---
_id: '62913'
author:
- first_name: Anna
full_name: Hunstig, Anna
id: '73659'
last_name: Hunstig
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Hendrik
full_name: Rose, Hendrik
id: '55958'
last_name: Rose
orcid: 0000-0002-3079-5428
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
citation:
ama: 'Hunstig A, Peitz S, Rose H, Meier T. Accelerating the analysis of optical
quantum systems using the Koopman operator. In: 2024 IEEE 63rd Conference on
Decision and Control (CDC). IEEE; 2025. doi:10.1109/cdc56724.2024.10886589'
apa: Hunstig, A., Peitz, S., Rose, H., & Meier, T. (2025). Accelerating the
analysis of optical quantum systems using the Koopman operator. 2024 IEEE 63rd
Conference on Decision and Control (CDC). https://doi.org/10.1109/cdc56724.2024.10886589
bibtex: '@inproceedings{Hunstig_Peitz_Rose_Meier_2025, title={Accelerating the analysis
of optical quantum systems using the Koopman operator}, DOI={10.1109/cdc56724.2024.10886589},
booktitle={2024 IEEE 63rd Conference on Decision and Control (CDC)}, publisher={IEEE},
author={Hunstig, Anna and Peitz, Sebastian and Rose, Hendrik and Meier, Torsten},
year={2025} }'
chicago: Hunstig, Anna, Sebastian Peitz, Hendrik Rose, and Torsten Meier. “Accelerating
the Analysis of Optical Quantum Systems Using the Koopman Operator.” In 2024
IEEE 63rd Conference on Decision and Control (CDC). IEEE, 2025. https://doi.org/10.1109/cdc56724.2024.10886589.
ieee: 'A. Hunstig, S. Peitz, H. Rose, and T. Meier, “Accelerating the analysis of
optical quantum systems using the Koopman operator,” 2025, doi: 10.1109/cdc56724.2024.10886589.'
mla: Hunstig, Anna, et al. “Accelerating the Analysis of Optical Quantum Systems
Using the Koopman Operator.” 2024 IEEE 63rd Conference on Decision and Control
(CDC), IEEE, 2025, doi:10.1109/cdc56724.2024.10886589.
short: 'A. Hunstig, S. Peitz, H. Rose, T. Meier, in: 2024 IEEE 63rd Conference on
Decision and Control (CDC), IEEE, 2025.'
date_created: 2025-12-05T09:37:58Z
date_updated: 2025-12-05T09:40:24Z
department:
- _id: '15'
- _id: '170'
- _id: '293'
- _id: '230'
- _id: '623'
- _id: '35'
doi: 10.1109/cdc56724.2024.10886589
language:
- iso: eng
project:
- _id: '266'
name: 'PhoQC: Photonisches Quantencomputing'
publication: 2024 IEEE 63rd Conference on Decision and Control (CDC)
publication_status: published
publisher: IEEE
status: public
title: Accelerating the analysis of optical quantum systems using the Koopman operator
type: conference
user_id: '16199'
year: '2025'
...
---
_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."
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. Extended
Dynamic Mode Decomposition: Sharp bounds on the sample efficiency. arXiv:240202494.
Published online 2024.'
apa: 'Philipp, F. M., Schaller, M., Boshoff, S., Peitz, S., Nüske, F., & Worthmann,
K. (2024). Extended Dynamic Mode Decomposition: Sharp bounds on the sample efficiency.
In arXiv:2402.02494.'
bibtex: '@article{Philipp_Schaller_Boshoff_Peitz_Nüske_Worthmann_2024, title={Extended
Dynamic Mode Decomposition: Sharp bounds on the sample efficiency}, journal={arXiv:2402.02494},
author={Philipp, Friedrich M. and Schaller, Manuel and Boshoff, Septimus and Peitz,
Sebastian and Nüske, Feliks and Worthmann, Karl}, year={2024} }'
chicago: 'Philipp, Friedrich M., Manuel Schaller, Septimus Boshoff, Sebastian Peitz,
Feliks Nüske, and Karl Worthmann. “Extended Dynamic Mode Decomposition: Sharp
Bounds on the Sample Efficiency.” ArXiv:2402.02494, 2024.'
ieee: 'F. M. Philipp, M. Schaller, S. Boshoff, S. Peitz, F. Nüske, and K. Worthmann,
“Extended Dynamic Mode Decomposition: Sharp bounds on the sample efficiency,”
arXiv:2402.02494. 2024.'
mla: 'Philipp, Friedrich M., et al. “Extended Dynamic Mode Decomposition: Sharp
Bounds on the Sample Efficiency.” ArXiv:2402.02494, 2024.'
short: F.M. Philipp, M. Schaller, S. Boshoff, S. Peitz, F. Nüske, K. Worthmann,
ArXiv:2402.02494 (2024).
date_created: 2024-02-06T08:52:21Z
date_updated: 2024-02-06T08:52:44Z
department:
- _id: '655'
external_id:
arxiv:
- '2402.02494'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2402.02494.pdf
oa: '1'
publication: arXiv:2402.02494
status: public
title: 'Extended Dynamic Mode Decomposition: Sharp bounds on the sample efficiency'
type: preprint
user_id: '47427'
year: '2024'
...
---
_id: '46019'
abstract:
- lang: eng
text: We derive efficient algorithms to compute weakly Pareto optimal solutions
for smooth, convex and unconstrained multiobjective optimization problems in general
Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical
system in the multiobjective setting, which trajectories converge weakly to Pareto
optimal solutions. Discretization of this system yields an inertial multiobjective
algorithm which generates sequences that converge weakly to Pareto optimal solutions.
We employ Nesterov acceleration to define an algorithm with an improved convergence
rate compared to the plain multiobjective steepest descent method (Algorithm 1).
A further improvement in terms of efficiency is achieved by avoiding the solution
of a quadratic subproblem to compute a common step direction for all objective
functions, which is usually required in first-order methods. Using a different
discretization of our inertial gradient-like dynamical system, we obtain an accelerated
multiobjective gradient method that does not require the solution of a subproblem
in each step (Algorithm 2). While this algorithm does not converge in general,
it yields good results on test problems while being faster than standard steepest
descent.
author:
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Sonntag K, Peitz S. Fast Multiobjective Gradient Methods with Nesterov Acceleration
via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications.
Published online 2024. doi:10.1007/s10957-024-02389-3
apa: Sonntag, K., & Peitz, S. (2024). Fast Multiobjective Gradient Methods with
Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization
Theory and Applications. https://doi.org/10.1007/s10957-024-02389-3
bibtex: '@article{Sonntag_Peitz_2024, title={Fast Multiobjective Gradient Methods
with Nesterov Acceleration via Inertial Gradient-Like Systems}, DOI={10.1007/s10957-024-02389-3},
journal={Journal of Optimization Theory and Applications}, publisher={Springer},
author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024} }'
chicago: Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient
Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal
of Optimization Theory and Applications, 2024. https://doi.org/10.1007/s10957-024-02389-3.
ieee: 'K. Sonntag and S. Peitz, “Fast Multiobjective Gradient Methods with Nesterov
Acceleration via Inertial Gradient-Like Systems,” Journal of Optimization Theory
and Applications, 2024, doi: 10.1007/s10957-024-02389-3.'
mla: Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods
with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal of
Optimization Theory and Applications, Springer, 2024, doi:10.1007/s10957-024-02389-3.
short: K. Sonntag, S. Peitz, Journal of Optimization Theory and Applications (2024).
date_created: 2023-07-12T06:35:58Z
date_updated: 2024-02-21T10:13:33Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s10957-024-02389-3
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf
oa: '1'
publication: Journal of Optimization Theory and Applications
publication_status: published
publisher: Springer
status: public
title: Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial
Gradient-Like Systems
type: journal_article
user_id: '56399'
year: '2024'
...
---
_id: '51334'
abstract:
- lang: eng
text: The efficient optimization method for locally Lipschitz continuous multiobjective
optimization problems from [1] is extended from finite-dimensional problems to
general Hilbert spaces. The method iteratively computes Pareto critical points,
where in each iteration, an approximation of the subdifferential is computed in
an efficient manner and then used to compute a common descent direction for all
objective functions. To prove convergence, we present some new optimality results
for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these,
we can show that every accumulation point of the sequence generated by our algorithm
is Pareto critical under common assumptions. Computational efficiency for finding
Pareto critical points is numerically demonstrated for multiobjective optimal
control of an obstacle problem.
author:
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Georg
full_name: Müller, Georg
last_name: Müller
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Stefan
full_name: Volkwein, Stefan
last_name: Volkwein
citation:
ama: Sonntag K, Gebken B, Müller G, Peitz S, Volkwein S. A Descent Method for Nonsmooth
Multiobjective Optimization in Hilbert Spaces. arXiv:240206376. Published
online 2024.
apa: Sonntag, K., Gebken, B., Müller, G., Peitz, S., & Volkwein, S. (2024).
A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.
In arXiv:2402.06376.
bibtex: '@article{Sonntag_Gebken_Müller_Peitz_Volkwein_2024, title={A Descent Method
for Nonsmooth Multiobjective Optimization in Hilbert Spaces}, journal={arXiv:2402.06376},
author={Sonntag, Konstantin and Gebken, Bennet and Müller, Georg and Peitz, Sebastian
and Volkwein, Stefan}, year={2024} }'
chicago: Sonntag, Konstantin, Bennet Gebken, Georg Müller, Sebastian Peitz, and
Stefan Volkwein. “A Descent Method for Nonsmooth Multiobjective Optimization in
Hilbert Spaces.” ArXiv:2402.06376, 2024.
ieee: K. Sonntag, B. Gebken, G. Müller, S. Peitz, and S. Volkwein, “A Descent Method
for Nonsmooth Multiobjective Optimization in Hilbert Spaces,” arXiv:2402.06376.
2024.
mla: Sonntag, Konstantin, et al. “A Descent Method for Nonsmooth Multiobjective
Optimization in Hilbert Spaces.” ArXiv:2402.06376, 2024.
short: K. Sonntag, B. Gebken, G. Müller, S. Peitz, S. Volkwein, ArXiv:2402.06376
(2024).
date_created: 2024-02-13T09:35:26Z
date_updated: 2024-02-21T10:21:03Z
department:
- _id: '101'
- _id: '655'
external_id:
arxiv:
- "\t2402.06376"
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2402.06376
oa: '1'
publication: arXiv:2402.06376
status: public
title: A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces
type: preprint
user_id: '56399'
year: '2024'
...
---
_id: '40171'
abstract:
- lang: eng
text: We present a convolutional framework which significantly reduces the complexity
and thus, the computational effort for distributed reinforcement learning control
of dynamical systems governed by partial differential equations (PDEs). Exploiting
translational equivariances, the high-dimensional distributed control problem
can be transformed into a multi-agent control problem with many identical, uncoupled
agents. Furthermore, using the fact that information is transported with finite
velocity in many cases, the dimension of the agents’ environment can be drastically
reduced using a convolution operation over the state space of the PDE, by which
we effectively tackle the curse of dimensionality otherwise present in deep reinforcement
learning. In this setting, the complexity can be flexibly adjusted via the kernel
width or by using a stride greater than one (meaning that we do not place an actuator
at each sensor location). Moreover, scaling from smaller to larger domains – or
the transfer between different domains – becomes a straightforward task requiring
little effort. We demonstrate the performance of the proposed framework using
several PDE examples with increasing complexity, where stabilization is achieved
by training a low-dimensional deep deterministic policy gradient agent using minimal
computing resources.
article_type: original
author:
- 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: Vikas
full_name: Chidananda, Vikas
last_name: Chidananda
- first_name: Oliver
full_name: Wallscheid, Oliver
id: '11291'
last_name: Wallscheid
orcid: https://orcid.org/0000-0001-9362-8777
- first_name: Steven L.
full_name: Brunton, Steven L.
last_name: Brunton
- first_name: Kunihiko
full_name: Taira, Kunihiko
last_name: Taira
citation:
ama: 'Peitz S, Stenner J, Chidananda V, Wallscheid O, Brunton SL, Taira K. Distributed
Control of Partial Differential Equations Using Convolutional Reinforcement Learning.
Physica D: Nonlinear Phenomena. 2024;461:134096. doi:10.1016/j.physd.2024.134096'
apa: 'Peitz, S., Stenner, J., Chidananda, V., Wallscheid, O., Brunton, S. L., &
Taira, K. (2024). Distributed Control of Partial Differential Equations Using
Convolutional Reinforcement Learning. Physica D: Nonlinear Phenomena, 461,
134096. https://doi.org/10.1016/j.physd.2024.134096'
bibtex: '@article{Peitz_Stenner_Chidananda_Wallscheid_Brunton_Taira_2024, title={Distributed
Control of Partial Differential Equations Using Convolutional Reinforcement Learning},
volume={461}, DOI={10.1016/j.physd.2024.134096},
journal={Physica D: Nonlinear Phenomena}, publisher={Elsevier}, author={Peitz,
Sebastian and Stenner, Jan and Chidananda, Vikas and Wallscheid, Oliver and Brunton,
Steven L. and Taira, Kunihiko}, year={2024}, pages={134096} }'
chicago: 'Peitz, Sebastian, Jan Stenner, Vikas Chidananda, Oliver Wallscheid, Steven
L. Brunton, and Kunihiko Taira. “Distributed Control of Partial Differential Equations
Using Convolutional Reinforcement Learning.” Physica D: Nonlinear Phenomena
461 (2024): 134096. https://doi.org/10.1016/j.physd.2024.134096.'
ieee: 'S. Peitz, J. Stenner, V. Chidananda, O. Wallscheid, S. L. Brunton, and K.
Taira, “Distributed Control of Partial Differential Equations Using Convolutional
Reinforcement Learning,” Physica D: Nonlinear Phenomena, vol. 461, p. 134096,
2024, doi: 10.1016/j.physd.2024.134096.'
mla: 'Peitz, Sebastian, et al. “Distributed Control of Partial Differential Equations
Using Convolutional Reinforcement Learning.” Physica D: Nonlinear Phenomena,
vol. 461, Elsevier, 2024, p. 134096, doi:10.1016/j.physd.2024.134096.'
short: 'S. Peitz, J. Stenner, V. Chidananda, O. Wallscheid, S.L. Brunton, K. Taira,
Physica D: Nonlinear Phenomena 461 (2024) 134096.'
date_created: 2023-01-26T07:56:26Z
date_updated: 2024-02-23T10:53:42Z
department:
- _id: '655'
doi: 10.1016/j.physd.2024.134096
intvolume: ' 461'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1016/j.physd.2024.134096
oa: '1'
page: '134096'
publication: 'Physica D: Nonlinear Phenomena'
publisher: Elsevier
status: public
title: Distributed Control of Partial Differential Equations Using Convolutional
Reinforcement Learning
type: journal_article
user_id: '47427'
volume: 461
year: '2024'
...
---
_id: '33461'
abstract:
- lang: eng
text: Data-driven models for nonlinear dynamical systems based on approximating
the underlying Koopman operator or generator have proven to be successful tools
for forecasting, feature learning, state estimation, and control. It has become
well known that the Koopman generators for control-affine systems also have affine
dependence on the input, leading to convenient finite-dimensional bilinear approximations
of the dynamics. Yet there are still two main obstacles that limit the scope of
current approaches for approximating the Koopman generators of systems with actuation.
First, the performance of existing methods depends heavily on the choice of basis
functions over which the Koopman generator is to be approximated; and there is
currently no universal way to choose them for systems that are not measure preserving.
Secondly, if we do not observe the full state, we may not gain access to a sufficiently
rich collection of such functions to describe the dynamics. This is because the
commonly used method of forming time-delayed observables fails when there is actuation.
To remedy these issues, we write the dynamics of observables governed by the Koopman
generator as a bilinear hidden Markov model, and determine the model parameters
using the expectation-maximization (EM) algorithm. The E-step involves a standard
Kalman filter and smoother, while the M-step resembles control-affine dynamic
mode decomposition for the generator. We demonstrate the performance of this method
on three examples, including recovery of a finite-dimensional Koopman-invariant
subspace for an actuated system with a slow manifold; estimation of Koopman eigenfunctions
for the unforced Duffing equation; and model-predictive control of a fluidic pinball
system based only on noisy observations of lift and drag.
author:
- first_name: Samuel E.
full_name: Otto, Samuel E.
last_name: Otto
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Clarence W.
full_name: Rowley, Clarence W.
last_name: Rowley
citation:
ama: Otto SE, Peitz S, Rowley CW. Learning Bilinear Models of Actuated Koopman Generators
from Partially-Observed Trajectories. SIAM Journal on Applied Dynamical Systems.
2024;23(1):885-923. doi:10.1137/22M1523601
apa: Otto, S. E., Peitz, S., & Rowley, C. W. (2024). Learning Bilinear Models
of Actuated Koopman Generators from Partially-Observed Trajectories. SIAM
Journal on Applied Dynamical Systems, 23(1), 885–923. https://doi.org/10.1137/22M1523601
bibtex: '@article{Otto_Peitz_Rowley_2024, title={Learning Bilinear Models of Actuated
Koopman Generators from Partially-Observed Trajectories}, volume={23}, DOI={10.1137/22M1523601}, number={1},
journal={SIAM Journal on Applied Dynamical Systems}, publisher={SIAM}, author={Otto,
Samuel E. and Peitz, Sebastian and Rowley, Clarence W.}, year={2024}, pages={885–923}
}'
chicago: 'Otto, Samuel E., Sebastian Peitz, and Clarence W. Rowley. “Learning Bilinear
Models of Actuated Koopman Generators from Partially-Observed Trajectories.”
SIAM Journal on Applied Dynamical Systems 23, no. 1 (2024): 885–923. https://doi.org/10.1137/22M1523601.'
ieee: 'S. E. Otto, S. Peitz, and C. W. Rowley, “Learning Bilinear Models of Actuated
Koopman Generators from Partially-Observed Trajectories,” SIAM Journal on
Applied Dynamical Systems, vol. 23, no. 1, pp. 885–923, 2024, doi: 10.1137/22M1523601.'
mla: Otto, Samuel E., et al. “Learning Bilinear Models of Actuated Koopman Generators
from Partially-Observed Trajectories.” SIAM Journal on Applied Dynamical Systems,
vol. 23, no. 1, SIAM, 2024, pp. 885–923, doi:10.1137/22M1523601.
short: S.E. Otto, S. Peitz, C.W. Rowley, SIAM Journal on Applied Dynamical Systems
23 (2024) 885–923.
date_created: 2022-09-22T07:21:40Z
date_updated: 2024-03-18T10:40:08Z
department:
- _id: '655'
doi: 10.1137/22M1523601
external_id:
arxiv:
- '2209.09977'
intvolume: ' 23'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2209.09977.pdf
oa: '1'
page: 885-923
project:
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: SIAM Journal on Applied Dynamical Systems
publication_status: published
publisher: SIAM
status: public
title: Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed
Trajectories
type: journal_article
user_id: '47427'
volume: 23
year: '2024'
...
---
_id: '38031'
abstract:
- lang: eng
text: "We consider the data-driven approximation of the Koopman operator for\r\nstochastic
differential equations on reproducing kernel Hilbert spaces (RKHS).\r\nOur focus
is on the estimation error if the data are collected from long-term\r\nergodic
simulations. We derive both an exact expression for the variance of the\r\nkernel
cross-covariance operator, measured in the Hilbert-Schmidt norm, and\r\nprobabilistic
bounds for the finite-data estimation error. Moreover, we derive\r\na bound on
the prediction error of observables in the RKHS using a finite\r\nMercer series
expansion. Further, assuming Koopman-invariance of the RKHS, we\r\nprovide bounds
on the full approximation error. Numerical experiments using the\r\nOrnstein-Uhlenbeck
process illustrate our results."
article_number: '101657'
author:
- 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
- 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
citation:
ama: Philipp F, Schaller M, Worthmann K, Peitz S, Nüske F. Error bounds for kernel-based
approximations of the Koopman operator. Applied and Computational Harmonic
Analysis . 2024;71. doi:10.1016/j.acha.2024.101657
apa: Philipp, F., Schaller, M., Worthmann, K., Peitz, S., & Nüske, F. (2024).
Error bounds for kernel-based approximations of the Koopman operator. Applied
and Computational Harmonic Analysis , 71, Article 101657. https://doi.org/10.1016/j.acha.2024.101657
bibtex: '@article{Philipp_Schaller_Worthmann_Peitz_Nüske_2024, title={Error bounds
for kernel-based approximations of the Koopman operator}, volume={71}, DOI={10.1016/j.acha.2024.101657},
number={101657}, journal={Applied and Computational Harmonic Analysis }, publisher={Springer
}, author={Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl and Peitz,
Sebastian and Nüske, Feliks}, year={2024} }'
chicago: Philipp, Friedrich, Manuel Schaller, Karl Worthmann, Sebastian Peitz, and
Feliks Nüske. “Error Bounds for Kernel-Based Approximations of the Koopman Operator.”
Applied and Computational Harmonic Analysis 71 (2024). https://doi.org/10.1016/j.acha.2024.101657.
ieee: 'F. Philipp, M. Schaller, K. Worthmann, S. Peitz, and F. Nüske, “Error bounds
for kernel-based approximations of the Koopman operator,” Applied and Computational
Harmonic Analysis , vol. 71, Art. no. 101657, 2024, doi: 10.1016/j.acha.2024.101657.'
mla: Philipp, Friedrich, et al. “Error Bounds for Kernel-Based Approximations of
the Koopman Operator.” Applied and Computational Harmonic Analysis , vol.
71, 101657, Springer , 2024, doi:10.1016/j.acha.2024.101657.
short: F. Philipp, M. Schaller, K. Worthmann, S. Peitz, F. Nüske, Applied and Computational
Harmonic Analysis 71 (2024).
date_created: 2023-01-23T07:03:39Z
date_updated: 2024-04-11T12:41:13Z
department:
- _id: '655'
doi: 10.1016/j.acha.2024.101657
external_id:
arxiv:
- '2301.08637'
intvolume: ' 71'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2301.08637
oa: '1'
publication: 'Applied and Computational Harmonic Analysis '
publication_status: published
publisher: 'Springer '
status: public
title: Error bounds for kernel-based approximations of the Koopman operator
type: journal_article
user_id: '47427'
volume: 71
year: '2024'
...
---
_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. Predicting PDEs Fast and Efficiently with Equivariant Extreme
Learning Machines.
apa: Harder, H., & Peitz, S. (n.d.). Predicting PDEs Fast and Efficiently
with Equivariant Extreme Learning Machines.
bibtex: '@article{Harder_Peitz, title={Predicting PDEs Fast and Efficiently with
Equivariant Extreme Learning Machines}, author={Harder, Hans and Peitz, Sebastian}
}'
chicago: Harder, Hans, and Sebastian Peitz. “Predicting PDEs Fast and Efficiently
with Equivariant Extreme Learning Machines,” n.d.
ieee: H. Harder and S. Peitz, “Predicting PDEs Fast and Efficiently with Equivariant
Extreme Learning Machines.” .
mla: Harder, Hans, and Sebastian Peitz. Predicting PDEs Fast and Efficiently
with Equivariant Extreme Learning Machines.
short: H. Harder, S. Peitz, (n.d.).
date_created: 2024-04-30T08:43:14Z
date_updated: 2024-04-30T08:45:24Z
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'
publication_status: unpublished
status: public
title: Predicting PDEs Fast and Efficiently with Equivariant Extreme Learning Machines
type: preprint
user_id: '98879'
year: '2024'
...
---
_id: '52758'
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. On the continuity and smoothness of the value function in
reinforcement learning and optimal control. Published online 2024.
apa: Harder, H., & Peitz, S. (2024). On the continuity and smoothness of
the value function in reinforcement learning and optimal control.
bibtex: '@article{Harder_Peitz_2024, title={On the continuity and smoothness of
the value function in reinforcement learning and optimal control}, author={Harder,
Hans and Peitz, Sebastian}, year={2024} }'
chicago: Harder, Hans, and Sebastian Peitz. “On the Continuity and Smoothness of
the Value Function in Reinforcement Learning and Optimal Control,” 2024.
ieee: H. Harder and S. Peitz, “On the continuity and smoothness of the value function
in reinforcement learning and optimal control.” 2024.
mla: Harder, Hans, and Sebastian Peitz. On the Continuity and Smoothness of the
Value Function in Reinforcement Learning and Optimal Control. 2024.
short: H. Harder, S. Peitz, (2024).
date_created: 2024-03-25T08:20:37Z
date_updated: 2024-04-30T08:45:54Z
language:
- iso: eng
status: public
title: On the continuity and smoothness of the value function in reinforcement learning
and optimal control
type: preprint
user_id: '98879'
year: '2024'
...
---
_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. arXiv. Published online
2024.
apa: Akhter, J., Fährmann, P. D., Sonntag, K., & Peitz, S. (2024). Common pitfalls
to avoid while using multiobjective optimization in machine learning. In arXiv.
bibtex: '@article{Akhter_Fährmann_Sonntag_Peitz_2024, title={Common pitfalls to
avoid while using multiobjective optimization in machine learning}, journal={arXiv},
author={Akhter, Junaid and Fährmann, Paul David and Sonntag, Konstantin and Peitz,
Sebastian}, year={2024} }'
chicago: Akhter, Junaid, Paul David Fährmann, Konstantin Sonntag, and Sebastian
Peitz. “Common Pitfalls to Avoid While Using Multiobjective Optimization in Machine
Learning.” ArXiv, 2024.
ieee: J. Akhter, P. D. Fährmann, K. Sonntag, and S. Peitz, “Common pitfalls to avoid
while using multiobjective optimization in machine learning,” arXiv. 2024.
mla: Akhter, Junaid, et al. “Common Pitfalls to Avoid While Using Multiobjective
Optimization in Machine Learning.” ArXiv, 2024.
short: J. Akhter, P.D. Fährmann, K. Sonntag, S. Peitz, ArXiv (2024).
date_created: 2024-05-03T13:38:34Z
date_updated: 2024-05-06T08:29:38Z
department:
- _id: '655'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2405.01480
oa: '1'
publication: arXiv
status: public
title: Common pitfalls to avoid while using multiobjective optimization in machine
learning
type: preprint
user_id: '47427'
year: '2024'
...
---
_id: '32447'
abstract:
- lang: eng
text: 'We present a new gradient-like dynamical system related to unconstrained
convex smooth multiobjective optimization which involves inertial effects and
asymptotic vanishing damping. To the best of our knowledge, this system is the
first inertial gradient-like system for multiobjective optimization problems including
asymptotic vanishing damping, expanding the ideas previously laid out in [H. Attouch
and G. Garrigos, Multiobjective Optimization: An Inertial Dynamical Approach to
Pareto Optima, preprint, arXiv:1506.02823, 2015]. We prove existence of solutions
to this system in finite dimensions and further prove that its bounded solutions
converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence
rate of order \(\mathcal{O}(t^{-2})\) for the function values measured with a
merit function. This approach presents a good basis for the development of fast
gradient methods for multiobjective optimization.'
article_type: original
author:
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Sonntag K, Peitz S. Fast Convergence of Inertial Multiobjective Gradient-Like
Systems with Asymptotic Vanishing Damping. SIAM Journal on Optimization.
2024;34(3):2259-2286. doi:10.1137/23M1588512
apa: Sonntag, K., & Peitz, S. (2024). Fast Convergence of Inertial Multiobjective
Gradient-Like Systems with Asymptotic Vanishing Damping. SIAM Journal on Optimization,
34(3), 2259–2286. https://doi.org/10.1137/23M1588512
bibtex: '@article{Sonntag_Peitz_2024, title={Fast Convergence of Inertial Multiobjective
Gradient-Like Systems with Asymptotic Vanishing Damping}, volume={34}, DOI={10.1137/23M1588512}, number={3},
journal={SIAM Journal on Optimization}, publisher={Society for Industrial and
Applied Mathematics}, author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024},
pages={2259–2286} }'
chicago: 'Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial
Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping.” SIAM
Journal on Optimization 34, no. 3 (2024): 2259–86. https://doi.org/10.1137/23M1588512.'
ieee: 'K. Sonntag and S. Peitz, “Fast Convergence of Inertial Multiobjective Gradient-Like
Systems with Asymptotic Vanishing Damping,” SIAM Journal on Optimization,
vol. 34, no. 3, pp. 2259–2286, 2024, doi: 10.1137/23M1588512.'
mla: Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial Multiobjective
Gradient-Like Systems with Asymptotic Vanishing Damping.” SIAM Journal on Optimization,
vol. 34, no. 3, Society for Industrial and Applied Mathematics, 2024, pp. 2259–86,
doi:10.1137/23M1588512.
short: K. Sonntag, S. Peitz, SIAM Journal on Optimization 34 (2024) 2259–2286.
date_created: 2022-07-28T11:53:02Z
date_updated: 2024-07-02T09:27:39Z
department:
- _id: '101'
- _id: '655'
doi: 10.1137/23M1588512
intvolume: ' 34'
issue: '3'
keyword:
- multiobjective optimization
- Pareto optimization
- Lyapunov analysis
- gradient-likedynamical systems
- inertial dynamics
- asymptotic vanishing damping
- fast convergence
language:
- iso: eng
page: 2259 - 2286
publication: SIAM Journal on Optimization
publication_identifier:
issn:
- 1095-7189
publication_status: published
publisher: Society for Industrial and Applied Mathematics
status: public
title: Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic
Vanishing Damping
type: journal_article
user_id: '56399'
volume: 34
year: '2024'
...
---
_id: '46649'
abstract:
- lang: eng
text: "Different conflicting optimization criteria arise naturally in various Deep\r\nLearning
scenarios. These can address different main tasks (i.e., in the\r\nsetting of
Multi-Task Learning), but also main and secondary tasks such as loss\r\nminimization
versus sparsity. The usual approach is a simple weighting of the\r\ncriteria,
which formally only works in the convex setting. In this paper, we\r\npresent
a Multi-Objective Optimization algorithm using a modified Weighted\r\nChebyshev
scalarization for training Deep Neural Networks (DNNs) with respect\r\nto several
tasks. By employing this scalarization technique, the algorithm can\r\nidentify
all optimal solutions of the original problem while reducing its\r\ncomplexity
to a sequence of single-objective problems. The simplified problems\r\nare then
solved using an Augmented Lagrangian method, enabling the use of\r\npopular optimization
techniques such as Adam and Stochastic Gradient Descent,\r\nwhile efficaciously
handling constraints. Our work aims to address the\r\n(economical and also ecological)
sustainability issue of DNN models, with a\r\nparticular focus on Deep Multi-Task
models, which are typically designed with a\r\nvery large number of weights to
perform equally well on multiple tasks. Through\r\nexperiments conducted on two
Machine Learning datasets, we demonstrate the\r\npossibility of adaptively sparsifying
the model during training without\r\nsignificantly impacting its performance,
if we are willing to apply\r\ntask-specific adaptations to the network weights.
Code is available at\r\nhttps://github.com/salomonhotegni/MDMTN."
author:
- first_name: Sedjro Salomon
full_name: Hotegni, Sedjro Salomon
id: '97995'
last_name: Hotegni
- 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: 'Hotegni SS, Berkemeier MB, Peitz S. Multi-Objective Optimization for Sparse
Deep Multi-Task Learning. In: 2024 International Joint Conference on Neural
Networks (IJCNN). IEEE; 2024:9. doi:10.1109/IJCNN60899.2024.10650994'
apa: Hotegni, S. S., Berkemeier, M. B., & Peitz, S. (2024). Multi-Objective
Optimization for Sparse Deep Multi-Task Learning. 2024 International Joint
Conference on Neural Networks (IJCNN), 9. https://doi.org/10.1109/IJCNN60899.2024.10650994
bibtex: '@inproceedings{Hotegni_Berkemeier_Peitz_2024, place={Yokohama, Japan},
title={Multi-Objective Optimization for Sparse Deep Multi-Task Learning}, DOI={10.1109/IJCNN60899.2024.10650994},
booktitle={2024 International Joint Conference on Neural Networks (IJCNN)}, publisher={IEEE},
author={Hotegni, Sedjro Salomon and Berkemeier, Manuel Bastian and Peitz, Sebastian},
year={2024}, pages={9} }'
chicago: 'Hotegni, Sedjro Salomon, Manuel Bastian Berkemeier, and Sebastian Peitz.
“Multi-Objective Optimization for Sparse Deep Multi-Task Learning.” In 2024
International Joint Conference on Neural Networks (IJCNN), 9. Yokohama, Japan:
IEEE, 2024. https://doi.org/10.1109/IJCNN60899.2024.10650994.'
ieee: 'S. S. Hotegni, M. B. Berkemeier, and S. Peitz, “Multi-Objective Optimization
for Sparse Deep Multi-Task Learning,” in 2024 International Joint Conference
on Neural Networks (IJCNN), Yokohama, Japan, 2024, p. 9, doi: 10.1109/IJCNN60899.2024.10650994.'
mla: Hotegni, Sedjro Salomon, et al. “Multi-Objective Optimization for Sparse Deep
Multi-Task Learning.” 2024 International Joint Conference on Neural Networks
(IJCNN), IEEE, 2024, p. 9, doi:10.1109/IJCNN60899.2024.10650994.
short: 'S.S. Hotegni, M.B. Berkemeier, S. Peitz, in: 2024 International Joint Conference
on Neural Networks (IJCNN), IEEE, Yokohama, Japan, 2024, p. 9.'
conference:
end_date: 2024-07-05
location: Yokohama, Japan
name: 2024 International Joint Conference on Neural Networks (IJCNN)
start_date: 2024-06-30
date_created: 2023-08-24T07:44:36Z
date_updated: 2024-09-27T10:24:22Z
department:
- _id: '655'
doi: 10.1109/IJCNN60899.2024.10650994
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://ieeexplore.ieee.org/document/10650994
oa: '1'
page: '9'
place: Yokohama, Japan
publication: 2024 International Joint Conference on Neural Networks (IJCNN)
publication_identifier:
eisbn:
- 979-8-3503-5931-2
eissn:
- ' 2161-4407'
publication_status: published
publisher: IEEE
status: public
title: Multi-Objective Optimization for Sparse Deep Multi-Task Learning
type: conference
user_id: '97995'
year: '2024'
...
---
_id: '21199'
abstract:
- lang: eng
text: "As in almost every other branch of science, the major advances in data\r\nscience
and machine learning have also resulted in significant improvements\r\nregarding
the modeling and simulation of nonlinear dynamical systems. It is\r\nnowadays
possible to make accurate medium to long-term predictions of highly\r\ncomplex
systems such as the weather, the dynamics within a nuclear fusion\r\nreactor,
of disease models or the stock market in a very efficient manner. In\r\nmany cases,
predictive methods are advertised to ultimately be useful for\r\ncontrol, as the
control of high-dimensional nonlinear systems is an engineering\r\ngrand challenge
with huge potential in areas such as clean and efficient energy\r\nproduction,
or the development of advanced medical devices. However, the\r\nquestion of how
to use a predictive model for control is often left unanswered\r\ndue to the associated
challenges, namely a significantly higher system\r\ncomplexity, the requirement
of much larger data sets and an increased and often\r\nproblem-specific modeling
effort. To solve these issues, we present a universal\r\nframework (which we call
QuaSiModO:\r\nQuantization-Simulation-Modeling-Optimization) to transform arbitrary\r\npredictive
models into control systems and use them for feedback control. The\r\nadvantages
of our approach are a linear increase in data requirements with\r\nrespect to
the control dimension, performance guarantees that rely exclusively\r\non the
accuracy of the predictive model, and only little prior knowledge\r\nrequirements
in control theory to solve complex control problems. In particular\r\nthe latter
point is of key importance to enable a large number of researchers\r\nand practitioners
to exploit the ever increasing capabilities of predictive\r\nmodels for control
in a straight-forward and systematic fashion."
article_number: '110840'
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Katharina
full_name: Bieker, Katharina
id: '32829'
last_name: Bieker
citation:
ama: Peitz S, Bieker K. On the Universal Transformation of Data-Driven Models to
Control Systems. Automatica. 2023;149. doi:10.1016/j.automatica.2022.110840
apa: Peitz, S., & Bieker, K. (2023). On the Universal Transformation of Data-Driven
Models to Control Systems. Automatica, 149, Article 110840. https://doi.org/10.1016/j.automatica.2022.110840
bibtex: '@article{Peitz_Bieker_2023, title={On the Universal Transformation of Data-Driven
Models to Control Systems}, volume={149}, DOI={10.1016/j.automatica.2022.110840},
number={110840}, journal={Automatica}, publisher={Elsevier}, author={Peitz, Sebastian
and Bieker, Katharina}, year={2023} }'
chicago: Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation
of Data-Driven Models to Control Systems.” Automatica 149 (2023). https://doi.org/10.1016/j.automatica.2022.110840.
ieee: 'S. Peitz and K. Bieker, “On the Universal Transformation of Data-Driven Models
to Control Systems,” Automatica, vol. 149, Art. no. 110840, 2023, doi:
10.1016/j.automatica.2022.110840.'
mla: Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of
Data-Driven Models to Control Systems.” Automatica, vol. 149, 110840, Elsevier,
2023, doi:10.1016/j.automatica.2022.110840.
short: S. Peitz, K. Bieker, Automatica 149 (2023).
date_created: 2021-02-10T07:04:15Z
date_updated: 2023-01-07T12:01:58Z
department:
- _id: '101'
- _id: '655'
doi: 10.1016/j.automatica.2022.110840
intvolume: ' 149'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/S0005109822007075/pdfft?isDTMRedir=true&download=true
oa: '1'
project:
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Automatica
publication_status: published
publisher: Elsevier
status: public
title: On the Universal Transformation of Data-Driven Models to Control Systems
type: journal_article
user_id: '47427'
volume: 149
year: '2023'
...
---
_id: '48502'
abstract:
- lang: eng
text: The prediction of photon echoes is an important technique for gaining an understanding
of optical quantum systems. However, this requires a large number of simulations
with varying parameters and/or input pulses, which renders numerical studies expensive.
This article investigates how we can use data-driven surrogate models based on
the Koopman operator to accelerate this process. In order to be successful, we
require a model that is accurate over a large number of time steps. To this end,
we employ a bilinear Koopman model using extended dynamic mode decomposition and
simulate the optical Bloch equations for an ensemble of inhomogeneously broadened
two-level systems. Such systems are well suited to describe the excitation of
excitonic resonances in semiconductor nanostructures, for example, ensembles of
semiconductor quantum dots. We perform a detailed study on the required number
of system simulations such that the resulting data-driven Koopman model is sufficiently
accurate for a wide range of parameter settings. We analyze the L2 error and the
relative error of the photon echo peak and investigate how the control positions
relate to the stabilization. After proper training, the dynamics of the quantum
ensemble can be predicted accurately and numerically very efficiently by our methods.
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Anna
full_name: Hunstig, Anna
last_name: Hunstig
- first_name: Hendrik
full_name: Rose, Hendrik
id: '55958'
last_name: Rose
orcid: 0000-0002-3079-5428
- first_name: Torsten
full_name: Meier, Torsten
id: '344'
last_name: Meier
orcid: 0000-0001-8864-2072
citation:
ama: Peitz S, Hunstig A, Rose H, Meier T. Accelerating the analysis of optical quantum
systems using the Koopman operator. Published online 2023.
apa: Peitz, S., Hunstig, A., Rose, H., & Meier, T. (2023). Accelerating the
analysis of optical quantum systems using the Koopman operator.
bibtex: '@article{Peitz_Hunstig_Rose_Meier_2023, title={Accelerating the analysis
of optical quantum systems using the Koopman operator}, author={Peitz, Sebastian
and Hunstig, Anna and Rose, Hendrik and Meier, Torsten}, year={2023} }'
chicago: Peitz, Sebastian, Anna Hunstig, Hendrik Rose, and Torsten Meier. “Accelerating
the Analysis of Optical Quantum Systems Using the Koopman Operator,” 2023.
ieee: S. Peitz, A. Hunstig, H. Rose, and T. Meier, “Accelerating the analysis of
optical quantum systems using the Koopman operator.” 2023.
mla: Peitz, Sebastian, et al. Accelerating the Analysis of Optical Quantum Systems
Using the Koopman Operator. 2023.
short: S. Peitz, A. Hunstig, H. Rose, T. Meier, (2023).
date_created: 2023-10-27T09:40:59Z
date_updated: 2023-10-27T10:05:07Z
department:
- _id: '655'
- _id: '623'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2310.16578.pdf
oa: '1'
status: public
title: Accelerating the analysis of optical quantum systems using the Koopman operator
type: preprint
user_id: '47427'
year: '2023'
...
---
_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.
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
- 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. arXiv. Published online
2023.
apa: Amakor, A. C., Sonntag, K., & Peitz, S. (2023). A multiobjective continuation
method to compute the regularization path of deep neural networks. In arXiv.
bibtex: '@article{Amakor_Sonntag_Peitz_2023, title={A multiobjective continuation
method to compute the regularization path of deep neural networks}, journal={arXiv},
author={Amakor, Augustina Chidinma and Sonntag, Konstantin and Peitz, Sebastian},
year={2023} }'
chicago: Amakor, Augustina Chidinma, Konstantin Sonntag, and Sebastian Peitz. “A
Multiobjective Continuation Method to Compute the Regularization Path of Deep
Neural Networks.” ArXiv, 2023.
ieee: A. C. Amakor, K. Sonntag, and S. Peitz, “A multiobjective continuation method
to compute the regularization path of deep neural networks,” arXiv. 2023.
mla: Amakor, Augustina Chidinma, et al. “A Multiobjective Continuation Method to
Compute the Regularization Path of Deep Neural Networks.” ArXiv, 2023.
short: A.C. Amakor, K. Sonntag, S. Peitz, ArXiv (2023).
date_created: 2024-02-06T08:51:00Z
date_updated: 2024-02-06T08:52:07Z
department:
- _id: '655'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2308.12044.pdf
oa: '1'
publication: arXiv
status: public
title: A multiobjective continuation method to compute the regularization path of
deep neural networks
type: preprint
user_id: '47427'
year: '2023'
...
---
_id: '51158'
abstract:
- lang: eng
text: "Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method
to\r\napproximate the Koopman operator for deterministic and stochastic (control)\r\nsystems.
This operator is linear and encompasses full information on the\r\n(expected stochastic)
dynamics. In this paper, we analyze a kernel-based EDMD\r\nalgorithm, known as
kEDMD, where the dictionary consists of the canonical\r\nkernel features at the
data points. The latter are acquired by i.i.d. samples\r\nfrom a user-defined
and application-driven distribution on a compact set. We\r\nprove bounds on the
prediction error of the kEDMD estimator when sampling from\r\nthis (not necessarily
ergodic) distribution. The error analysis is further\r\nextended to control-affine
systems, where the considered invariance of the\r\nReproducing Kernel Hilbert
Space is significantly less restrictive in\r\ncomparison to invariance assumptions
on an a-priori chosen dictionary."
author:
- 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
- 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
citation:
ama: Philipp F, Schaller M, Worthmann K, Peitz S, Nüske F. Error analysis of kernel
EDMD for prediction and control in the Koopman framework. arXiv:231210460.
Published online 2023.
apa: Philipp, F., Schaller, M., Worthmann, K., Peitz, S., & Nüske, F. (2023).
Error analysis of kernel EDMD for prediction and control in the Koopman framework.
In arXiv:2312.10460.
bibtex: '@article{Philipp_Schaller_Worthmann_Peitz_Nüske_2023, title={Error analysis
of kernel EDMD for prediction and control in the Koopman framework}, journal={arXiv:2312.10460},
author={Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl and Peitz,
Sebastian and Nüske, Feliks}, year={2023} }'
chicago: Philipp, Friedrich, Manuel Schaller, Karl Worthmann, Sebastian Peitz, and
Feliks Nüske. “Error Analysis of Kernel EDMD for Prediction and Control in the
Koopman Framework.” ArXiv:2312.10460, 2023.
ieee: F. Philipp, M. Schaller, K. Worthmann, S. Peitz, and F. Nüske, “Error analysis
of kernel EDMD for prediction and control in the Koopman framework,” arXiv:2312.10460.
2023.
mla: Philipp, Friedrich, et al. “Error Analysis of Kernel EDMD for Prediction and
Control in the Koopman Framework.” ArXiv:2312.10460, 2023.
short: F. Philipp, M. Schaller, K. Worthmann, S. Peitz, F. Nüske, ArXiv:2312.10460
(2023).
date_created: 2024-02-06T08:49:50Z
date_updated: 2024-02-06T08:50:32Z
department:
- _id: '655'
external_id:
arxiv:
- '2312.10460'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2312.10460.pdf
oa: '1'
publication: arXiv:2312.10460
status: public
title: Error analysis of kernel EDMD for prediction and control in the Koopman framework
type: preprint
user_id: '47427'
year: '2023'
...
---
_id: '46578'
abstract:
- lang: eng
text: 'Multiobjective optimization plays an increasingly important role in modern
applications, where several criteria are often of equal importance. The task in
multiobjective optimization and multiobjective optimal control is therefore to
compute the set of optimal compromises (the Pareto set) between the conflicting
objectives. The advances in algorithms and the increasing interest in Pareto-optimal
solutions have led to a wide range of new applications related to optimal and
feedback control - potentially with non-smoothness both on the level of the objectives
or in the system dynamics. This results in new challenges such as dealing with
expensive models (e.g., governed by partial differential equations (PDEs)) and
developing dedicated algorithms handling the non-smoothness. Since in contrast
to single-objective optimization, the Pareto set generally consists of an infinite
number of solutions, the computational effort can quickly become challenging,
which is particularly problematic when the objectives are costly to evaluate or
when a solution has to be presented very quickly. This article gives an overview
of recent developments in the field of multiobjective optimization of non-smooth
PDE-constrained problems. In particular we report on the advances achieved within
Project 2 "Multiobjective Optimization of Non-Smooth PDE-Constrained Problems
- Switches, State Constraints and Model Order Reduction" of the DFG Priority Programm
1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation
and Hierarchical Optimization".'
author:
- first_name: Marco
full_name: Bernreuther, Marco
last_name: Bernreuther
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Georg
full_name: Müller, Georg
last_name: Müller
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Stefan
full_name: Volkwein, Stefan
last_name: Volkwein
citation:
ama: Bernreuther M, Dellnitz M, Gebken B, et al. Multiobjective Optimization of
Non-Smooth PDE-Constrained Problems. arXiv:230801113. Published online
2023.
apa: Bernreuther, M., Dellnitz, M., Gebken, B., Müller, G., Peitz, S., Sonntag,
K., & Volkwein, S. (2023). Multiobjective Optimization of Non-Smooth PDE-Constrained
Problems. In arXiv:2308.01113.
bibtex: '@article{Bernreuther_Dellnitz_Gebken_Müller_Peitz_Sonntag_Volkwein_2023,
title={Multiobjective Optimization of Non-Smooth PDE-Constrained Problems}, journal={arXiv:2308.01113},
author={Bernreuther, Marco and Dellnitz, Michael and Gebken, Bennet and Müller,
Georg and Peitz, Sebastian and Sonntag, Konstantin and Volkwein, Stefan}, year={2023}
}'
chicago: Bernreuther, Marco, Michael Dellnitz, Bennet Gebken, Georg Müller, Sebastian
Peitz, Konstantin Sonntag, and Stefan Volkwein. “Multiobjective Optimization of
Non-Smooth PDE-Constrained Problems.” ArXiv:2308.01113, 2023.
ieee: M. Bernreuther et al., “Multiobjective Optimization of Non-Smooth PDE-Constrained
Problems,” arXiv:2308.01113. 2023.
mla: Bernreuther, Marco, et al. “Multiobjective Optimization of Non-Smooth PDE-Constrained
Problems.” ArXiv:2308.01113, 2023.
short: M. Bernreuther, M. Dellnitz, B. Gebken, G. Müller, S. Peitz, K. Sonntag,
S. Volkwein, ArXiv:2308.01113 (2023).
date_created: 2023-08-21T05:50:12Z
date_updated: 2024-02-21T12:22:20Z
department:
- _id: '655'
- _id: '101'
external_id:
arxiv:
- '2308.01113'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2308.01113
oa: '1'
publication: arXiv:2308.01113
status: public
title: Multiobjective Optimization of Non-Smooth PDE-Constrained Problems
type: preprint
user_id: '47427'
year: '2023'
...
---
_id: '54838'
author:
- first_name: Septimus
full_name: Boshoff, Septimus
last_name: Boshoff
- 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: Marvin
full_name: Meyer, Marvin
last_name: Meyer
- first_name: Vikas
full_name: Chidananda, Vikas
last_name: Chidananda
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Oliver
full_name: Wallscheid, Oliver
id: '11291'
last_name: Wallscheid
orcid: https://orcid.org/0000-0001-9362-8777
citation:
ama: 'Boshoff S, Stenner J, Weber D, et al. Hybrid control of interconnected power
converters using both expert-driven droop and data-driven reinforcement learning
approaches. In: IEEE Power and Energy Student Summit (PESS). VDE; 2023:124-129.'
apa: Boshoff, S., Stenner, J., Weber, D., Meyer, M., Chidananda, V., Peitz, S.,
& Wallscheid, O. (2023). Hybrid control of interconnected power converters
using both expert-driven droop and data-driven reinforcement learning approaches.
IEEE Power and Energy Student Summit (PESS), 124–129.
bibtex: '@inproceedings{Boshoff_Stenner_Weber_Meyer_Chidananda_Peitz_Wallscheid_2023,
title={Hybrid control of interconnected power converters using both expert-driven
droop and data-driven reinforcement learning approaches}, booktitle={IEEE Power
and Energy Student Summit (PESS)}, publisher={VDE}, author={Boshoff, Septimus
and Stenner, Jan and Weber, Daniel and Meyer, Marvin and Chidananda, Vikas and
Peitz, Sebastian and Wallscheid, Oliver}, year={2023}, pages={124–129} }'
chicago: Boshoff, Septimus, Jan Stenner, Daniel Weber, Marvin Meyer, Vikas Chidananda,
Sebastian Peitz, and Oliver Wallscheid. “Hybrid Control of Interconnected Power
Converters Using Both Expert-Driven Droop and Data-Driven Reinforcement Learning
Approaches.” In IEEE Power and Energy Student Summit (PESS), 124–29. VDE,
2023.
ieee: S. Boshoff et al., “Hybrid control of interconnected power converters
using both expert-driven droop and data-driven reinforcement learning approaches,”
in IEEE Power and Energy Student Summit (PESS), 2023, pp. 124–129.
mla: Boshoff, Septimus, et al. “Hybrid Control of Interconnected Power Converters
Using Both Expert-Driven Droop and Data-Driven Reinforcement Learning Approaches.”
IEEE Power and Energy Student Summit (PESS), VDE, 2023, pp. 124–29.
short: 'S. Boshoff, J. Stenner, D. Weber, M. Meyer, V. Chidananda, S. Peitz, O.
Wallscheid, in: IEEE Power and Energy Student Summit (PESS), VDE, 2023, pp. 124–129.'
date_created: 2024-06-21T07:12:10Z
date_updated: 2024-06-21T08:28:45Z
department:
- _id: '655'
- _id: '52'
language:
- iso: eng
main_file_link:
- url: https://ieeexplore.ieee.org/document/10564542
page: 124-129
project:
- _id: '286'
grant_number: 01IS20164
name: 'DARE: DARE: Trainings-, Validierungs- und Benchmarkwerkzeuge zur Entwicklung
datengetriebener Betriebs- und Regelungsverfahren für intelligente, lokale Energiesysteme'
publication: IEEE Power and Energy Student Summit (PESS)
publication_identifier:
isbn:
- 978-3-8007-6318-4
publisher: VDE
status: public
title: Hybrid control of interconnected power converters using both expert-driven
droop and data-driven reinforcement learning approaches
type: conference
user_id: '47427'
year: '2023'
...
---
_id: '54839'
author:
- first_name: Marvin
full_name: Meyer, Marvin
last_name: Meyer
- first_name: Daniel
full_name: Weber, Daniel
id: '24041'
last_name: Weber
orcid: 0000-0003-3367-5998
- first_name: Vikas
full_name: Chidananda, Vikas
last_name: Chidananda
- first_name: Oliver
full_name: Schweins, Oliver
last_name: Schweins
- first_name: Jan
full_name: Stenner, Jan
id: '65520'
last_name: Stenner
- 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: Oliver
full_name: Wallscheid, Oliver
id: '11291'
last_name: Wallscheid
orcid: https://orcid.org/0000-0001-9362-8777
citation:
ama: 'Meyer M, Weber D, Chidananda V, et al. ElectricGrid.jl – Automated modeling
of decentralized electrical energy grids. In: IEEE Power and Energy Student
Summit (PESS). VDE; 2023:112-117.'
apa: Meyer, M., Weber, D., Chidananda, V., Schweins, O., Stenner, J., Boshoff, S.,
Peitz, S., & Wallscheid, O. (2023). ElectricGrid.jl – Automated modeling of
decentralized electrical energy grids. IEEE Power and Energy Student Summit
(PESS), 112–117.
bibtex: '@inproceedings{Meyer_Weber_Chidananda_Schweins_Stenner_Boshoff_Peitz_Wallscheid_2023,
title={ElectricGrid.jl – Automated modeling of decentralized electrical energy
grids}, booktitle={IEEE Power and Energy Student Summit (PESS)}, publisher={VDE},
author={Meyer, Marvin and Weber, Daniel and Chidananda, Vikas and Schweins, Oliver
and Stenner, Jan and Boshoff, Septimus and Peitz, Sebastian and Wallscheid, Oliver},
year={2023}, pages={112–117} }'
chicago: Meyer, Marvin, Daniel Weber, Vikas Chidananda, Oliver Schweins, Jan Stenner,
Septimus Boshoff, Sebastian Peitz, and Oliver Wallscheid. “ElectricGrid.Jl – Automated
Modeling of Decentralized Electrical Energy Grids.” In IEEE Power and Energy
Student Summit (PESS), 112–17. VDE, 2023.
ieee: M. Meyer et al., “ElectricGrid.jl – Automated modeling of decentralized
electrical energy grids,” in IEEE Power and Energy Student Summit (PESS),
2023, pp. 112–117.
mla: Meyer, Marvin, et al. “ElectricGrid.Jl – Automated Modeling of Decentralized
Electrical Energy Grids.” IEEE Power and Energy Student Summit (PESS),
VDE, 2023, pp. 112–17.
short: 'M. Meyer, D. Weber, V. Chidananda, O. Schweins, J. Stenner, S. Boshoff,
S. Peitz, O. Wallscheid, in: IEEE Power and Energy Student Summit (PESS), VDE,
2023, pp. 112–117.'
date_created: 2024-06-21T07:13:11Z
date_updated: 2024-06-21T08:28:35Z
department:
- _id: '655'
- _id: '52'
language:
- iso: eng
main_file_link:
- url: https://ieeexplore.ieee.org/document/10564557
page: 112-117
project:
- _id: '286'
grant_number: 01IS20164
name: 'DARE: DARE: Trainings-, Validierungs- und Benchmarkwerkzeuge zur Entwicklung
datengetriebener Betriebs- und Regelungsverfahren für intelligente, lokale Energiesysteme'
publication: IEEE Power and Energy Student Summit (PESS)
publication_identifier:
isbn:
- 978-3-8007-6318-4
publisher: VDE
status: public
title: ElectricGrid.jl – Automated modeling of decentralized electrical energy grids
type: conference
user_id: '47427'
year: '2023'
...
---
_id: '42160'
abstract:
- lang: eng
text: The goal of this paper is to make a strong point for the usage of dynamical
models when using reinforcement learning (RL) for feedback control of dynamical
systems governed by partial differential equations (PDEs). To breach the gap between
the immense promises we see in RL and the applicability in complex engineering
systems, the main challenges are the massive requirements in terms of the training
data, as well as the lack of performance guarantees. We present a solution for
the first issue using a data-driven surrogate model in the form of a convolutional
LSTM with actuation. We demonstrate that learning an actuated model in parallel
to training the RL agent significantly reduces the total amount of required data
sampled from the real system. Furthermore, we show that iteratively updating the
model is of major importance to avoid biases in the RL training. Detailed ablation
studies reveal the most important ingredients of the modeling process. We use
the chaotic Kuramoto-Sivashinsky equation do demonstarte our findings.
author:
- first_name: Stefan
full_name: Werner, Stefan
last_name: Werner
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Werner S, Peitz S. Learning a model is paramount for sample efficiency in reinforcement
learning control of PDEs. arXiv:230207160. Published online 2023.
apa: Werner, S., & Peitz, S. (2023). Learning a model is paramount for sample
efficiency in reinforcement learning control of PDEs. In arXiv:2302.07160.
bibtex: '@article{Werner_Peitz_2023, title={Learning a model is paramount for sample
efficiency in reinforcement learning control of PDEs}, journal={arXiv:2302.07160},
author={Werner, Stefan and Peitz, Sebastian}, year={2023} }'
chicago: Werner, Stefan, and Sebastian Peitz. “Learning a Model Is Paramount for
Sample Efficiency in Reinforcement Learning Control of PDEs.” ArXiv:2302.07160,
2023.
ieee: S. Werner and S. Peitz, “Learning a model is paramount for sample efficiency
in reinforcement learning control of PDEs,” arXiv:2302.07160. 2023.
mla: Werner, Stefan, and Sebastian Peitz. “Learning a Model Is Paramount for Sample
Efficiency in Reinforcement Learning Control of PDEs.” ArXiv:2302.07160,
2023.
short: S. Werner, S. Peitz, ArXiv:2302.07160 (2023).
date_created: 2023-02-15T20:57:20Z
date_updated: 2023-02-15T20:58:33Z
department:
- _id: '655'
external_id:
arxiv:
- '2302.07160'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2302.07160
oa: '1'
publication: arXiv:2302.07160
status: public
title: Learning a model is paramount for sample efficiency in reinforcement learning
control of PDEs
type: preprint
user_id: '47427'
year: '2023'
...