---
_id: '45695'
author:
- first_name: Sedjro Salomon
full_name: Hotegni, Sedjro Salomon
id: '97995'
last_name: Hotegni
- first_name: Sepideh
full_name: Mahabadi, Sepideh
last_name: Mahabadi
- first_name: Ali
full_name: Vakilian, Ali
last_name: Vakilian
citation:
ama: 'Hotegni SS, Mahabadi S, Vakilian A. Approximation Algorithms for Fair Range
Clustering. In: Proceedings of the 40th International Conference on Machine
Learning, Honolulu, Hawaii, USA. PMLR 202, 2023.'
apa: Hotegni, S. S., Mahabadi, S., & Vakilian, A. (n.d.). Approximation Algorithms
for Fair Range Clustering. Proceedings of the 40th International Conference
on Machine Learning, Honolulu, Hawaii, USA. PMLR 202, 2023. International
Conference on Machine Learning, Honolulu, Hawaii, USA.
bibtex: '@inproceedings{Hotegni_Mahabadi_Vakilian, title={Approximation Algorithms
for Fair Range Clustering}, booktitle={Proceedings of the 40th International Conference
on Machine Learning, Honolulu, Hawaii, USA. PMLR 202, 2023.}, author={Hotegni,
Sedjro Salomon and Mahabadi, Sepideh and Vakilian, Ali} }'
chicago: Hotegni, Sedjro Salomon, Sepideh Mahabadi, and Ali Vakilian. “Approximation
Algorithms for Fair Range Clustering.” In Proceedings of the 40th International
Conference on Machine Learning, Honolulu, Hawaii, USA. PMLR 202, 2023., n.d.
ieee: S. S. Hotegni, S. Mahabadi, and A. Vakilian, “Approximation Algorithms for
Fair Range Clustering,” presented at the International Conference on Machine Learning,
Honolulu, Hawaii, USA.
mla: Hotegni, Sedjro Salomon, et al. “Approximation Algorithms for Fair Range Clustering.”
Proceedings of the 40th International Conference on Machine Learning, Honolulu,
Hawaii, USA. PMLR 202, 2023.
short: 'S.S. Hotegni, S. Mahabadi, A. Vakilian, in: Proceedings of the 40th International
Conference on Machine Learning, Honolulu, Hawaii, USA. PMLR 202, 2023., n.d.'
conference:
end_date: 2023-07-29
location: Honolulu, Hawaii, USA
name: International Conference on Machine Learning
start_date: 2023-07-23
date_created: 2023-06-20T22:29:33Z
date_updated: 2023-06-20T23:03:12Z
department:
- _id: '655'
keyword:
- Fair range clustering
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://openreview.net/forum?id=gBoKJT5JhM
oa: '1'
publication: Proceedings of the 40th International Conference on Machine Learning,
Honolulu, Hawaii, USA. PMLR 202, 2023.
publication_status: accepted
status: public
title: Approximation Algorithms for Fair Range Clustering
type: conference
user_id: '97995'
year: '2023'
...
---
_id: '46579'
abstract:
- lang: eng
text: "The Koopman operator has become an essential tool for data-driven analysis,
prediction and control of complex systems, the main reason being the enormous
potential of identifying linear function space representations of nonlinear\r\ndynamics
from measurements. Until now, the situation where for large-scale systems, we
(i) only have access to partial observations (i.e., measurements, as is very common
for experimental data) or (ii) deliberately perform coarse\r\ngraining (for efficiency
reasons) has not been treated to its full extent. In this paper, we address the
pitfall associated with this situation, that the classical EDMD algorithm does
not automatically provide a Koopman operator approximation for the underlying
system if we do not carefully select the number of observables. Moreover, we show
that symmetries in the system dynamics can be carried over to the Koopman operator,
which allows us to massively increase the model efficiency. We also briefly draw
a connection to domain decomposition techniques for partial differential equations
and present numerical evidence using the Kuramoto--Sivashinsky equation."
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Hans
full_name: Harder, Hans
id: '98879'
last_name: Harder
- first_name: Feliks
full_name: Nüske, Feliks
last_name: Nüske
- first_name: Friedrich
full_name: Philipp, Friedrich
last_name: Philipp
- first_name: Manuel
full_name: Schaller, Manuel
last_name: Schaller
- first_name: Karl
full_name: Worthmann, Karl
last_name: Worthmann
citation:
ama: Peitz S, Harder H, Nüske F, Philipp F, Schaller M, Worthmann K. Partial observations,
coarse graining and equivariance in Koopman operator theory for large-scale dynamical
systems. arXiv:230715325. Published online 2023.
apa: Peitz, S., Harder, H., Nüske, F., Philipp, F., Schaller, M., & Worthmann,
K. (2023). Partial observations, coarse graining and equivariance in Koopman
operator theory for large-scale dynamical systems. In arXiv:2307.15325.
bibtex: '@article{Peitz_Harder_Nüske_Philipp_Schaller_Worthmann_2023, title={Partial
observations, coarse graining and equivariance in Koopman operator theory for
large-scale dynamical systems}, journal={arXiv:2307.15325}, author={Peitz, Sebastian
and Harder, Hans and Nüske, Feliks and Philipp, Friedrich and Schaller, Manuel
and Worthmann, Karl}, year={2023} }'
chicago: Peitz, Sebastian, Hans Harder, Feliks Nüske, Friedrich Philipp, Manuel
Schaller, and Karl Worthmann. “Partial Observations, Coarse Graining and Equivariance
in Koopman Operator Theory for Large-Scale Dynamical Systems.” ArXiv:2307.15325,
2023.
ieee: S. Peitz, H. Harder, F. Nüske, F. Philipp, M. Schaller, and K. Worthmann,
“Partial observations, coarse graining and equivariance in Koopman operator theory
for large-scale dynamical systems,” arXiv:2307.15325. 2023.
mla: Peitz, Sebastian, et al. “Partial Observations, Coarse Graining and Equivariance
in Koopman Operator Theory for Large-Scale Dynamical Systems.” ArXiv:2307.15325,
2023.
short: S. Peitz, H. Harder, F. Nüske, F. Philipp, M. Schaller, K. Worthmann, ArXiv:2307.15325
(2023).
date_created: 2023-08-21T05:52:24Z
date_updated: 2023-08-21T05:53:35Z
department:
- _id: '655'
external_id:
arxiv:
- '2307.15325'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2307.15325
oa: '1'
publication: arXiv:2307.15325
status: public
title: Partial observations, coarse graining and equivariance in Koopman operator
theory for large-scale dynamical systems
type: preprint
user_id: '47427'
year: '2023'
...
---
_id: '23428'
abstract:
- lang: eng
text: "The Koopman operator has become an essential tool for data-driven approximation
of dynamical (control) systems in recent years, e.g., via extended dynamic mode
decomposition. Despite its popularity, convergence results and, in particular,
error bounds are still quite scarce. In this paper, we derive probabilistic bounds
for the approximation error and the prediction error depending on the number of
training data points; for both ordinary and stochastic differential equations.
Moreover, we extend our analysis to nonlinear control-affine systems using either
ergodic trajectories or i.i.d.\r\nsamples. Here, we exploit the linearity of the
Koopman generator to obtain a bilinear system and, thus, circumvent the curse
of dimensionality since we do not autonomize the system by augmenting the state
by the control inputs. To the\r\nbest of our knowledge, this is the first finite-data
error analysis in the stochastic and/or control setting. Finally, we demonstrate
the effectiveness of the proposed approach by comparing it with state-of-the-art
techniques showing its superiority whenever state and control are coupled."
article_number: '14'
author:
- 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
- first_name: Friedrich
full_name: Philipp, Friedrich
last_name: Philipp
- first_name: Manuel
full_name: Schaller, Manuel
last_name: Schaller
- first_name: Karl
full_name: Worthmann, Karl
last_name: Worthmann
citation:
ama: Nüske F, Peitz S, Philipp F, Schaller M, Worthmann K. Finite-data error bounds
for Koopman-based prediction and control. Journal of Nonlinear Science.
2023;33. doi:10.1007/s00332-022-09862-1
apa: Nüske, F., Peitz, S., Philipp, F., Schaller, M., & Worthmann, K. (2023).
Finite-data error bounds for Koopman-based prediction and control. Journal
of Nonlinear Science, 33, Article 14. https://doi.org/10.1007/s00332-022-09862-1
bibtex: '@article{Nüske_Peitz_Philipp_Schaller_Worthmann_2023, title={Finite-data
error bounds for Koopman-based prediction and control}, volume={33}, DOI={10.1007/s00332-022-09862-1},
number={14}, journal={Journal of Nonlinear Science}, author={Nüske, Feliks and
Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl},
year={2023} }'
chicago: Nüske, Feliks, Sebastian Peitz, Friedrich Philipp, Manuel Schaller, and
Karl Worthmann. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.”
Journal of Nonlinear Science 33 (2023). https://doi.org/10.1007/s00332-022-09862-1.
ieee: 'F. Nüske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann, “Finite-data
error bounds for Koopman-based prediction and control,” Journal of Nonlinear
Science, vol. 33, Art. no. 14, 2023, doi: 10.1007/s00332-022-09862-1.'
mla: Nüske, Feliks, et al. “Finite-Data Error Bounds for Koopman-Based Prediction
and Control.” Journal of Nonlinear Science, vol. 33, 14, 2023, doi:10.1007/s00332-022-09862-1.
short: F. Nüske, S. Peitz, F. Philipp, M. Schaller, K. Worthmann, Journal of Nonlinear
Science 33 (2023).
date_created: 2021-08-17T12:25:09Z
date_updated: 2023-08-24T07:50:12Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s00332-022-09862-1
intvolume: ' 33'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf
oa: '1'
publication: Journal of Nonlinear Science
publication_status: published
status: public
title: Finite-data error bounds for Koopman-based prediction and control
type: journal_article
user_id: '47427'
volume: 33
year: '2023'
...
---
_id: '21600'
abstract:
- lang: eng
text: Many problems in science and engineering require an efficient numerical approximation
of integrals or solutions to differential equations. For systems with rapidly
changing dynamics, an equidistant discretization is often inadvisable as it results
in prohibitively large errors or computational effort. To this end, adaptive schemes,
such as solvers based on Runge–Kutta pairs, have been developed which adapt the
step size based on local error estimations at each step. While the classical schemes
apply very generally and are highly efficient on regular systems, they can behave
suboptimally when an inefficient step rejection mechanism is triggered by structurally
complex systems such as chaotic systems. To overcome these issues, we propose
a method to tailor numerical schemes to the problem class at hand. This is achieved
by combining simple, classical quadrature rules or ODE solvers with data-driven
time-stepping controllers. Compared with learning solution operators to ODEs directly,
it generalizes better to unseen initial data as our approach employs classical
numerical schemes as base methods. At the same time it can make use of identified
structures of a problem class and, therefore, outperforms state-of-the-art adaptive
schemes. Several examples demonstrate superior efficiency. Source code is available
at https://github.com/lueckem/quadrature-ML.
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Eyke
full_name: Hüllermeier, Eyke
id: '48129'
last_name: Hüllermeier
- first_name: Marvin
full_name: Lücke, Marvin
last_name: Lücke
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Karlson
full_name: Pfannschmidt, Karlson
id: '13472'
last_name: Pfannschmidt
orcid: 0000-0001-9407-7903
citation:
ama: Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical
integration using reinforcement learning. SIAM Journal on Scientific Computing.
2023;45(2):A579-A595. doi:10.1137/21M1412682
apa: Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz,
S., & Pfannschmidt, K. (2023). Efficient time stepping for numerical integration
using reinforcement learning. SIAM Journal on Scientific Computing, 45(2),
A579–A595. https://doi.org/10.1137/21M1412682
bibtex: '@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023,
title={Efficient time stepping for numerical integration using reinforcement
learning}, volume={45}, DOI={10.1137/21M1412682},
number={2}, journal={SIAM Journal on Scientific Computing}, author={Dellnitz,
Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen,
Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, year={2023}, pages={A579–A595}
}'
chicago: 'Dellnitz, Michael, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum,
Christian Offen, Sebastian Peitz, and Karlson Pfannschmidt. “Efficient Time Stepping
for Numerical Integration Using Reinforcement Learning.” SIAM Journal on Scientific
Computing 45, no. 2 (2023): A579–95. https://doi.org/10.1137/21M1412682.'
ieee: 'M. Dellnitz et al., “Efficient time stepping for numerical integration
using reinforcement learning,” SIAM Journal on Scientific Computing, vol.
45, no. 2, pp. A579–A595, 2023, doi: 10.1137/21M1412682.'
mla: Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration
Using Reinforcement Learning.” SIAM Journal on Scientific Computing, vol.
45, no. 2, 2023, pp. A579–95, doi:10.1137/21M1412682.
short: M. Dellnitz, E. Hüllermeier, M. Lücke, S. Ober-Blöbaum, C. Offen, S. Peitz,
K. Pfannschmidt, SIAM Journal on Scientific Computing 45 (2023) A579–A595.
date_created: 2021-04-09T07:59:19Z
date_updated: 2023-08-25T09:24:50Z
ddc:
- '510'
department:
- _id: '101'
- _id: '636'
- _id: '355'
- _id: '655'
doi: 10.1137/21M1412682
external_id:
arxiv:
- arXiv:2104.03562
has_accepted_license: '1'
intvolume: ' 45'
issue: '2'
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/reader/10.1137/21M1412682
page: A579-A595
publication: SIAM Journal on Scientific Computing
publication_status: published
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/lueckem/quadrature-ML
status: public
title: Efficient time stepping for numerical integration using reinforcement learning
type: journal_article
user_id: '47427'
volume: 45
year: '2023'
...
---
_id: '46784'
article_number: '5616'
author:
- first_name: Oliver
full_name: Wallscheid, Oliver
id: '11291'
last_name: Wallscheid
orcid: https://orcid.org/0000-0001-9362-8777
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Jan
full_name: Stenner, Jan
id: '65520'
last_name: Stenner
- first_name: Daniel
full_name: Weber, Daniel
id: '24041'
last_name: Weber
orcid: 0000-0003-3367-5998
- first_name: Septimus
full_name: Boshoff, Septimus
last_name: Boshoff
- first_name: Marvin
full_name: Meyer, Marvin
last_name: Meyer
- first_name: Vikas
full_name: Chidananda, Vikas
last_name: Chidananda
- first_name: Oliver
full_name: Schweins, Oliver
last_name: Schweins
citation:
ama: Wallscheid O, Peitz S, Stenner J, et al. ElectricGrid.jl - A Julia-based modeling
and simulationtool for power electronics-driven electric energy grids. Journal
of Open Source Software. 2023;8(89). doi:10.21105/joss.05616
apa: Wallscheid, O., Peitz, S., Stenner, J., Weber, D., Boshoff, S., Meyer, M.,
Chidananda, V., & Schweins, O. (2023). ElectricGrid.jl - A Julia-based modeling
and simulationtool for power electronics-driven electric energy grids. Journal
of Open Source Software, 8(89), Article 5616. https://doi.org/10.21105/joss.05616
bibtex: '@article{Wallscheid_Peitz_Stenner_Weber_Boshoff_Meyer_Chidananda_Schweins_2023,
title={ElectricGrid.jl - A Julia-based modeling and simulationtool for power electronics-driven
electric energy grids}, volume={8}, DOI={10.21105/joss.05616},
number={895616}, journal={Journal of Open Source Software}, publisher={The Open
Journal}, author={Wallscheid, Oliver and Peitz, Sebastian and Stenner, Jan and
Weber, Daniel and Boshoff, Septimus and Meyer, Marvin and Chidananda, Vikas and
Schweins, Oliver}, year={2023} }'
chicago: Wallscheid, Oliver, Sebastian Peitz, Jan Stenner, Daniel Weber, Septimus
Boshoff, Marvin Meyer, Vikas Chidananda, and Oliver Schweins. “ElectricGrid.Jl
- A Julia-Based Modeling and Simulationtool for Power Electronics-Driven Electric
Energy Grids.” Journal of Open Source Software 8, no. 89 (2023). https://doi.org/10.21105/joss.05616.
ieee: 'O. Wallscheid et al., “ElectricGrid.jl - A Julia-based modeling and
simulationtool for power electronics-driven electric energy grids,” Journal
of Open Source Software, vol. 8, no. 89, Art. no. 5616, 2023, doi: 10.21105/joss.05616.'
mla: Wallscheid, Oliver, et al. “ElectricGrid.Jl - A Julia-Based Modeling and Simulationtool
for Power Electronics-Driven Electric Energy Grids.” Journal of Open Source
Software, vol. 8, no. 89, 5616, The Open Journal, 2023, doi:10.21105/joss.05616.
short: O. Wallscheid, S. Peitz, J. Stenner, D. Weber, S. Boshoff, M. Meyer, V. Chidananda,
O. Schweins, Journal of Open Source Software 8 (2023).
date_created: 2023-09-04T11:05:03Z
date_updated: 2023-09-04T11:06:06Z
department:
- _id: '655'
- _id: '52'
doi: 10.21105/joss.05616
intvolume: ' 8'
issue: '89'
keyword:
- General Earth and Planetary Sciences
- General Environmental Science
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://joss.theoj.org/papers/10.21105/joss.05616
oa: '1'
publication: Journal of Open Source Software
publication_identifier:
issn:
- 2475-9066
publication_status: published
publisher: The Open Journal
status: public
title: ElectricGrid.jl - A Julia-based modeling and simulationtool for power electronics-driven
electric energy grids
type: journal_article
user_id: '47427'
volume: 8
year: '2023'
...
---
_id: '46813'
abstract:
- lang: eng
text: Modelling of dynamic systems plays an important role in many engineering disciplines.
Two different approaches are physical modelling and data‐driven modelling, both
of which have their respective advantages and disadvantages. By combining these
two approaches, hybrid models can be created in which the respective disadvantages
are mitigated, with discrepancy models being a particular subclass. Here, the
basic system behaviour is described physically, that is, in the form of differential
equations. Inaccuracies resulting from insufficient modelling or numerics lead
to a discrepancy between the measurements and the model, which can be compensated
by a data‐driven error correction term. Since discrepancy methods still require
a large amount of measurement data, this paper investigates the extent to which
a single discrepancy model can be trained for a physical model with additional
parameter dependencies without the need for retraining. As an example, a damped
electromagnetic oscillating circuit is used. The physical model is realised by
a differential equation describing the electric current, considering only inductance
and capacitance; dissipation due to resistance is neglected. This creates a discrepancy
between measurement and model, which is corrected by a data‐driven model. In the
experiments, the inductance and the capacity are varied. It is found that the
same data‐driven model can only be used if additional parametric dependencies
in the data‐driven term are considered as well.
author:
- first_name: Meike Claudia
full_name: Wohlleben, Meike Claudia
id: '43991'
last_name: Wohlleben
orcid: 0009-0009-9767-7168
- first_name: Lars
full_name: Muth, Lars
id: '77313'
last_name: Muth
orcid: 0000-0002-2938-5616
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Walter
full_name: Sextro, Walter
id: '21220'
last_name: Sextro
citation:
ama: 'Wohlleben MC, Muth L, Peitz S, Sextro W. Transferability of a discrepancy
model for the dynamics of electromagnetic oscillating circuits. In: Proceedings
in Applied Mathematics and Mechanics. Wiley; 2023. doi:10.1002/pamm.202300039'
apa: Wohlleben, M. C., Muth, L., Peitz, S., & Sextro, W. (2023). Transferability
of a discrepancy model for the dynamics of electromagnetic oscillating circuits.
Proceedings in Applied Mathematics and Mechanics. https://doi.org/10.1002/pamm.202300039
bibtex: '@inproceedings{Wohlleben_Muth_Peitz_Sextro_2023, title={Transferability
of a discrepancy model for the dynamics of electromagnetic oscillating circuits},
DOI={10.1002/pamm.202300039},
booktitle={Proceedings in Applied Mathematics and Mechanics}, publisher={Wiley},
author={Wohlleben, Meike Claudia and Muth, Lars and Peitz, Sebastian and Sextro,
Walter}, year={2023} }'
chicago: Wohlleben, Meike Claudia, Lars Muth, Sebastian Peitz, and Walter Sextro.
“Transferability of a Discrepancy Model for the Dynamics of Electromagnetic Oscillating
Circuits.” In Proceedings in Applied Mathematics and Mechanics. Wiley,
2023. https://doi.org/10.1002/pamm.202300039.
ieee: 'M. C. Wohlleben, L. Muth, S. Peitz, and W. Sextro, “Transferability of a
discrepancy model for the dynamics of electromagnetic oscillating circuits,” 2023,
doi: 10.1002/pamm.202300039.'
mla: Wohlleben, Meike Claudia, et al. “Transferability of a Discrepancy Model for
the Dynamics of Electromagnetic Oscillating Circuits.” Proceedings in Applied
Mathematics and Mechanics, Wiley, 2023, doi:10.1002/pamm.202300039.
short: 'M.C. Wohlleben, L. Muth, S. Peitz, W. Sextro, in: Proceedings in Applied
Mathematics and Mechanics, Wiley, 2023.'
date_created: 2023-09-06T05:18:05Z
date_updated: 2023-09-21T14:47:20Z
department:
- _id: '655'
- _id: '151'
doi: 10.1002/pamm.202300039
keyword:
- Electrical and Electronic Engineering
- Atomic and Molecular Physics
- and Optics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://onlinelibrary.wiley.com/doi/epdf/10.1002/pamm.202300039
oa: '1'
publication: Proceedings in Applied Mathematics and Mechanics
publication_identifier:
issn:
- 1617-7061
- 1617-7061
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: Transferability of a discrepancy model for the dynamics of electromagnetic
oscillating circuits
type: conference
user_id: '77313'
year: '2023'
...
---
_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: '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: '29727'
author:
- first_name: Meike Claudia
full_name: Wohlleben, Meike Claudia
id: '43991'
last_name: Wohlleben
- first_name: Amelie
full_name: Bender, Amelie
id: '54290'
last_name: Bender
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Walter
full_name: Sextro, Walter
id: '21220'
last_name: Sextro
citation:
ama: 'Wohlleben MC, Bender A, Peitz S, Sextro W. Development of a Hybrid Modeling
Methodology for Oscillating Systems with Friction. In: Machine Learning, Optimization,
and Data Science. Springer International Publishing; 2022. doi:10.1007/978-3-030-95470-3_8'
apa: Wohlleben, M. C., Bender, A., Peitz, S., & Sextro, W. (2022). Development
of a Hybrid Modeling Methodology for Oscillating Systems with Friction. In Machine
Learning, Optimization, and Data Science. Springer International Publishing.
https://doi.org/10.1007/978-3-030-95470-3_8
bibtex: '@inbook{Wohlleben_Bender_Peitz_Sextro_2022, place={Cham}, title={Development
of a Hybrid Modeling Methodology for Oscillating Systems with Friction}, DOI={10.1007/978-3-030-95470-3_8},
booktitle={Machine Learning, Optimization, and Data Science}, publisher={Springer
International Publishing}, author={Wohlleben, Meike Claudia and Bender, Amelie
and Peitz, Sebastian and Sextro, Walter}, year={2022} }'
chicago: 'Wohlleben, Meike Claudia, Amelie Bender, Sebastian Peitz, and Walter Sextro.
“Development of a Hybrid Modeling Methodology for Oscillating Systems with Friction.”
In Machine Learning, Optimization, and Data Science. Cham: Springer International
Publishing, 2022. https://doi.org/10.1007/978-3-030-95470-3_8.'
ieee: 'M. C. Wohlleben, A. Bender, S. Peitz, and W. Sextro, “Development of a Hybrid
Modeling Methodology for Oscillating Systems with Friction,” in Machine Learning,
Optimization, and Data Science, Cham: Springer International Publishing, 2022.'
mla: Wohlleben, Meike Claudia, et al. “Development of a Hybrid Modeling Methodology
for Oscillating Systems with Friction.” Machine Learning, Optimization, and
Data Science, Springer International Publishing, 2022, doi:10.1007/978-3-030-95470-3_8.
short: 'M.C. Wohlleben, A. Bender, S. Peitz, W. Sextro, in: Machine Learning, Optimization,
and Data Science, Springer International Publishing, Cham, 2022.'
date_created: 2022-02-03T10:30:23Z
date_updated: 2023-04-26T12:10:58Z
department:
- _id: '151'
- _id: '655'
doi: 10.1007/978-3-030-95470-3_8
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/content/pdf/10.1007%2F978-3-030-95470-3_8.pdf
place: Cham
publication: Machine Learning, Optimization, and Data Science
publication_identifier:
isbn:
- '9783030954697'
- '9783030954703'
issn:
- 0302-9743
- 1611-3349
publication_status: published
publisher: Springer International Publishing
quality_controlled: '1'
status: public
title: Development of a Hybrid Modeling Methodology for Oscillating Systems with Friction
type: book_chapter
user_id: '43991'
year: '2022'
...
---
_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'
...