---
_id: '51160'
abstract:
- lang: eng
text: "We rigorously derive novel and sharp finite-data error bounds for highly\r\nsample-efficient
Extended Dynamic Mode Decomposition (EDMD) for both i.i.d. and\r\nergodic sampling.
In particular, we show all results in a very general setting\r\nremoving most
of the typically imposed assumptions such that, among others,\r\ndiscrete- and
continuous-time stochastic processes as well as nonlinear partial\r\ndifferential
equations are contained in the considered system class. Besides\r\nshowing an
exponential rate for i.i.d. sampling, we prove, to the best of our\r\nknowledge,
the first superlinear convergence rates for ergodic sampling of\r\ndeterministic
systems. We verify sharpness of the derived error bounds by\r\nconducting numerical
simulations for highly-complex applications from molecular\r\ndynamics and chaotic
flame propagation."
article_number: '135223'
article_type: original
author:
- first_name: Friedrich M.
full_name: Philipp, Friedrich M.
last_name: Philipp
- first_name: Manuel
full_name: Schaller, Manuel
last_name: Schaller
- first_name: Septimus
full_name: Boshoff, Septimus
last_name: Boshoff
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Feliks
full_name: Nüske, Feliks
last_name: Nüske
- first_name: Karl
full_name: Worthmann, Karl
last_name: Worthmann
citation:
ama: 'Philipp FM, Schaller M, Boshoff S, Peitz S, Nüske F, Worthmann K. Variance
representations and convergence rates for data-driven approximations of Koopman
operators. Physica D: Nonlinear Phenomena. 2026;492. doi:10.1016/j.physd.2026.135223'
apa: 'Philipp, F. M., Schaller, M., Boshoff, S., Peitz, S., Nüske, F., & Worthmann,
K. (2026). Variance representations and convergence rates for data-driven approximations
of Koopman operators. Physica D: Nonlinear Phenomena, 492, Article
135223. https://doi.org/10.1016/j.physd.2026.135223'
bibtex: '@article{Philipp_Schaller_Boshoff_Peitz_Nüske_Worthmann_2026, title={Variance
representations and convergence rates for data-driven approximations of Koopman
operators}, volume={492}, DOI={10.1016/j.physd.2026.135223},
number={135223}, journal={Physica D: Nonlinear Phenomena}, author={Philipp, Friedrich
M. and Schaller, Manuel and Boshoff, Septimus and Peitz, Sebastian and Nüske,
Feliks and Worthmann, Karl}, year={2026} }'
chicago: 'Philipp, Friedrich M., Manuel Schaller, Septimus Boshoff, Sebastian Peitz,
Feliks Nüske, and Karl Worthmann. “Variance Representations and Convergence Rates
for Data-Driven Approximations of Koopman Operators.” Physica D: Nonlinear
Phenomena 492 (2026). https://doi.org/10.1016/j.physd.2026.135223.'
ieee: 'F. M. Philipp, M. Schaller, S. Boshoff, S. Peitz, F. Nüske, and K. Worthmann,
“Variance representations and convergence rates for data-driven approximations
of Koopman operators,” Physica D: Nonlinear Phenomena, vol. 492, Art. no.
135223, 2026, doi: 10.1016/j.physd.2026.135223.'
mla: 'Philipp, Friedrich M., et al. “Variance Representations and Convergence Rates
for Data-Driven Approximations of Koopman Operators.” Physica D: Nonlinear
Phenomena, vol. 492, 135223, 2026, doi:10.1016/j.physd.2026.135223.'
short: 'F.M. Philipp, M. Schaller, S. Boshoff, S. Peitz, F. Nüske, K. Worthmann,
Physica D: Nonlinear Phenomena 492 (2026).'
date_created: 2024-02-06T08:52:21Z
date_updated: 2026-10-01T11:43:13Z
ddc:
- '510'
department:
- _id: '655'
doi: 10.1016/j.physd.2026.135223
external_id:
arxiv:
- '2402.02494'
file:
- access_level: closed
content_type: application/pdf
creator: speitz
date_created: 2026-10-01T11:42:54Z
date_updated: 2026-10-01T11:42:54Z
file_id: '67297'
file_name: Philipp2026variancerepresentations.pdf
file_size: 2767910
relation: main_file
success: 1
file_date_updated: 2026-10-01T11:42:54Z
has_accepted_license: '1'
intvolume: ' 492'
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
publication: 'Physica D: Nonlinear Phenomena'
quality_controlled: '1'
status: public
title: Variance representations and convergence rates for data-driven approximations
of Koopman operators
type: journal_article
user_id: '47427'
volume: 492
year: '2026'
...
---
_id: '53858'
author:
- first_name: Junaid
full_name: Akhter, Junaid
id: '97994'
last_name: Akhter
- first_name: Paul David
full_name: Fährmann, Paul David
last_name: Fährmann
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Akhter J, Fährmann PD, Sonntag K, Peitz S. Common pitfalls to avoid while using
multiobjective optimization in machine learning. SIAM Review. 2026;68(3):656-683.
doi:10.1137/24M1658875
apa: Akhter, J., Fährmann, P. D., Sonntag, K., & Peitz, S. (2026). Common pitfalls
to avoid while using multiobjective optimization in machine learning. SIAM
Review, 68(3), 656–683. https://doi.org/10.1137/24M1658875
bibtex: '@article{Akhter_Fährmann_Sonntag_Peitz_2026, title={Common pitfalls to
avoid while using multiobjective optimization in machine learning}, volume={68},
DOI={10.1137/24M1658875}, number={3},
journal={SIAM Review}, publisher={SIAM}, author={Akhter, Junaid and Fährmann,
Paul David and Sonntag, Konstantin and Peitz, Sebastian}, year={2026}, pages={656–683}
}'
chicago: 'Akhter, Junaid, Paul David Fährmann, Konstantin Sonntag, and Sebastian
Peitz. “Common Pitfalls to Avoid While Using Multiobjective Optimization in Machine
Learning.” SIAM Review 68, no. 3 (2026): 656–83. https://doi.org/10.1137/24M1658875.'
ieee: 'J. Akhter, P. D. Fährmann, K. Sonntag, and S. Peitz, “Common pitfalls to
avoid while using multiobjective optimization in machine learning,” SIAM Review,
vol. 68, no. 3, pp. 656–683, 2026, doi: 10.1137/24M1658875.'
mla: Akhter, Junaid, et al. “Common Pitfalls to Avoid While Using Multiobjective
Optimization in Machine Learning.” SIAM Review, vol. 68, no. 3, SIAM, 2026,
pp. 656–83, doi:10.1137/24M1658875.
short: J. Akhter, P.D. Fährmann, K. Sonntag, S. Peitz, SIAM Review 68 (2026) 656–683.
date_created: 2024-05-03T13:38:34Z
date_updated: 2026-10-01T11:36:01Z
department:
- _id: '655'
doi: 10.1137/24M1658875
intvolume: ' 68'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2405.01480
oa: '1'
page: 656-683
publication: SIAM Review
publisher: SIAM
status: public
title: Common pitfalls to avoid while using multiobjective optimization in machine
learning
type: journal_article
user_id: '47427'
volume: 68
year: '2026'
...
---
_id: '67308'
abstract:
- lang: eng
text: Optimizing large-scale multibody systems is a challenging task, particularly
in the presence of multiple conflicting criteria. To prevent high simulation costs,
surrogate models constructed from a small number of expensive model evaluations
are very popular. However, it is difficult to ensure the optimality of the obtained
solutions using a single pre-computed model. We present a back-and-forth approach
between surrogate modeling and multi-objective optimization, and we compare different
strategies for optimization, sampling, and surrogate modeling, to identify the
most promising approach in terms of computational efficiency and solution quality.
author:
- first_name: Augustina Chidinma
full_name: Amakor, Augustina Chidinma
id: '97916'
last_name: Amakor
- first_name: Manuel B.
full_name: Berkemeier, Manuel B.
last_name: Berkemeier
- first_name: Meike Claudia
full_name: Wohlleben, Meike Claudia
id: '43991'
last_name: Wohlleben
orcid: 0009-0009-9767-7168
- first_name: Walter
full_name: Sextro, Walter
id: '21220'
last_name: Sextro
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: 'Amakor AC, Berkemeier MB, Wohlleben MC, Sextro W, Peitz S. Surrogate-Assisted
Multi-objective Design of Complex Multibody Systems. In: Senn W, Sanguineti M,
Saudargiene A, et al., eds. Artificial Neural Networks and Machine Learning
– ICANN 2025. Springer Nature Switzerland; 2026:251–262. doi:10.1007/978-3-032-04555-3_21'
apa: Amakor, A. C., Berkemeier, M. B., Wohlleben, M. C., Sextro, W., & Peitz,
S. (2026). Surrogate-Assisted Multi-objective Design of Complex Multibody Systems.
In W. Senn, M. Sanguineti, A. Saudargiene, I. V. Tetko, A. E. P. Villa, V. Jirsa,
& Y. Bengio (Eds.), Artificial Neural Networks and Machine Learning – ICANN
2025 (pp. 251–262). Springer Nature Switzerland. https://doi.org/10.1007/978-3-032-04555-3_21
bibtex: '@inproceedings{Amakor_Berkemeier_Wohlleben_Sextro_Peitz_2026, place={Cham},
title={Surrogate-Assisted Multi-objective Design of Complex Multibody Systems},
DOI={10.1007/978-3-032-04555-3_21},
booktitle={Artificial Neural Networks and Machine Learning – ICANN 2025}, publisher={Springer
Nature Switzerland}, author={Amakor, Augustina Chidinma and Berkemeier, Manuel
B. and Wohlleben, Meike Claudia and Sextro, Walter and Peitz, Sebastian}, editor={Senn,
Walter and Sanguineti, Marcello and Saudargiene, Ausra and Tetko, Igor V. and
Villa, Alessandro E. P. and Jirsa, Viktor and Bengio, Yoshua}, year={2026}, pages={251–262}
}'
chicago: 'Amakor, Augustina Chidinma, Manuel B. Berkemeier, Meike Claudia Wohlleben,
Walter Sextro, and Sebastian Peitz. “Surrogate-Assisted Multi-Objective Design
of Complex Multibody Systems.” In Artificial Neural Networks and Machine Learning
– ICANN 2025, edited by Walter Senn, Marcello Sanguineti, Ausra Saudargiene,
Igor V. Tetko, Alessandro E. P. Villa, Viktor Jirsa, and Yoshua Bengio, 251–262.
Cham: Springer Nature Switzerland, 2026. https://doi.org/10.1007/978-3-032-04555-3_21.'
ieee: 'A. C. Amakor, M. B. Berkemeier, M. C. Wohlleben, W. Sextro, and S. Peitz,
“Surrogate-Assisted Multi-objective Design of Complex Multibody Systems,” in Artificial
Neural Networks and Machine Learning – ICANN 2025, 2026, pp. 251–262, doi:
10.1007/978-3-032-04555-3_21.'
mla: Amakor, Augustina Chidinma, et al. “Surrogate-Assisted Multi-Objective Design
of Complex Multibody Systems.” Artificial Neural Networks and Machine Learning
– ICANN 2025, edited by Walter Senn et al., Springer Nature Switzerland, 2026,
pp. 251–262, doi:10.1007/978-3-032-04555-3_21.
short: 'A.C. Amakor, M.B. Berkemeier, M.C. Wohlleben, W. Sextro, S. Peitz, in: W.
Senn, M. Sanguineti, A. Saudargiene, I.V. Tetko, A.E.P. Villa, V. Jirsa, Y. Bengio
(Eds.), Artificial Neural Networks and Machine Learning – ICANN 2025, Springer
Nature Switzerland, Cham, 2026, pp. 251–262.'
date_created: 2026-10-01T12:02:40Z
date_updated: 2026-10-01T12:03:16Z
department:
- _id: '655'
doi: 10.1007/978-3-032-04555-3_21
editor:
- first_name: Walter
full_name: Senn, Walter
last_name: Senn
- first_name: Marcello
full_name: Sanguineti, Marcello
last_name: Sanguineti
- first_name: Ausra
full_name: Saudargiene, Ausra
last_name: Saudargiene
- first_name: Igor V.
full_name: Tetko, Igor V.
last_name: Tetko
- first_name: Alessandro E. P.
full_name: Villa, Alessandro E. P.
last_name: Villa
- first_name: Viktor
full_name: Jirsa, Viktor
last_name: Jirsa
- first_name: Yoshua
full_name: Bengio, Yoshua
last_name: Bengio
keyword:
- own
- own-conference
language:
- iso: eng
page: 251–262
place: Cham
publication: Artificial Neural Networks and Machine Learning – ICANN 2025
publication_identifier:
isbn:
- 978-3-032-04555-3
publisher: Springer Nature Switzerland
status: public
title: Surrogate-Assisted Multi-objective Design of Complex Multibody Systems
type: conference
user_id: '47427'
year: '2026'
...
---
_id: '67307'
author:
- first_name: Sedjro Salomon
full_name: Hotegni, Sedjro Salomon
id: '97995'
last_name: Hotegni
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: 'Hotegni SS, Peitz S. SPREAD: Sampling-based Pareto front Refinement via Efficient
Adaptive Diffusion. In: 14th International Conference on Learning Representations
(ICLR). ; 2026. doi:10.48550/arXiv.2509.21058'
apa: 'Hotegni, S. S., & Peitz, S. (2026). SPREAD: Sampling-based Pareto front
Refinement via Efficient Adaptive Diffusion. 14th International Conference
on Learning Representations (ICLR). https://doi.org/10.48550/arXiv.2509.21058'
bibtex: '@inproceedings{Hotegni_Peitz_2026, title={SPREAD: Sampling-based Pareto
front Refinement via Efficient Adaptive Diffusion}, DOI={10.48550/arXiv.2509.21058},
booktitle={14th International Conference on Learning Representations (ICLR)},
author={Hotegni, Sedjro Salomon and Peitz, Sebastian}, year={2026} }'
chicago: 'Hotegni, Sedjro Salomon, and Sebastian Peitz. “SPREAD: Sampling-Based
Pareto Front Refinement via Efficient Adaptive Diffusion.” In 14th International
Conference on Learning Representations (ICLR), 2026. https://doi.org/10.48550/arXiv.2509.21058.'
ieee: 'S. S. Hotegni and S. Peitz, “SPREAD: Sampling-based Pareto front Refinement
via Efficient Adaptive Diffusion,” 2026, doi: 10.48550/arXiv.2509.21058.'
mla: 'Hotegni, Sedjro Salomon, and Sebastian Peitz. “SPREAD: Sampling-Based Pareto
Front Refinement via Efficient Adaptive Diffusion.” 14th International Conference
on Learning Representations (ICLR), 2026, doi:10.48550/arXiv.2509.21058.'
short: 'S.S. Hotegni, S. Peitz, in: 14th International Conference on Learning Representations
(ICLR), 2026.'
date_created: 2026-10-01T12:01:30Z
date_updated: 2026-10-01T12:02:30Z
department:
- _id: '655'
doi: 10.48550/arXiv.2509.21058
keyword:
- own
- own-conference
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://openreview.net/pdf?id=4731mIqv89
oa: '1'
publication: 14th International Conference on Learning Representations (ICLR)
status: public
title: 'SPREAD: Sampling-based Pareto front Refinement via Efficient Adaptive Diffusion'
type: conference
user_id: '47427'
year: '2026'
...
---
_id: '67306'
author:
- first_name: Jan
full_name: Stenner, Jan
last_name: Stenner
- first_name: Hans
full_name: Harder, Hans
id: '98879'
last_name: Harder
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Stenner J, Harder H, Peitz S. Sparse Sensor Placement in Multi-Agent Reinforcement
Learning Control of Rayleigh-Bénard Convection. arXiv:260630238. Published
online 2026.
apa: Stenner, J., Harder, H., & Peitz, S. (2026). Sparse Sensor Placement in
Multi-Agent Reinforcement Learning Control of Rayleigh-Bénard Convection. In arXiv:2606.30238.
bibtex: '@article{Stenner_Harder_Peitz_2026, title={Sparse Sensor Placement in Multi-Agent
Reinforcement Learning Control of Rayleigh-Bénard Convection}, journal={arXiv:2606.30238},
author={Stenner, Jan and Harder, Hans and Peitz, Sebastian}, year={2026} }'
chicago: Stenner, Jan, Hans Harder, and Sebastian Peitz. “Sparse Sensor Placement
in Multi-Agent Reinforcement Learning Control of Rayleigh-Bénard Convection.”
ArXiv:2606.30238, 2026.
ieee: J. Stenner, H. Harder, and S. Peitz, “Sparse Sensor Placement in Multi-Agent
Reinforcement Learning Control of Rayleigh-Bénard Convection,” arXiv:2606.30238.
2026.
mla: Stenner, Jan, et al. “Sparse Sensor Placement in Multi-Agent Reinforcement
Learning Control of Rayleigh-Bénard Convection.” ArXiv:2606.30238, 2026.
short: J. Stenner, H. Harder, S. Peitz, ArXiv:2606.30238 (2026).
date_created: 2026-10-01T12:00:58Z
date_updated: 2026-10-01T12:01:23Z
department:
- _id: '655'
keyword:
- own
- own-preprint
- erc
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2606.30238
oa: '1'
publication: arXiv:2606.30238
status: public
title: Sparse Sensor Placement in Multi-Agent Reinforcement Learning Control of Rayleigh-Bénard
Convection
type: preprint
user_id: '47427'
year: '2026'
...
---
_id: '67309'
author:
- first_name: Jan
full_name: Stenner, Jan
id: '65520'
last_name: Stenner
- first_name: Alexander
full_name: Kilian, Alexander
last_name: Kilian
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Hermann
full_name: de Meer, Hermann
last_name: de Meer
citation:
ama: Stenner J, Kilian A, Peitz S, de Meer H. Toward an Energy-Optimized Operation
of Data Centers Located in Wind Farms Using Reinforcement Learning. arXiv:260630316.
Published online 2026.
apa: Stenner, J., Kilian, A., Peitz, S., & de Meer, H. (2026). Toward an Energy-Optimized
Operation of Data Centers Located in Wind Farms Using Reinforcement Learning.
In arXiv:2606.30316.
bibtex: '@article{Stenner_Kilian_Peitz_de Meer_2026, title={Toward an Energy-Optimized
Operation of Data Centers Located in Wind Farms Using Reinforcement Learning},
journal={arXiv:2606.30316}, author={Stenner, Jan and Kilian, Alexander and Peitz,
Sebastian and de Meer, Hermann}, year={2026} }'
chicago: Stenner, Jan, Alexander Kilian, Sebastian Peitz, and Hermann de Meer. “Toward
an Energy-Optimized Operation of Data Centers Located in Wind Farms Using Reinforcement
Learning.” ArXiv:2606.30316, 2026.
ieee: J. Stenner, A. Kilian, S. Peitz, and H. de Meer, “Toward an Energy-Optimized
Operation of Data Centers Located in Wind Farms Using Reinforcement Learning,”
arXiv:2606.30316. 2026.
mla: Stenner, Jan, et al. “Toward an Energy-Optimized Operation of Data Centers
Located in Wind Farms Using Reinforcement Learning.” ArXiv:2606.30316,
2026.
short: J. Stenner, A. Kilian, S. Peitz, H. de Meer, ArXiv:2606.30316 (2026).
date_created: 2026-10-01T12:03:21Z
date_updated: 2026-10-01T12:03:35Z
department:
- _id: '655'
keyword:
- own
- own-preprint
language:
- iso: eng
publication: arXiv:2606.30316
status: public
title: Toward an Energy-Optimized Operation of Data Centers Located in Wind Farms
Using Reinforcement Learning
type: preprint
user_id: '47427'
year: '2026'
...
---
_id: '67300'
abstract:
- lang: eng
text: Deep neural networks (DNNs) are vulnerable to small adversarial perturbations,
which are tiny changes to the input data that appear insignificant but cause the
model to produce drastically different outputs. Many defense methods require modifying
model architectures during evaluation or performing test-time data purification.
This not only introduces additional complexity but is often architecture-dependent.
We show, however, that robust feature learning during training can significantly
enhance DNN robustness. We propose MOREL, a multi-objective approach that aligns
natural and adversarial features using cosine similarity and multi-positive contrastive
losses to encourage similar features for same-class inputs. Extensive experiments
demonstrate that MOREL significantly improves robustness against both white-box
and black-box attacks. Our code is available at https://github.com/salomonhotegni/MOREL.
author:
- first_name: Sedjro Salomon
full_name: Hotegni, Sedjro Salomon
id: '97995'
last_name: Hotegni
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: 'Hotegni SS, Peitz S. Enhancing Adversarial Robustness Through Multi-objective
Representation Learning. In: Senn W, Sanguineti M, Saudargiene A, et al., eds.
Artificial Neural Networks and Machine Learning – ICANN 2025. Springer
Nature Switzerland; 2026:442–454. doi:10.1007/978-3-032-04558-4_35'
apa: Hotegni, S. S., & Peitz, S. (2026). Enhancing Adversarial Robustness Through
Multi-objective Representation Learning. In W. Senn, M. Sanguineti, A. Saudargiene,
I. V. Tetko, A. E. P. Villa, V. Jirsa, & Y. Bengio (Eds.), Artificial Neural
Networks and Machine Learning – ICANN 2025 (pp. 442–454). Springer Nature
Switzerland. https://doi.org/10.1007/978-3-032-04558-4_35
bibtex: '@inproceedings{Hotegni_Peitz_2026, place={Cham}, title={Enhancing Adversarial
Robustness Through Multi-objective Representation Learning}, DOI={10.1007/978-3-032-04558-4_35},
booktitle={Artificial Neural Networks and Machine Learning – ICANN 2025}, publisher={Springer
Nature Switzerland}, author={Hotegni, Sedjro Salomon and Peitz, Sebastian}, editor={Senn,
Walter and Sanguineti, Marcello and Saudargiene, Ausra and Tetko, Igor V. and
Villa, Alessandro E. P. and Jirsa, Viktor and Bengio, Yoshua}, year={2026}, pages={442–454}
}'
chicago: 'Hotegni, Sedjro Salomon, and Sebastian Peitz. “Enhancing Adversarial Robustness
Through Multi-Objective Representation Learning.” In Artificial Neural Networks
and Machine Learning – ICANN 2025, edited by Walter Senn, Marcello Sanguineti,
Ausra Saudargiene, Igor V. Tetko, Alessandro E. P. Villa, Viktor Jirsa, and Yoshua
Bengio, 442–454. Cham: Springer Nature Switzerland, 2026. https://doi.org/10.1007/978-3-032-04558-4_35.'
ieee: 'S. S. Hotegni and S. Peitz, “Enhancing Adversarial Robustness Through Multi-objective
Representation Learning,” in Artificial Neural Networks and Machine Learning
– ICANN 2025, 2026, pp. 442–454, doi: 10.1007/978-3-032-04558-4_35.'
mla: Hotegni, Sedjro Salomon, and Sebastian Peitz. “Enhancing Adversarial Robustness
Through Multi-Objective Representation Learning.” Artificial Neural Networks
and Machine Learning – ICANN 2025, edited by Walter Senn et al., Springer
Nature Switzerland, 2026, pp. 442–454, doi:10.1007/978-3-032-04558-4_35.
short: 'S.S. Hotegni, S. Peitz, in: W. Senn, M. Sanguineti, A. Saudargiene, I.V.
Tetko, A.E.P. Villa, V. Jirsa, Y. Bengio (Eds.), Artificial Neural Networks and
Machine Learning – ICANN 2025, Springer Nature Switzerland, Cham, 2026, pp. 442–454.'
date_created: 2026-10-01T11:53:11Z
date_updated: 2026-10-01T11:53:46Z
department:
- _id: '655'
doi: 10.1007/978-3-032-04558-4_35
editor:
- first_name: Walter
full_name: Senn, Walter
last_name: Senn
- first_name: Marcello
full_name: Sanguineti, Marcello
last_name: Sanguineti
- first_name: Ausra
full_name: Saudargiene, Ausra
last_name: Saudargiene
- first_name: Igor V.
full_name: Tetko, Igor V.
last_name: Tetko
- first_name: Alessandro E. P.
full_name: Villa, Alessandro E. P.
last_name: Villa
- first_name: Viktor
full_name: Jirsa, Viktor
last_name: Jirsa
- first_name: Yoshua
full_name: Bengio, Yoshua
last_name: Bengio
keyword:
- own
- own-conference
language:
- iso: eng
page: 442–454
place: Cham
publication: Artificial Neural Networks and Machine Learning – ICANN 2025
publication_identifier:
isbn:
- 978-3-032-04558-4
publisher: Springer Nature Switzerland
status: public
title: Enhancing Adversarial Robustness Through Multi-objective Representation Learning
type: conference
user_id: '47427'
year: '2026'
...
---
_id: '67302'
abstract:
- lang: eng
text: Data-driven surrogate models provide fast and fully differentiable approximations
of complex dynamical systems. In this work, we develop such surrogates for the
Rayleigh–Bénard convection (RBC), which governs thermally driven flows in natural
and industrial environments. Specifically, the proposed models approximate the
discrete-time flow map of the RBC system, advancing the full system state by a
fixed time step. We train Fourier Neural Operator (FNO)–based models to learn
the dynamics of RBC in two and three dimensions and compare them to a convolutional
U-Net baseline and a Koopman-based Linear Recurrent Autoencoder Network (LRAN).
The two-dimensional system serves as a baseline for the more challenging three-dimensional
case, which exhibits increased spatial complexity and turbulent dynamics. Across
all settings, FNO-based models consistently outperform the LRAN, while achieving
performance comparable to the U-Net in several regimes. Incorporating spatio-temporal
inputs via FNOs leads to improved long-term prediction accuracy, particularly
for turbulent flows. The physical fidelity of the predictions is assessed using
convective heat flux statistics, profiles, and fluctuations, showing that FNOs
most closely reproduce the ground-truth flow statistics. In addition, we demonstrate
that FNOs enable zero-shot super-resolution across unseen spatial discretizations,
a capability not shared by the convolutional baselines. These results highlight
the potential of neural operator–based models as accurate, physically consistent,
and resolution-independent surrogates for downstream tasks such as flow control.
author:
- first_name: Thorben
full_name: Markmann, Thorben
last_name: Markmann
- first_name: Michiel
full_name: Straat, Michiel
last_name: Straat
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Barbara
full_name: Hammer, Barbara
last_name: Hammer
citation:
ama: Markmann T, Straat M, Peitz S, Hammer B. Fourier neural operators as data-driven
surrogates for two- and three-dimensional Rayleigh–Bénard convection. Neurocomputing.
2026;679:133201. doi:10.1016/j.neucom.2026.133201
apa: Markmann, T., Straat, M., Peitz, S., & Hammer, B. (2026). Fourier neural
operators as data-driven surrogates for two- and three-dimensional Rayleigh–Bénard
convection. Neurocomputing, 679, 133201. https://doi.org/10.1016/j.neucom.2026.133201
bibtex: '@article{Markmann_Straat_Peitz_Hammer_2026, title={Fourier neural operators
as data-driven surrogates for two- and three-dimensional Rayleigh–Bénard convection},
volume={679}, DOI={10.1016/j.neucom.2026.133201},
journal={Neurocomputing}, author={Markmann, Thorben and Straat, Michiel and Peitz,
Sebastian and Hammer, Barbara}, year={2026}, pages={133201} }'
chicago: 'Markmann, Thorben, Michiel Straat, Sebastian Peitz, and Barbara Hammer.
“Fourier Neural Operators as Data-Driven Surrogates for Two- and Three-Dimensional
Rayleigh–Bénard Convection.” Neurocomputing 679 (2026): 133201. https://doi.org/10.1016/j.neucom.2026.133201.'
ieee: 'T. Markmann, M. Straat, S. Peitz, and B. Hammer, “Fourier neural operators
as data-driven surrogates for two- and three-dimensional Rayleigh–Bénard convection,”
Neurocomputing, vol. 679, p. 133201, 2026, doi: 10.1016/j.neucom.2026.133201.'
mla: Markmann, Thorben, et al. “Fourier Neural Operators as Data-Driven Surrogates
for Two- and Three-Dimensional Rayleigh–Bénard Convection.” Neurocomputing,
vol. 679, 2026, p. 133201, doi:10.1016/j.neucom.2026.133201.
short: T. Markmann, M. Straat, S. Peitz, B. Hammer, Neurocomputing 679 (2026) 133201.
date_created: 2026-10-01T11:55:20Z
date_updated: 2026-10-01T11:56:04Z
department:
- _id: '655'
doi: 10.1016/j.neucom.2026.133201
intvolume: ' 679'
keyword:
- own
- own-journal
- erc
language:
- iso: eng
page: '133201'
publication: Neurocomputing
publication_identifier:
issn:
- 0925-2312
status: public
title: Fourier neural operators as data-driven surrogates for two- and three-dimensional
Rayleigh–Bénard convection
type: journal_article
user_id: '47427'
volume: 679
year: '2026'
...
---
_id: '67299'
author:
- first_name: Hans
full_name: Harder, Hans
id: '98879'
last_name: Harder
- first_name: Abhijeet
full_name: Vishwasrao, Abhijeet
last_name: Vishwasrao
- first_name: Luca
full_name: Guastoni, Luca
last_name: Guastoni
- first_name: Ricardo
full_name: Vinuesa, Ricardo
last_name: Vinuesa
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: 'Harder H, Vishwasrao A, Guastoni L, Vinuesa R, Peitz S. Efficient probabilistic
surrogate modeling techniques for partially-observed large-scale dynamical systems.
In: Sukhatme G, Lindemann L, Tu S, Wierman A, Atanasov N, eds. Proceedings
of The 8th Annual Learning for Dynamics and Control Conference. Vol 331. Proceedings
of Machine Learning Research. PMLR; 2026:1601–1619. doi:10.48550/arXiv.2511.04641'
apa: Harder, H., Vishwasrao, A., Guastoni, L., Vinuesa, R., & Peitz, S. (2026).
Efficient probabilistic surrogate modeling techniques for partially-observed large-scale
dynamical systems. In G. Sukhatme, L. Lindemann, S. Tu, A. Wierman, & N. Atanasov
(Eds.), Proceedings of The 8th Annual Learning for Dynamics and Control Conference
(Vol. 331, pp. 1601–1619). PMLR. https://doi.org/10.48550/arXiv.2511.04641
bibtex: '@inproceedings{Harder_Vishwasrao_Guastoni_Vinuesa_Peitz_2026, series={Proceedings
of Machine Learning Research}, title={Efficient probabilistic surrogate modeling
techniques for partially-observed large-scale dynamical systems}, volume={331},
DOI={10.48550/arXiv.2511.04641},
booktitle={Proceedings of The 8th Annual Learning for Dynamics and Control Conference},
publisher={PMLR}, author={Harder, Hans and Vishwasrao, Abhijeet and Guastoni,
Luca and Vinuesa, Ricardo and Peitz, Sebastian}, editor={Sukhatme, Gaurav and
Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, year={2026},
pages={1601–1619}, collection={Proceedings of Machine Learning Research} }'
chicago: Harder, Hans, Abhijeet Vishwasrao, Luca Guastoni, Ricardo Vinuesa, and
Sebastian Peitz. “Efficient Probabilistic Surrogate Modeling Techniques for Partially-Observed
Large-Scale Dynamical Systems.” In Proceedings of The 8th Annual Learning for
Dynamics and Control Conference, edited by Gaurav Sukhatme, Lars Lindemann,
Stephen Tu, Adam Wierman, and Nikolay Atanasov, 331:1601–1619. Proceedings of
Machine Learning Research. PMLR, 2026. https://doi.org/10.48550/arXiv.2511.04641.
ieee: 'H. Harder, A. Vishwasrao, L. Guastoni, R. Vinuesa, and S. Peitz, “Efficient
probabilistic surrogate modeling techniques for partially-observed large-scale
dynamical systems,” in Proceedings of The 8th Annual Learning for Dynamics
and Control Conference, 2026, vol. 331, pp. 1601–1619, doi: 10.48550/arXiv.2511.04641.'
mla: Harder, Hans, et al. “Efficient Probabilistic Surrogate Modeling Techniques
for Partially-Observed Large-Scale Dynamical Systems.” Proceedings of The 8th
Annual Learning for Dynamics and Control Conference, edited by Gaurav Sukhatme
et al., vol. 331, PMLR, 2026, pp. 1601–1619, doi:10.48550/arXiv.2511.04641.
short: 'H. Harder, A. Vishwasrao, L. Guastoni, R. Vinuesa, S. Peitz, in: G. Sukhatme,
L. Lindemann, S. Tu, A. Wierman, N. Atanasov (Eds.), Proceedings of The 8th Annual
Learning for Dynamics and Control Conference, PMLR, 2026, pp. 1601–1619.'
date_created: 2026-10-01T11:51:57Z
date_updated: 2026-10-01T11:52:48Z
department:
- _id: '655'
doi: 10.48550/arXiv.2511.04641
editor:
- first_name: Gaurav
full_name: Sukhatme, Gaurav
last_name: Sukhatme
- first_name: Lars
full_name: Lindemann, Lars
last_name: Lindemann
- first_name: Stephen
full_name: Tu, Stephen
last_name: Tu
- first_name: Adam
full_name: Wierman, Adam
last_name: Wierman
- first_name: Nikolay
full_name: Atanasov, Nikolay
last_name: Atanasov
intvolume: ' 331'
keyword:
- own
- own-conference
- erc
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://openreview.net/pdf?id=Z9srtyqVLE
oa: '1'
page: 1601–1619
publication: Proceedings of The 8th Annual Learning for Dynamics and Control Conference
publisher: PMLR
series_title: Proceedings of Machine Learning Research
status: public
title: Efficient probabilistic surrogate modeling techniques for partially-observed
large-scale dynamical systems
type: conference
user_id: '47427'
volume: 331
year: '2026'
...
---
_id: '67303'
author:
- first_name: Augustina Chidinma
full_name: Amakor, Augustina Chidinma
id: '97916'
last_name: Amakor
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: 'Amakor AC, Sonntag K, Peitz S. Interactive Pareto navigation for deep multi-task
learning. In: European Conference on Machine Learning and Principles and Practice
of Knowledge Discovery in Databases (ECML PKDD). ; 2026:652-668. doi:10.1007/978-3-032-37667-1_37'
apa: Amakor, A. C., Sonntag, K., & Peitz, S. (2026). Interactive Pareto navigation
for deep multi-task learning. European Conference on Machine Learning and Principles
and Practice of Knowledge Discovery in Databases (ECML PKDD), 652–668. https://doi.org/10.1007/978-3-032-37667-1_37
bibtex: '@inproceedings{Amakor_Sonntag_Peitz_2026, title={Interactive Pareto navigation
for deep multi-task learning}, DOI={10.1007/978-3-032-37667-1_37},
booktitle={European Conference on Machine Learning and Principles and Practice
of Knowledge Discovery in Databases (ECML PKDD)}, author={Amakor, Augustina Chidinma
and Sonntag, Konstantin and Peitz, Sebastian}, year={2026}, pages={652–668} }'
chicago: Amakor, Augustina Chidinma, Konstantin Sonntag, and Sebastian Peitz. “Interactive
Pareto Navigation for Deep Multi-Task Learning.” In European Conference on
Machine Learning and Principles and Practice of Knowledge Discovery in Databases
(ECML PKDD), 652–68, 2026. https://doi.org/10.1007/978-3-032-37667-1_37.
ieee: 'A. C. Amakor, K. Sonntag, and S. Peitz, “Interactive Pareto navigation for
deep multi-task learning,” in European Conference on Machine Learning and Principles
and Practice of Knowledge Discovery in Databases (ECML PKDD), 2026, pp. 652–668,
doi: 10.1007/978-3-032-37667-1_37.'
mla: Amakor, Augustina Chidinma, et al. “Interactive Pareto Navigation for Deep
Multi-Task Learning.” European Conference on Machine Learning and Principles
and Practice of Knowledge Discovery in Databases (ECML PKDD), 2026, pp. 652–68,
doi:10.1007/978-3-032-37667-1_37.
short: 'A.C. Amakor, K. Sonntag, S. Peitz, in: European Conference on Machine Learning
and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD), 2026,
pp. 652–668.'
date_created: 2026-10-01T11:56:15Z
date_updated: 2026-10-01T11:58:43Z
department:
- _id: '655'
doi: 10.1007/978-3-032-37667-1_37
keyword:
- own
- own-conference
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2606.19521
oa: '1'
page: 652-668
publication: European Conference on Machine Learning and Principles and Practice of
Knowledge Discovery in Databases (ECML PKDD)
status: public
title: Interactive Pareto navigation for deep multi-task learning
type: conference
user_id: '47427'
year: '2026'
...
---
_id: '67305'
author:
- first_name: Jannis
full_name: Becktepe, Jannis
last_name: Becktepe
- first_name: Aleksandra
full_name: Franz, Aleksandra
last_name: Franz
- first_name: Nils
full_name: Thuerey, Nils
last_name: Thuerey
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: 'Becktepe J, Franz A, Thuerey N, Peitz S. Plug-and-Play Benchmarking of Reinforcement
Learning Algorithms for Large-Scale Flow Control. In: International Conference
on Machine Learning (ICML). ; 2026. doi:10.48550/arXiv.2601.15015'
apa: Becktepe, J., Franz, A., Thuerey, N., & Peitz, S. (2026). Plug-and-Play
Benchmarking of Reinforcement Learning Algorithms for Large-Scale Flow Control.
International Conference on Machine Learning (ICML). https://doi.org/10.48550/arXiv.2601.15015
bibtex: '@inproceedings{Becktepe_Franz_Thuerey_Peitz_2026, title={Plug-and-Play
Benchmarking of Reinforcement Learning Algorithms for Large-Scale Flow Control},
DOI={10.48550/arXiv.2601.15015},
booktitle={International Conference on Machine Learning (ICML)}, author={Becktepe,
Jannis and Franz, Aleksandra and Thuerey, Nils and Peitz, Sebastian}, year={2026}
}'
chicago: Becktepe, Jannis, Aleksandra Franz, Nils Thuerey, and Sebastian Peitz.
“Plug-and-Play Benchmarking of Reinforcement Learning Algorithms for Large-Scale
Flow Control.” In International Conference on Machine Learning (ICML),
2026. https://doi.org/10.48550/arXiv.2601.15015.
ieee: 'J. Becktepe, A. Franz, N. Thuerey, and S. Peitz, “Plug-and-Play Benchmarking
of Reinforcement Learning Algorithms for Large-Scale Flow Control,” 2026, doi:
10.48550/arXiv.2601.15015.'
mla: Becktepe, Jannis, et al. “Plug-and-Play Benchmarking of Reinforcement Learning
Algorithms for Large-Scale Flow Control.” International Conference on Machine
Learning (ICML), 2026, doi:10.48550/arXiv.2601.15015.
short: 'J. Becktepe, A. Franz, N. Thuerey, S. Peitz, in: International Conference
on Machine Learning (ICML), 2026.'
date_created: 2026-10-01T11:59:35Z
date_updated: 2026-10-01T12:00:51Z
department:
- _id: '655'
doi: 10.48550/arXiv.2601.15015
keyword:
- own
- own-conference
- erc
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://safe-autonomous-systems.github.io/fluidgym/
oa: '1'
publication: International Conference on Machine Learning (ICML)
status: public
title: Plug-and-Play Benchmarking of Reinforcement Learning Algorithms for Large-Scale
Flow Control
type: conference
user_id: '47427'
year: '2026'
...
---
_id: '67301'
author:
- first_name: Meike Claudia
full_name: Wohlleben, Meike Claudia
id: '43991'
last_name: Wohlleben
orcid: 0009-0009-9767-7168
- first_name: Jan
full_name: Schütte, Jan
id: '22109'
last_name: Schütte
orcid: 0000-0001-9025-9742
- first_name: Manuel
full_name: Berkemeier, Manuel
last_name: Berkemeier
- first_name: Walter
full_name: Sextro, Walter
id: '21220'
last_name: Sextro
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Wohlleben MC, Schütte J, Berkemeier M, Sextro W, Peitz S. Evaluating Physics-Based,
Hybrid, and Data-Driven Models for Rubber-Metal Bushings. Multibody System
Dynamics. Published online 2026. doi:10.1007/s11044-026-10146-9
apa: Wohlleben, M. C., Schütte, J., Berkemeier, M., Sextro, W., & Peitz, S.
(2026). Evaluating Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal
Bushings. Multibody System Dynamics. https://doi.org/10.1007/s11044-026-10146-9
bibtex: '@article{Wohlleben_Schütte_Berkemeier_Sextro_Peitz_2026, title={Evaluating
Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal Bushings}, DOI={10.1007/s11044-026-10146-9},
journal={Multibody System Dynamics}, author={Wohlleben, Meike Claudia and Schütte,
Jan and Berkemeier, Manuel and Sextro, Walter and Peitz, Sebastian}, year={2026}
}'
chicago: Wohlleben, Meike Claudia, Jan Schütte, Manuel Berkemeier, Walter Sextro,
and Sebastian Peitz. “Evaluating Physics-Based, Hybrid, and Data-Driven Models
for Rubber-Metal Bushings.” Multibody System Dynamics, 2026. https://doi.org/10.1007/s11044-026-10146-9.
ieee: 'M. C. Wohlleben, J. Schütte, M. Berkemeier, W. Sextro, and S. Peitz, “Evaluating
Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal Bushings,” Multibody
System Dynamics, 2026, doi: 10.1007/s11044-026-10146-9.'
mla: Wohlleben, Meike Claudia, et al. “Evaluating Physics-Based, Hybrid, and Data-Driven
Models for Rubber-Metal Bushings.” Multibody System Dynamics, 2026, doi:10.1007/s11044-026-10146-9.
short: M.C. Wohlleben, J. Schütte, M. Berkemeier, W. Sextro, S. Peitz, Multibody
System Dynamics (2026).
date_created: 2026-10-01T11:53:54Z
date_updated: 2026-10-01T11:54:23Z
department:
- _id: '655'
doi: 10.1007/s11044-026-10146-9
keyword:
- own
- own-journal
language:
- iso: eng
publication: Multibody System Dynamics
status: public
title: Evaluating Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal Bushings
type: journal_article
user_id: '47427'
year: '2026'
...
---
_id: '67298'
author:
- first_name: Christian
full_name: Mugisho Zagabe, Christian
last_name: Mugisho Zagabe
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Mugisho Zagabe C, Peitz S. Automatic feature identification in least-squares
policy iteration using the Koopman operator framework. arXiv:260326464.
Published online 2026.
apa: Mugisho Zagabe, C., & Peitz, S. (2026). Automatic feature identification
in least-squares policy iteration using the Koopman operator framework. In arXiv:2603.26464.
bibtex: '@article{Mugisho Zagabe_Peitz_2026, title={Automatic feature identification
in least-squares policy iteration using the Koopman operator framework}, journal={arXiv:2603.26464},
author={Mugisho Zagabe, Christian and Peitz, Sebastian}, year={2026} }'
chicago: Mugisho Zagabe, Christian, and Sebastian Peitz. “Automatic Feature Identification
in Least-Squares Policy Iteration Using the Koopman Operator Framework.” ArXiv:2603.26464,
2026.
ieee: C. Mugisho Zagabe and S. Peitz, “Automatic feature identification in least-squares
policy iteration using the Koopman operator framework,” arXiv:2603.26464.
2026.
mla: Mugisho Zagabe, Christian, and Sebastian Peitz. “Automatic Feature Identification
in Least-Squares Policy Iteration Using the Koopman Operator Framework.” ArXiv:2603.26464,
2026.
short: C. Mugisho Zagabe, S. Peitz, ArXiv:2603.26464 (2026).
date_created: 2026-10-01T11:50:28Z
date_updated: 2026-10-01T11:51:41Z
department:
- _id: '655'
keyword:
- own
- own-preprint
- erc
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2603.26464
oa: '1'
publication: arXiv:2603.26464
status: public
title: Automatic feature identification in least-squares policy iteration using the
Koopman operator framework
type: preprint
user_id: '47427'
year: '2026'
...
---
_id: '67304'
author:
- first_name: Tim
full_name: Plotzki, Tim
last_name: Plotzki
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Plotzki T, Peitz S. Koopman-based surrogate modeling for reinforcement-learning-control
of Rayleigh-Benard convection. arXiv:260328074. Published online 2026.
apa: Plotzki, T., & Peitz, S. (2026). Koopman-based surrogate modeling for reinforcement-learning-control
of Rayleigh-Benard convection. In arXiv:2603.28074.
bibtex: '@article{Plotzki_Peitz_2026, title={Koopman-based surrogate modeling for
reinforcement-learning-control of Rayleigh-Benard convection}, journal={arXiv:2603.28074},
author={Plotzki, Tim and Peitz, Sebastian}, year={2026} }'
chicago: Plotzki, Tim, and Sebastian Peitz. “Koopman-Based Surrogate Modeling for
Reinforcement-Learning-Control of Rayleigh-Benard Convection.” ArXiv:2603.28074,
2026.
ieee: T. Plotzki and S. Peitz, “Koopman-based surrogate modeling for reinforcement-learning-control
of Rayleigh-Benard convection,” arXiv:2603.28074. 2026.
mla: Plotzki, Tim, and Sebastian Peitz. “Koopman-Based Surrogate Modeling for Reinforcement-Learning-Control
of Rayleigh-Benard Convection.” ArXiv:2603.28074, 2026.
short: T. Plotzki, S. Peitz, ArXiv:2603.28074 (2026).
date_created: 2026-10-01T11:59:03Z
date_updated: 2026-10-01T11:59:27Z
department:
- _id: '655'
keyword:
- own
- own-preprint
- erc
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2603.28074
oa: '1'
publication: arXiv:2603.28074
status: public
title: Koopman-based surrogate modeling for reinforcement-learning-control of Rayleigh-Benard
convection
type: preprint
user_id: '47427'
year: '2026'
...
---
_id: '51159'
abstract:
- lang: eng
text: Sparsity is a highly desired feature in deep neural networks (DNNs) since
it ensures numerical efficiency, improves the interpretability of models (due
to the smaller number of relevant features), and robustness. In machine learning
approaches based on linear models, it is well known that there exists a connecting
path between the sparsest solution in terms of the $\ell^1$ norm,i.e., zero weights
and the non-regularized solution, which is called the regularization path. Very
recently, there was a first attempt to extend the concept of regularization paths
to DNNs by means of treating the empirical loss and sparsity ($\ell^1$ norm) as
two conflicting criteria and solving the resulting multiobjective optimization
problem. However, due to the non-smoothness of the $\ell^1$ norm and the high
number of parameters, this approach is not very efficient from a computational
perspective. To overcome this limitation, we present an algorithm that allows
for the approximation of the entire Pareto front for the above-mentioned objectives
in a very efficient manner. We present numerical examples using both deterministic
and stochastic gradients. We furthermore demonstrate that knowledge of the regularization
path allows for a well-generalizing network parametrization.
article_number: '100625'
author:
- first_name: Augustina Chidinma
full_name: Amakor, Augustina Chidinma
id: '97916'
last_name: Amakor
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Amakor AC, Sonntag K, Peitz S. A multiobjective continuation method to compute
the regularization path of deep neural networks. Machine Learning with Applications.
2025;19. doi:10.1016/j.mlwa.2025.100625
apa: Amakor, A. C., Sonntag, K., & Peitz, S. (2025). A multiobjective continuation
method to compute the regularization path of deep neural networks. Machine
Learning with Applications, 19, Article 100625. https://doi.org/10.1016/j.mlwa.2025.100625
bibtex: '@article{Amakor_Sonntag_Peitz_2025, title={A multiobjective continuation
method to compute the regularization path of deep neural networks}, volume={19},
DOI={10.1016/j.mlwa.2025.100625},
number={100625}, journal={Machine Learning with Applications}, publisher={Elsevier},
author={Amakor, Augustina Chidinma and Sonntag, Konstantin and Peitz, Sebastian},
year={2025} }'
chicago: Amakor, Augustina Chidinma, Konstantin Sonntag, and Sebastian Peitz. “A
Multiobjective Continuation Method to Compute the Regularization Path of Deep
Neural Networks.” Machine Learning with Applications 19 (2025). https://doi.org/10.1016/j.mlwa.2025.100625.
ieee: 'A. C. Amakor, K. Sonntag, and S. Peitz, “A multiobjective continuation method
to compute the regularization path of deep neural networks,” Machine Learning
with Applications, vol. 19, Art. no. 100625, 2025, doi: 10.1016/j.mlwa.2025.100625.'
mla: Amakor, Augustina Chidinma, et al. “A Multiobjective Continuation Method to
Compute the Regularization Path of Deep Neural Networks.” Machine Learning
with Applications, vol. 19, 100625, Elsevier, 2025, doi:10.1016/j.mlwa.2025.100625.
short: A.C. Amakor, K. Sonntag, S. Peitz, Machine Learning with Applications 19
(2025).
date_created: 2024-02-06T08:51:00Z
date_updated: 2026-10-01T11:33:45Z
ddc:
- '000'
department:
- _id: '655'
doi: 10.1016/j.mlwa.2025.100625
file:
- access_level: closed
content_type: application/pdf
creator: speitz
date_created: 2026-10-01T11:24:57Z
date_updated: 2026-10-01T11:24:57Z
file_id: '67296'
file_name: ASP25_A multiobjective continuation method to compute the regularization
path of deep neural networks.pdf
file_size: 2433955
relation: main_file
success: 1
file_date_updated: 2026-10-01T11:24:57Z
has_accepted_license: '1'
intvolume: ' 19'
language:
- iso: eng
publication: Machine Learning with Applications
publisher: Elsevier
quality_controlled: '1'
status: public
title: A multiobjective continuation method to compute the regularization path of
deep neural networks
type: journal_article
user_id: '47427'
volume: 19
year: '2025'
...
---
_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. Equivariance
and partial observations in Koopman operator theory for partial differential equations.
Journal of Computational Dynamics. 2025;12:305-324. doi:10.3934/jcd.2024035
apa: Peitz, S., Harder, H., Nüske, F., Philipp, F., Schaller, M., & Worthmann,
K. (2025). Equivariance and partial observations in Koopman operator theory for
partial differential equations. Journal of Computational Dynamics, 12,
305–324. https://doi.org/10.3934/jcd.2024035
bibtex: '@article{Peitz_Harder_Nüske_Philipp_Schaller_Worthmann_2025, title={Equivariance
and partial observations in Koopman operator theory for partial differential equations},
volume={12}, DOI={10.3934/jcd.2024035},
journal={Journal of Computational Dynamics}, author={Peitz, Sebastian and Harder,
Hans and Nüske, Feliks and Philipp, Friedrich and Schaller, Manuel and Worthmann,
Karl}, year={2025}, pages={305–324} }'
chicago: 'Peitz, Sebastian, Hans Harder, Feliks Nüske, Friedrich Philipp, Manuel
Schaller, and Karl Worthmann. “Equivariance and Partial Observations in Koopman
Operator Theory for Partial Differential Equations.” Journal of Computational
Dynamics 12 (2025): 305–24. https://doi.org/10.3934/jcd.2024035.'
ieee: 'S. Peitz, H. Harder, F. Nüske, F. Philipp, M. Schaller, and K. Worthmann,
“Equivariance and partial observations in Koopman operator theory for partial
differential equations,” Journal of Computational Dynamics, vol. 12, pp.
305–324, 2025, doi: 10.3934/jcd.2024035.'
mla: Peitz, Sebastian, et al. “Equivariance and Partial Observations in Koopman
Operator Theory for Partial Differential Equations.” Journal of Computational
Dynamics, vol. 12, 2025, pp. 305–24, doi:10.3934/jcd.2024035.
short: S. Peitz, H. Harder, F. Nüske, F. Philipp, M. Schaller, K. Worthmann, Journal
of Computational Dynamics 12 (2025) 305–324.
date_created: 2023-08-21T05:52:24Z
date_updated: 2026-10-01T11:32:34Z
department:
- _id: '655'
doi: 10.3934/jcd.2024035
external_id:
arxiv:
- '2307.15325'
intvolume: ' 12'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2307.15325
oa: '1'
page: 305-324
publication: Journal of Computational Dynamics
status: public
title: Equivariance and partial observations in Koopman operator theory for partial
differential equations
type: journal_article
user_id: '47427'
volume: 12
year: '2025'
...
---
_id: '53793'
abstract:
- lang: eng
text: We utilize extreme learning machines for the prediction of partial differential
equations (PDEs). Our method splits the state space into multiple windows that
are predicted individually using a single model. Despite requiring only few data
points (in some cases, our method can learn from a single full-state snapshot),
it still achieves high accuracy and can predict the flow of PDEs over long time
horizons. Moreover, we show how additional symmetries can be exploited to increase
sample efficiency and to enforce equivariance.
author:
- first_name: Hans
full_name: Harder, Hans
id: '98879'
last_name: Harder
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: 'Harder H, Peitz S. Solving partial differential equations with equivariant
extreme learning machines. In: Berberich J, Ianelli A, Allgöwer F, eds. Systems
Theory in Data and Optimization. Springer; 2025:153-168. doi:10.1007/978-3-031-83191-1_10'
apa: Harder, H., & Peitz, S. (2025). Solving partial differential equations
with equivariant extreme learning machines. In J. Berberich, A. Ianelli, &
F. Allgöwer (Eds.), Systems theory in data and optimization (pp. 153–168).
Springer. https://doi.org/10.1007/978-3-031-83191-1_10
bibtex: '@inproceedings{Harder_Peitz_2025, place={Cham}, title={Solving partial
differential equations with equivariant extreme learning machines}, DOI={10.1007/978-3-031-83191-1_10},
booktitle={Systems theory in data and optimization}, publisher={Springer}, author={Harder,
Hans and Peitz, Sebastian}, editor={Berberich, J. and Ianelli, A. and Allgöwer,
F.}, year={2025}, pages={153–168} }'
chicago: 'Harder, Hans, and Sebastian Peitz. “Solving Partial Differential Equations
with Equivariant Extreme Learning Machines.” In Systems Theory in Data and
Optimization, edited by J. Berberich, A. Ianelli, and F. Allgöwer, 153–68.
Cham: Springer, 2025. https://doi.org/10.1007/978-3-031-83191-1_10.'
ieee: 'H. Harder and S. Peitz, “Solving partial differential equations with equivariant
extreme learning machines,” in Systems theory in data and optimization,
2025, pp. 153–168, doi: 10.1007/978-3-031-83191-1_10.'
mla: Harder, Hans, and Sebastian Peitz. “Solving Partial Differential Equations
with Equivariant Extreme Learning Machines.” Systems Theory in Data and Optimization,
edited by J. Berberich et al., Springer, 2025, pp. 153–68, doi:10.1007/978-3-031-83191-1_10.
short: 'H. Harder, S. Peitz, in: J. Berberich, A. Ianelli, F. Allgöwer (Eds.), Systems
Theory in Data and Optimization, Springer, Cham, 2025, pp. 153–168.'
date_created: 2024-04-30T08:43:14Z
date_updated: 2026-10-01T11:39:19Z
doi: 10.1007/978-3-031-83191-1_10
editor:
- first_name: J.
full_name: Berberich, J.
last_name: Berberich
- first_name: A.
full_name: Ianelli, A.
last_name: Ianelli
- first_name: F.
full_name: Allgöwer, F.
last_name: Allgöwer
keyword:
- extreme learning machines
- partial differential equations
- data-driven prediction
- high-dimensional systems
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2404.18530
oa: '1'
page: 153-168
place: Cham
publication: Systems theory in data and optimization
publication_identifier:
isbn:
- 978-3-031-83191-1
publication_status: published
publisher: Springer
status: public
title: Solving partial differential equations with equivariant extreme learning machines
type: conference
user_id: '47427'
year: '2025'
...
---
_id: '67313'
author:
- first_name: Diana
full_name: Voth, Diana
last_name: Voth
- first_name: Leonidas
full_name: Dane, Leonidas
last_name: Dane
- first_name: Jonas
full_name: Grebe, Jonas
last_name: Grebe
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Philipp
full_name: Terhörst, Philipp
last_name: Terhörst
citation:
ama: 'Voth D, Dane L, Grebe J, Peitz S, Terhörst P. Effective Backdoor Learning
on Open-Set Face Recognition Systems. In: 2025 IEEE/CVF Winter Conference on
Applications of Computer Vision (WACV). ; 2025:1027-1039. doi:10.1109/WACV61041.2025.00109'
apa: Voth, D., Dane, L., Grebe, J., Peitz, S., & Terhörst, P. (2025). Effective
Backdoor Learning on Open-Set Face Recognition Systems. 2025 IEEE/CVF Winter
Conference on Applications of Computer Vision (WACV), 1027–1039. https://doi.org/10.1109/WACV61041.2025.00109
bibtex: '@inproceedings{Voth_Dane_Grebe_Peitz_Terhörst_2025, title={Effective Backdoor
Learning on Open-Set Face Recognition Systems}, DOI={10.1109/WACV61041.2025.00109},
booktitle={2025 IEEE/CVF Winter Conference on Applications of Computer Vision
(WACV)}, author={Voth, Diana and Dane, Leonidas and Grebe, Jonas and Peitz, Sebastian
and Terhörst, Philipp}, year={2025}, pages={1027–1039} }'
chicago: Voth, Diana, Leonidas Dane, Jonas Grebe, Sebastian Peitz, and Philipp Terhörst.
“Effective Backdoor Learning on Open-Set Face Recognition Systems.” In 2025
IEEE/CVF Winter Conference on Applications of Computer Vision (WACV), 1027–39,
2025. https://doi.org/10.1109/WACV61041.2025.00109.
ieee: 'D. Voth, L. Dane, J. Grebe, S. Peitz, and P. Terhörst, “Effective Backdoor
Learning on Open-Set Face Recognition Systems,” in 2025 IEEE/CVF Winter Conference
on Applications of Computer Vision (WACV), 2025, pp. 1027–1039, doi: 10.1109/WACV61041.2025.00109.'
mla: Voth, Diana, et al. “Effective Backdoor Learning on Open-Set Face Recognition
Systems.” 2025 IEEE/CVF Winter Conference on Applications of Computer Vision
(WACV), 2025, pp. 1027–39, doi:10.1109/WACV61041.2025.00109.
short: 'D. Voth, L. Dane, J. Grebe, S. Peitz, P. Terhörst, in: 2025 IEEE/CVF Winter
Conference on Applications of Computer Vision (WACV), 2025, pp. 1027–1039.'
date_created: 2026-10-01T12:04:52Z
date_updated: 2026-10-01T12:05:02Z
department:
- _id: '655'
doi: 10.1109/WACV61041.2025.00109
keyword:
- own
- own-conference
language:
- iso: eng
page: 1027-1039
publication: 2025 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV)
status: public
title: Effective Backdoor Learning on Open-Set Face Recognition Systems
type: conference
user_id: '47427'
year: '2025'
...
---
_id: '67312'
author:
- first_name: Thorben
full_name: Markmann, Thorben
last_name: Markmann
- first_name: Michiel
full_name: Straat, Michiel
last_name: Straat
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Barbara
full_name: Hammer, Barbara
last_name: Hammer
citation:
ama: 'Markmann T, Straat M, Peitz S, Hammer B. Control of Rayleigh-Bénard Convection:
Effectiveness of Reinforcement Learning in the Turbulent Regime. arXiv:250412000.
Published online 2025.'
apa: 'Markmann, T., Straat, M., Peitz, S., & Hammer, B. (2025). Control of Rayleigh-Bénard
Convection: Effectiveness of Reinforcement Learning in the Turbulent Regime. In
arXiv:2504.12000.'
bibtex: '@article{Markmann_Straat_Peitz_Hammer_2025, title={Control of Rayleigh-Bénard
Convection: Effectiveness of Reinforcement Learning in the Turbulent Regime},
journal={arXiv:2504.12000}, author={Markmann, Thorben and Straat, Michiel and
Peitz, Sebastian and Hammer, Barbara}, year={2025} }'
chicago: 'Markmann, Thorben, Michiel Straat, Sebastian Peitz, and Barbara Hammer.
“Control of Rayleigh-Bénard Convection: Effectiveness of Reinforcement Learning
in the Turbulent Regime.” ArXiv:2504.12000, 2025.'
ieee: 'T. Markmann, M. Straat, S. Peitz, and B. Hammer, “Control of Rayleigh-Bénard
Convection: Effectiveness of Reinforcement Learning in the Turbulent Regime,”
arXiv:2504.12000. 2025.'
mla: 'Markmann, Thorben, et al. “Control of Rayleigh-Bénard Convection: Effectiveness
of Reinforcement Learning in the Turbulent Regime.” ArXiv:2504.12000, 2025.'
short: T. Markmann, M. Straat, S. Peitz, B. Hammer, ArXiv:2504.12000 (2025).
date_created: 2026-10-01T12:04:32Z
date_updated: 2026-10-01T12:04:44Z
department:
- _id: '655'
keyword:
- own
- own-preprint
language:
- iso: eng
publication: arXiv:2504.12000
status: public
title: 'Control of Rayleigh-Bénard Convection: Effectiveness of Reinforcement Learning
in the Turbulent Regime'
type: preprint
user_id: '47427'
year: '2025'
...
---
_id: '67310'
author:
- first_name: Septimus
full_name: Boshoff, Septimus
last_name: Boshoff
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
citation:
ama: Boshoff S, Peitz S, Klus S. Bayesian Transfer Operators in Reproducing Kernel
Hilbert Spaces. arXiv:250922482. Published online 2025.
apa: Boshoff, S., Peitz, S., & Klus, S. (2025). Bayesian Transfer Operators
in Reproducing Kernel Hilbert Spaces. In arXiv:2509.22482.
bibtex: '@article{Boshoff_Peitz_Klus_2025, title={Bayesian Transfer Operators in
Reproducing Kernel Hilbert Spaces}, journal={arXiv:2509.22482}, author={Boshoff,
Septimus and Peitz, Sebastian and Klus, Stefan}, year={2025} }'
chicago: Boshoff, Septimus, Sebastian Peitz, and Stefan Klus. “Bayesian Transfer
Operators in Reproducing Kernel Hilbert Spaces.” ArXiv:2509.22482, 2025.
ieee: S. Boshoff, S. Peitz, and S. Klus, “Bayesian Transfer Operators in Reproducing
Kernel Hilbert Spaces,” arXiv:2509.22482. 2025.
mla: Boshoff, Septimus, et al. “Bayesian Transfer Operators in Reproducing Kernel
Hilbert Spaces.” ArXiv:2509.22482, 2025.
short: S. Boshoff, S. Peitz, S. Klus, ArXiv:2509.22482 (2025).
date_created: 2026-10-01T12:03:40Z
date_updated: 2026-10-01T12:03:58Z
department:
- _id: '655'
keyword:
- own
- own-preprint
language:
- iso: eng
publication: arXiv:2509.22482
status: public
title: Bayesian Transfer Operators in Reproducing Kernel Hilbert Spaces
type: preprint
user_id: '47427'
year: '2025'
...