting, adapted
from single-objective optimization as well. Under standard assumptions, we prove
convergence of a subset of iterates to a quasi-stationary point and if constraint
qualifications hold, then the limit point is also a KKT-point of the multi-objective
problem.
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. Multi-Objective Trust-Region Filter Method for Nonlinear
Constraints using Inexact Gradients. arXiv:220812094. Published online
2022.
apa: Berkemeier, M. B., & Peitz, S. (2022). Multi-Objective Trust-Region Filter
Method for Nonlinear Constraints using Inexact Gradients. In arXiv:2208.12094.
bibtex: '@article{Berkemeier_Peitz_2022, title={Multi-Objective Trust-Region Filter
Method for Nonlinear Constraints using Inexact Gradients}, journal={arXiv:2208.12094},
author={Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2022} }'
chicago: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region
Filter Method for Nonlinear Constraints Using Inexact Gradients.” ArXiv:2208.12094,
2022.
ieee: M. B. Berkemeier and S. Peitz, “Multi-Objective Trust-Region Filter Method
for Nonlinear Constraints using Inexact Gradients,” arXiv:2208.12094. 2022.
mla: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region
Filter Method for Nonlinear Constraints Using Inexact Gradients.” ArXiv:2208.12094,
2022.
short: M.B. Berkemeier, S. Peitz, ArXiv:2208.12094 (2022).
date_created: 2022-08-26T06:08:06Z
date_updated: 2022-08-26T06:12:10Z
department:
- _id: '101'
- _id: '655'
external_id:
arxiv:
- '2208.12094'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2208.12094
oa: '1'
publication: arXiv:2208.12094
status: public
title: Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using
Inexact Gradients
type: preprint
user_id: '47427'
year: '2022'
...
---
_id: '20731'
abstract:
- lang: eng
text: We present a novel algorithm that allows us to gain detailed insight into
the effects of sparsity in linear and nonlinear optimization, which is of great
importance in many scientific areas such as image and signal processing, medical
imaging, compressed sensing, and machine learning (e.g., for the training of neural
networks). Sparsity is an important feature to ensure robustness against noisy
data, but also to find models that are interpretable and easy to analyze due to
the small number of relevant terms. It is common practice to enforce sparsity
by adding the ℓ1-norm as a weighted penalty term. In order to gain a better understanding
and to allow for an informed model selection, we directly solve the corresponding
multiobjective optimization problem (MOP) that arises when we minimize the main
objective and the ℓ1-norm simultaneously. As this MOP is in general non-convex
for nonlinear objectives, the weighting method will fail to provide all optimal
compromises. To avoid this issue, we present a continuation method which is specifically
tailored to MOPs with two objective functions one of which is the ℓ1-norm. Our
method can be seen as a generalization of well-known homotopy methods for linear
regression problems to the nonlinear case. Several numerical examples - including
neural network training - demonstrate our theoretical findings and the additional
insight that can be gained by this multiobjective approach.
article_type: original
author:
- first_name: Katharina
full_name: Bieker, Katharina
id: '32829'
last_name: Bieker
- 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: Bieker K, Gebken B, Peitz S. On the Treatment of Optimization Problems with
L1 Penalty Terms via Multiobjective Continuation. IEEE Transactions on Pattern
Analysis and Machine Intelligence. 2022;44(11):7797-7808. doi:10.1109/TPAMI.2021.3114962
apa: Bieker, K., Gebken, B., & Peitz, S. (2022). On the Treatment of Optimization
Problems with L1 Penalty Terms via Multiobjective Continuation. IEEE Transactions
on Pattern Analysis and Machine Intelligence, 44(11), 7797–7808. https://doi.org/10.1109/TPAMI.2021.3114962
bibtex: '@article{Bieker_Gebken_Peitz_2022, title={On the Treatment of Optimization
Problems with L1 Penalty Terms via Multiobjective Continuation}, volume={44},
DOI={10.1109/TPAMI.2021.3114962},
number={11}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
publisher={IEEE}, author={Bieker, Katharina and Gebken, Bennet and Peitz, Sebastian},
year={2022}, pages={7797–7808} }'
chicago: 'Bieker, Katharina, Bennet Gebken, and Sebastian Peitz. “On the Treatment
of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation.”
IEEE Transactions on Pattern Analysis and Machine Intelligence 44, no.
11 (2022): 7797–7808. https://doi.org/10.1109/TPAMI.2021.3114962.'
ieee: 'K. Bieker, B. Gebken, and S. Peitz, “On the Treatment of Optimization Problems
with L1 Penalty Terms via Multiobjective Continuation,” IEEE Transactions on
Pattern Analysis and Machine Intelligence, vol. 44, no. 11, pp. 7797–7808,
2022, doi: 10.1109/TPAMI.2021.3114962.'
mla: Bieker, Katharina, et al. “On the Treatment of Optimization Problems with L1
Penalty Terms via Multiobjective Continuation.” IEEE Transactions on Pattern
Analysis and Machine Intelligence, vol. 44, no. 11, IEEE, 2022, pp. 7797–808,
doi:10.1109/TPAMI.2021.3114962.
short: K. Bieker, B. Gebken, S. Peitz, IEEE Transactions on Pattern Analysis and
Machine Intelligence 44 (2022) 7797–7808.
date_created: 2020-12-15T07:46:36Z
date_updated: 2022-10-21T12:27:16Z
ddc:
- '510'
department:
- _id: '101'
- _id: '530'
- _id: '655'
doi: 10.1109/TPAMI.2021.3114962
file:
- access_level: closed
content_type: application/pdf
creator: speitz
date_created: 2021-09-25T11:59:15Z
date_updated: 2021-09-25T11:59:15Z
file_id: '25040'
file_name: On_the_Treatment_of_Optimization_Problems_with_L1_Penalty_Terms_via_Multiobjective_Continuation.pdf
file_size: 7990831
relation: main_file
success: 1
file_date_updated: 2021-09-25T11:59:15Z
has_accepted_license: '1'
intvolume: ' 44'
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9547772
oa: '1'
page: 7797-7808
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_status: epub_ahead
publisher: IEEE
status: public
title: On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective
Continuation
type: journal_article
user_id: '47427'
volume: 44
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: '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: '17411'
abstract:
- lang: eng
text: Many dynamical systems possess symmetries, e.g. rotational and translational
invariances of mechanical systems. These can be beneficially exploited in the
design of numerical optimal control methods. We present a model predictive control
scheme which is based on a library of precomputed motion primitives. The primitives
are equivalence classes w.r.t. the symmetry of the optimal control problems. Trim
primitives as relative equilibria w.r.t. this symmetry, play a crucial role in
the algorithm. The approach is illustrated using an academic mobile robot example.
author:
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: 'Flaßkamp K, Ober-Blöbaum S, Peitz S. Symmetry in Optimal Control: A Multiobjective
Model Predictive Control Approach. In: Junge O, Schütze O, Froyland G, Ober-Blöbaum
S, Padberg-Gehle K, eds. Advances in Dynamics, Optimization and Computation.
Cham: Springer; 2020. doi:10.1007/978-3-030-51264-4_9'
apa: 'Flaßkamp, K., Ober-Blöbaum, S., & Peitz, S. (2020). Symmetry in Optimal
Control: A Multiobjective Model Predictive Control Approach. In O. Junge, O. Schütze,
G. Froyland, S. Ober-Blöbaum, & K. Padberg-Gehle (Eds.), Advances in Dynamics,
Optimization and Computation. Cham: Springer. https://doi.org/10.1007/978-3-030-51264-4_9'
bibtex: '@inbook{Flaßkamp_Ober-Blöbaum_Peitz_2020, place={Cham}, title={Symmetry
in Optimal Control: A Multiobjective Model Predictive Control Approach}, DOI={10.1007/978-3-030-51264-4_9},
booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer},
author={Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Peitz, Sebastian}, editor={Junge,
Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle,
KathrinEditors}, year={2020} }'
chicago: 'Flaßkamp, Kathrin, Sina Ober-Blöbaum, and Sebastian Peitz. “Symmetry in
Optimal Control: A Multiobjective Model Predictive Control Approach.” In Advances
in Dynamics, Optimization and Computation, edited by Oliver Junge, Oliver
Schütze, Gary Froyland, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle. Cham: Springer,
2020. https://doi.org/10.1007/978-3-030-51264-4_9.'
ieee: 'K. Flaßkamp, S. Ober-Blöbaum, and S. Peitz, “Symmetry in Optimal Control:
A Multiobjective Model Predictive Control Approach,” in Advances in Dynamics,
Optimization and Computation, O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum,
and K. Padberg-Gehle, Eds. Cham: Springer, 2020.'
mla: 'Flaßkamp, Kathrin, et al. “Symmetry in Optimal Control: A Multiobjective Model
Predictive Control Approach.” Advances in Dynamics, Optimization and Computation,
edited by Oliver Junge et al., Springer, 2020, doi:10.1007/978-3-030-51264-4_9.'
short: 'K. Flaßkamp, S. Ober-Blöbaum, S. Peitz, in: O. Junge, O. Schütze, G. Froyland,
S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and
Computation, Springer, Cham, 2020.'
date_created: 2020-07-27T09:50:19Z
date_updated: 2022-01-06T06:53:11Z
department:
- _id: '101'
doi: 10.1007/978-3-030-51264-4_9
editor:
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Kathrin
full_name: Padberg-Gehle, Kathrin
last_name: Padberg-Gehle
language:
- iso: eng
place: Cham
publication: Advances in Dynamics, Optimization and Computation
publication_identifier:
isbn:
- '9783030512637'
- '9783030512644'
issn:
- 2198-4182
- 2198-4190
publication_status: published
publisher: Springer
status: public
title: 'Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach'
type: book_chapter
user_id: '47427'
year: '2020'
...
---
_id: '21819'
abstract:
- lang: eng
text: Many dimensionality and model reduction techniques rely on estimating
dominant eigenfunctions of associated dynamical operators from data. Important
examples include the Koopman operator and its generator, but also the Schrödinger
operator. We propose a kernel-based method for the approximation of differential
operators in reproducing kernel Hilbert spaces and show how eigenfunctions can
be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms
are applied to molecular dynamics and quantum chemistry examples. Furthermore,
we exploit that, under certain conditions, the Schrödinger operator can be transformed
into a Kolmogorov backward operator corresponding to a drift-diffusion process
and vice versa. This allows us to apply methods developed for the analysis of
high-dimensional stochastic differential equations to quantum mechanical systems.
article_number: '722'
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Boumediene
full_name: Hamzi, Boumediene
last_name: Hamzi
citation:
ama: Klus S, Nüske F, Hamzi B. Kernel-Based Approximation of the Koopman Generator
and Schrödinger Operator. Entropy. 2020. doi:10.3390/e22070722
apa: Klus, S., Nüske, F., & Hamzi, B. (2020). Kernel-Based Approximation of
the Koopman Generator and Schrödinger Operator. Entropy. https://doi.org/10.3390/e22070722
bibtex: '@article{Klus_Nüske_Hamzi_2020, title={Kernel-Based Approximation of the
Koopman Generator and Schrödinger Operator}, DOI={10.3390/e22070722},
number={722}, journal={Entropy}, author={Klus, Stefan and Nüske, Feliks and Hamzi,
Boumediene}, year={2020} }'
chicago: Klus, Stefan, Feliks Nüske, and Boumediene Hamzi. “Kernel-Based Approximation
of the Koopman Generator and Schrödinger Operator.” Entropy, 2020. https://doi.org/10.3390/e22070722.
ieee: S. Klus, F. Nüske, and B. Hamzi, “Kernel-Based Approximation of the Koopman
Generator and Schrödinger Operator,” Entropy, 2020.
mla: Klus, Stefan, et al. “Kernel-Based Approximation of the Koopman Generator and
Schrödinger Operator.” Entropy, 722, 2020, doi:10.3390/e22070722.
short: S. Klus, F. Nüske, B. Hamzi, Entropy (2020).
date_created: 2021-04-28T18:06:35Z
date_updated: 2022-01-06T06:55:16Z
department:
- _id: '101'
doi: 10.3390/e22070722
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.mdpi.com/1099-4300/22/7/722
oa: '1'
publication: Entropy
publication_identifier:
issn:
- 1099-4300
publication_status: published
status: public
title: Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator
type: journal_article
user_id: '81513'
year: '2020'
...
---
_id: '10596'
abstract:
- lang: eng
text: Multi-objective optimization is an active field of research that has many
applications. Owing to its success and because decision-making processes are becoming
more and more complex, there is a recent trend for incorporating many objectives
into such problems. The challenge with such problems, however, is that the dimensions
of the solution sets—the so-called Pareto sets and fronts—grow with the number
of objectives. It is thus no longer possible to compute or to approximate the
entire solution set of a given problem that contains many (e.g. more than three)
objectives. On the other hand, the computation of single solutions (e.g. via scalarization
methods) leads to unsatisfying results in many cases, even if user preferences
are incorporated. In this article, the Pareto Explorer tool is presented—a global/local
exploration tool for the treatment of many-objective optimization problems (MaOPs).
In the first step, a solution of the problem is computed via a global search algorithm
that ideally already includes user preferences. In the second step, a local search
along the Pareto set/front of the given MaOP is performed in user specified directions.
For this, several continuation-like procedures are proposed that can incorporate
preferences defined in decision, objective, or in weight space. The applicability
and usefulness of Pareto Explorer is demonstrated on benchmark problems as well
as on an application from industrial laundry design.
article_type: original
author:
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Oliver
full_name: Cuate, Oliver
last_name: Cuate
- first_name: Adanay
full_name: Martín, Adanay
last_name: Martín
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Schütze O, Cuate O, Martín A, Peitz S, Dellnitz M. Pareto Explorer: a global/local
exploration tool for many-objective optimization problems. Engineering Optimization.
2020;52(5):832-855. doi:10.1080/0305215x.2019.1617286'
apa: 'Schütze, O., Cuate, O., Martín, A., Peitz, S., & Dellnitz, M. (2020).
Pareto Explorer: a global/local exploration tool for many-objective optimization
problems. Engineering Optimization, 52(5), 832–855. https://doi.org/10.1080/0305215x.2019.1617286'
bibtex: '@article{Schütze_Cuate_Martín_Peitz_Dellnitz_2020, title={Pareto Explorer:
a global/local exploration tool for many-objective optimization problems}, volume={52},
DOI={10.1080/0305215x.2019.1617286},
number={5}, journal={Engineering Optimization}, author={Schütze, Oliver and Cuate,
Oliver and Martín, Adanay and Peitz, Sebastian and Dellnitz, Michael}, year={2020},
pages={832–855} }'
chicago: 'Schütze, Oliver, Oliver Cuate, Adanay Martín, Sebastian Peitz, and Michael
Dellnitz. “Pareto Explorer: A Global/Local Exploration Tool for Many-Objective
Optimization Problems.” Engineering Optimization 52, no. 5 (2020): 832–55.
https://doi.org/10.1080/0305215x.2019.1617286.'
ieee: 'O. Schütze, O. Cuate, A. Martín, S. Peitz, and M. Dellnitz, “Pareto Explorer:
a global/local exploration tool for many-objective optimization problems,” Engineering
Optimization, vol. 52, no. 5, pp. 832–855, 2020.'
mla: 'Schütze, Oliver, et al. “Pareto Explorer: A Global/Local Exploration Tool
for Many-Objective Optimization Problems.” Engineering Optimization, vol.
52, no. 5, 2020, pp. 832–55, doi:10.1080/0305215x.2019.1617286.'
short: O. Schütze, O. Cuate, A. Martín, S. Peitz, M. Dellnitz, Engineering Optimization
52 (2020) 832–855.
date_created: 2019-07-10T08:14:39Z
date_updated: 2022-01-06T06:50:46Z
department:
- _id: '101'
doi: 10.1080/0305215x.2019.1617286
intvolume: ' 52'
issue: '5'
language:
- iso: eng
page: 832-855
publication: Engineering Optimization
publication_identifier:
issn:
- 0305-215X
- 1029-0273
publication_status: published
status: public
title: 'Pareto Explorer: a global/local exploration tool for many-objective optimization
problems'
type: journal_article
user_id: '47427'
volume: 52
year: '2020'
...
---
_id: '16288'
abstract:
- lang: eng
text: We derive a data-driven method for the approximation of the Koopman generator
called gEDMD, which can be regarded as a straightforward extension of EDMD (extended
dynamic mode decomposition). This approach is applicable to deterministic and
stochastic dynamical systems. It can be used for computing eigenvalues, eigenfunctions,
and modes of the generator and for system identification. In addition to learning
the governing equations of deterministic systems, which then reduces to SINDy
(sparse identification of nonlinear dynamics), it is possible to identify the
drift and diffusion terms of stochastic differential equations from data. Moreover,
we apply gEDMD to derive coarse-grained models of high-dimensional systems, and
also to determine efficient model predictive control strategies. We highlight
relationships with other methods and demonstrate the efficacy of the proposed
methods using several guiding examples and prototypical molecular dynamics problems.
article_number: '132416'
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Jan-Hendrik
full_name: Niemann, Jan-Hendrik
last_name: Niemann
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
- first_name: Christof
full_name: Schütte, Christof
last_name: Schütte
citation:
ama: 'Klus S, Nüske F, Peitz S, Niemann J-H, Clementi C, Schütte C. Data-driven
approximation of the Koopman generator: Model reduction, system identification,
and control. Physica D: Nonlinear Phenomena. 2020;406. doi:10.1016/j.physd.2020.132416'
apa: 'Klus, S., Nüske, F., Peitz, S., Niemann, J.-H., Clementi, C., & Schütte,
C. (2020). Data-driven approximation of the Koopman generator: Model reduction,
system identification, and control. Physica D: Nonlinear Phenomena, 406.
https://doi.org/10.1016/j.physd.2020.132416'
bibtex: '@article{Klus_Nüske_Peitz_Niemann_Clementi_Schütte_2020, title={Data-driven
approximation of the Koopman generator: Model reduction, system identification,
and control}, volume={406}, DOI={10.1016/j.physd.2020.132416},
number={132416}, journal={Physica D: Nonlinear Phenomena}, author={Klus, Stefan
and Nüske, Feliks and Peitz, Sebastian and Niemann, Jan-Hendrik and Clementi,
Cecilia and Schütte, Christof}, year={2020} }'
chicago: 'Klus, Stefan, Feliks Nüske, Sebastian Peitz, Jan-Hendrik Niemann, Cecilia
Clementi, and Christof Schütte. “Data-Driven Approximation of the Koopman Generator:
Model Reduction, System Identification, and Control.” Physica D: Nonlinear
Phenomena 406 (2020). https://doi.org/10.1016/j.physd.2020.132416.'
ieee: 'S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, and C. Schütte,
“Data-driven approximation of the Koopman generator: Model reduction, system identification,
and control,” Physica D: Nonlinear Phenomena, vol. 406, 2020.'
mla: 'Klus, Stefan, et al. “Data-Driven Approximation of the Koopman Generator:
Model Reduction, System Identification, and Control.” Physica D: Nonlinear
Phenomena, vol. 406, 132416, 2020, doi:10.1016/j.physd.2020.132416.'
short: 'S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, C. Schütte, Physica
D: Nonlinear Phenomena 406 (2020).'
date_created: 2020-03-13T12:35:40Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1016/j.physd.2020.132416
intvolume: ' 406'
language:
- iso: eng
publication: 'Physica D: Nonlinear Phenomena'
publication_identifier:
issn:
- 0167-2789
publication_status: published
status: public
title: 'Data-driven approximation of the Koopman generator: Model reduction, system
identification, and control'
type: journal_article
user_id: '47427'
volume: 406
year: '2020'
...