---
_id: '46469'
abstract:
- lang: eng
text: 'We show how to learn discrete field theories from observational data of fields
on a space-time lattice. For this, we train a neural network model of a discrete
Lagrangian density such that the discrete Euler--Lagrange equations are consistent
with the given training data. We, thus, obtain a structure-preserving machine
learning architecture. Lagrangian densities are not uniquely defined by the solutions
of a field theory. We introduce a technique to derive regularisers for the training
process which optimise numerical regularity of the discrete field theory. Minimisation
of the regularisers guarantees that close to the training data the discrete field
theory behaves robust and efficient when used in numerical simulations. Further,
we show how to identify structurally simple solutions of the underlying continuous
field theory such as travelling waves. This is possible even when travelling waves
are not present in the training data. This is compared to data-driven model order
reduction based approaches, which struggle to identify suitable latent spaces
containing structurally simple solutions when these are not present in the training
data. Ideas are demonstrated on examples based on the wave equation and the Schrödinger
equation. '
article_number: '013104'
article_type: original
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: Offen C, Ober-Blöbaum S. Learning of discrete models of variational PDEs from
data. Chaos. 2024;34(1). doi:10.1063/5.0172287
apa: Offen, C., & Ober-Blöbaum, S. (2024). Learning of discrete models of variational
PDEs from data. Chaos, 34(1), Article 013104. https://doi.org/10.1063/5.0172287
bibtex: '@article{Offen_Ober-Blöbaum_2024, title={Learning of discrete models of
variational PDEs from data}, volume={34}, DOI={10.1063/5.0172287},
number={1013104}, journal={Chaos}, publisher={AIP Publishing}, author={Offen,
Christian and Ober-Blöbaum, Sina}, year={2024} }'
chicago: Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of
Variational PDEs from Data.” Chaos 34, no. 1 (2024). https://doi.org/10.1063/5.0172287.
ieee: 'C. Offen and S. Ober-Blöbaum, “Learning of discrete models of variational
PDEs from data,” Chaos, vol. 34, no. 1, Art. no. 013104, 2024, doi: 10.1063/5.0172287.'
mla: Offen, Christian, and Sina Ober-Blöbaum. “Learning of Discrete Models of Variational
PDEs from Data.” Chaos, vol. 34, no. 1, 013104, AIP Publishing, 2024, doi:10.1063/5.0172287.
short: C. Offen, S. Ober-Blöbaum, Chaos 34 (2024).
date_created: 2023-08-10T08:24:48Z
date_updated: 2024-01-09T11:29:06Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1063/5.0172287
external_id:
arxiv:
- '2308.05082 '
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2024-01-09T10:48:38Z
date_updated: 2024-01-09T10:48:38Z
file_id: '50376'
file_name: Accepted manuscript with AIP banner CHA23-AR-01370.pdf
file_size: 13222105
relation: main_file
title: Accepted Manuscript Chaos
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2024-01-09T11:19:49Z
date_updated: 2024-01-09T11:19:49Z
description: |-
We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train
a neural network model of a discrete Lagrangian density such that the discrete Euler–Lagrange equations are consistent
with the given training data. We, thus, obtain a structure-preserving machine learning architecture. Lagrangian
densities are not uniquely defined by the solutions of a field theory. We introduce a technique to derive regularisers for
the training process which optimise numerical regularity of the discrete field theory. Minimisation of the regularisers
guarantees that close to the training data the discrete field theory behaves robust and efficient when used in numerical
simulations. Further, we show how to identify structurally simple solutions of the underlying continuous field theory
such as travelling waves. This is possible even when travelling waves are not present in the training data. This is
compared to data-driven model order reduction based approaches, which struggle to identify suitable latent spaces
containing structurally simple solutions when these are not present in the training data. Ideas are demonstrated on
examples based on the wave equation and the Schrödinger equation.
file_id: '50390'
file_name: LDensityPDE_AIP.pdf
file_size: 12960884
relation: main_file
title: Learning of discrete models of variational PDEs from data
file_date_updated: 2024-01-09T11:19:49Z
has_accepted_license: '1'
intvolume: ' 34'
issue: '1'
language:
- iso: eng
oa: '1'
publication: Chaos
publication_identifier:
issn:
- 1054-1500
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Christian-Offen/DLNN_pde
status: public
title: Learning of discrete models of variational PDEs from data
type: journal_article
user_id: '85279'
volume: 34
year: '2024'
...
---
_id: '51208'
abstract:
- lang: eng
text: AbstractApproximation of subdifferentials
is one of the main tasks when computing descent directions for nonsmooth optimization
problems. In this article, we propose a bisection method for weakly lower semismooth
functions which is able to compute new subgradients that improve a given approximation
in case a direction with insufficient descent was computed. Combined with a recently
proposed deterministic gradient sampling approach, this yields a deterministic
and provably convergent way to approximate subdifferentials for computing descent
directions.
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
citation:
ama: Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth
optimization. Computational Optimization and Applications. Published online
2024. doi:10.1007/s10589-024-00552-0
apa: Gebken, B. (2024). A note on the convergence of deterministic gradient sampling
in nonsmooth optimization. Computational Optimization and Applications.
https://doi.org/10.1007/s10589-024-00552-0
bibtex: '@article{Gebken_2024, title={A note on the convergence of deterministic
gradient sampling in nonsmooth optimization}, DOI={10.1007/s10589-024-00552-0},
journal={Computational Optimization and Applications}, publisher={Springer Science
and Business Media LLC}, author={Gebken, Bennet}, year={2024} }'
chicago: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
in Nonsmooth Optimization.” Computational Optimization and Applications,
2024. https://doi.org/10.1007/s10589-024-00552-0.
ieee: 'B. Gebken, “A note on the convergence of deterministic gradient sampling
in nonsmooth optimization,” Computational Optimization and Applications,
2024, doi: 10.1007/s10589-024-00552-0.'
mla: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
in Nonsmooth Optimization.” Computational Optimization and Applications,
Springer Science and Business Media LLC, 2024, doi:10.1007/s10589-024-00552-0.
short: B. Gebken, Computational Optimization and Applications (2024).
date_created: 2024-02-07T07:23:23Z
date_updated: 2024-02-08T08:05:54Z
department:
- _id: '101'
doi: 10.1007/s10589-024-00552-0
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
language:
- iso: eng
publication: Computational Optimization and Applications
publication_identifier:
issn:
- 0926-6003
- 1573-2894
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A note on the convergence of deterministic gradient sampling in nonsmooth optimization
type: journal_article
user_id: '32643'
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: '52342'
abstract:
- lang: eng
text: 'We introduce the concept of a k-token signed graph and study some of its
combinatorial and algebraic properties. We prove that two switching isomorphic
signed graphs have switching isomorphic token graphs. Moreover, we show that the
Laplacian spectrum of a balanced signed graph is contained in the Laplacian spectra
of its k-token signed graph. Besides, we introduce and study the unbalance level
of a signed graph, which is a new parameter that measures how far a signed graph
is from being balanced. Moreover, we study the relation between the frustration
index and the unbalance level of signed graphs and their token signed graphs. '
author:
- first_name: C.
full_name: Dalfó, C.
last_name: Dalfó
- first_name: M. A.
full_name: Fiol, M. A.
last_name: Fiol
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
citation:
ama: Dalfó C, Fiol MA, Steffen E. On token signed graphs. arXiv:240302924.
Published online 2024.
apa: Dalfó, C., Fiol, M. A., & Steffen, E. (2024). On token signed graphs. In
arXiv:2403.02924.
bibtex: '@article{Dalfó_Fiol_Steffen_2024, title={On token signed graphs}, journal={arXiv:2403.02924},
author={Dalfó, C. and Fiol, M. A. and Steffen, Eckhard}, year={2024} }'
chicago: Dalfó, C., M. A. Fiol, and Eckhard Steffen. “On Token Signed Graphs.” ArXiv:2403.02924,
2024.
ieee: C. Dalfó, M. A. Fiol, and E. Steffen, “On token signed graphs,” arXiv:2403.02924.
2024.
mla: Dalfó, C., et al. “On Token Signed Graphs.” ArXiv:2403.02924, 2024.
short: C. Dalfó, M.A. Fiol, E. Steffen, ArXiv:2403.02924 (2024).
date_created: 2024-03-07T08:48:39Z
date_updated: 2024-03-07T08:50:33Z
department:
- _id: '542'
external_id:
arxiv:
- '2403.02924'
language:
- iso: eng
publication: arXiv:2403.02924
status: public
title: On token signed graphs
type: preprint
user_id: '15540'
year: '2024'
...
---
_id: '52726'
abstract:
- lang: eng
text: Heteroclinic structures organize global features of dynamical systems. We
analyse whether heteroclinic structures can arise in network dynamics with higher-order
interactions which describe the nonlinear interactions between three or more units.
We find that while commonly analysed model equations such as network dynamics
on undirected hypergraphs may be useful to describe local dynamics such as cluster
synchronization, they give rise to obstructions that allow to design of heteroclinic
structures in phase space. By contrast, directed hypergraphs break the homogeneity
and lead to vector fields that support heteroclinic structures.
article_type: original
author:
- first_name: Christian
full_name: Bick, Christian
last_name: Bick
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
citation:
ama: Bick C, von der Gracht S. Heteroclinic dynamics in network dynamical systems
with higher-order interactions. Journal of Complex Networks. 2024;12(2).
doi:10.1093/comnet/cnae009
apa: Bick, C., & von der Gracht, S. (2024). Heteroclinic dynamics in network
dynamical systems with higher-order interactions. Journal of Complex Networks,
12(2). https://doi.org/10.1093/comnet/cnae009
bibtex: '@article{Bick_von der Gracht_2024, title={Heteroclinic dynamics in network
dynamical systems with higher-order interactions}, volume={12}, DOI={10.1093/comnet/cnae009},
number={2}, journal={Journal of Complex Networks}, publisher={Oxford University
Press (OUP)}, author={Bick, Christian and von der Gracht, Sören}, year={2024}
}'
chicago: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network
Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks
12, no. 2 (2024). https://doi.org/10.1093/comnet/cnae009.
ieee: 'C. Bick and S. von der Gracht, “Heteroclinic dynamics in network dynamical
systems with higher-order interactions,” Journal of Complex Networks, vol.
12, no. 2, 2024, doi: 10.1093/comnet/cnae009.'
mla: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network
Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks,
vol. 12, no. 2, Oxford University Press (OUP), 2024, doi:10.1093/comnet/cnae009.
short: C. Bick, S. von der Gracht, Journal of Complex Networks 12 (2024).
date_created: 2024-03-22T09:04:57Z
date_updated: 2024-03-22T09:11:53Z
ddc:
- '510'
department:
- _id: '101'
doi: 10.1093/comnet/cnae009
external_id:
arxiv:
- '2309.02006'
file:
- access_level: closed
content_type: application/pdf
creator: svdg
date_created: 2024-03-22T09:06:07Z
date_updated: 2024-03-22T09:06:07Z
file_id: '52728'
file_name: heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf
file_size: 649155
relation: main_file
success: 1
file_date_updated: 2024-03-22T09:06:07Z
has_accepted_license: '1'
intvolume: ' 12'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
- Management Science and Operations Research
- Computer Networks and Communications
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf
oa: '1'
publication: Journal of Complex Networks
publication_identifier:
issn:
- 2051-1329
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Heteroclinic dynamics in network dynamical systems with higher-order interactions
type: journal_article
user_id: '97359'
volume: 12
year: '2024'
...
---
_id: '49905'
abstract:
- lang: eng
text: "For 0 ≤ t ≤ r let m(t, r) be the maximum number s such that every t-edge-connected
r-graph has s pairwise disjoint perfect matchings. There are only a few values
of m(t, r) known, for instance m(3, 3) = m(4, r) = 1, and m(t, r) ≤ r − 2 for
all t \x03 = 5,\r\nand m(t, r) ≤ r − 3 if r is even. We prove that m(2l, r) ≤
3l − 6 for every l ≥ 3 and r ≥ 2l."
author:
- first_name: Yulai
full_name: Ma, Yulai
id: '92748'
last_name: Ma
- first_name: Davide
full_name: Mattiolo, Davide
last_name: Mattiolo
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
- first_name: Isaak Hieronymus
full_name: Wolf, Isaak Hieronymus
id: '88145'
last_name: Wolf
citation:
ama: Ma Y, Mattiolo D, Steffen E, Wolf IH. Edge-Connectivity and Pairwise Disjoint
Perfect Matchings in Regular Graphs. Combinatorica. 2024;44:429-440. doi:10.1007/s00493-023-00078-9
apa: Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2024). Edge-Connectivity
and Pairwise Disjoint Perfect Matchings in Regular Graphs. Combinatorica,
44, 429–440. https://doi.org/10.1007/s00493-023-00078-9
bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2024, title={Edge-Connectivity and Pairwise
Disjoint Perfect Matchings in Regular Graphs}, volume={44}, DOI={10.1007/s00493-023-00078-9},
journal={Combinatorica}, publisher={Springer Science and Business Media LLC},
author={Ma, Yulai and Mattiolo, Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus},
year={2024}, pages={429–440} }'
chicago: 'Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf.
“Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs.”
Combinatorica 44 (2024): 429–40. https://doi.org/10.1007/s00493-023-00078-9.'
ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Edge-Connectivity and Pairwise
Disjoint Perfect Matchings in Regular Graphs,” Combinatorica, vol. 44,
pp. 429–440, 2024, doi: 10.1007/s00493-023-00078-9.'
mla: Ma, Yulai, et al. “Edge-Connectivity and Pairwise Disjoint Perfect Matchings
in Regular Graphs.” Combinatorica, vol. 44, Springer Science and Business
Media LLC, 2024, pp. 429–40, doi:10.1007/s00493-023-00078-9.
short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, Combinatorica 44 (2024) 429–440.
date_created: 2023-12-20T10:31:27Z
date_updated: 2024-03-22T12:11:35Z
department:
- _id: '542'
doi: 10.1007/s00493-023-00078-9
intvolume: ' 44'
keyword:
- Computational Mathematics
- Discrete Mathematics and Combinatorics
language:
- iso: eng
page: 429-440
publication: Combinatorica
publication_identifier:
issn:
- 0209-9683
- 1439-6912
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs
type: journal_article
user_id: '15540'
volume: 44
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: '27426'
abstract:
- lang: eng
text: "Regularization is used in many different areas of optimization when solutions\r\nare
sought which not only minimize a given function, but also possess a certain\r\ndegree
of regularity. Popular applications are image denoising, sparse\r\nregression
and machine learning. Since the choice of the regularization\r\nparameter is crucial
but often difficult, path-following methods are used to\r\napproximate the entire
regularization path, i.e., the set of all possible\r\nsolutions for all regularization
parameters. Due to their nature, the\r\ndevelopment of these methods requires
structural results about the\r\nregularization path. The goal of this article
is to derive these results for\r\nthe case of a smooth objective function which
is penalized by a piecewise\r\ndifferentiable regularization term. We do this
by treating regularization as a\r\nmultiobjective optimization problem. Our results
suggest that even in this\r\ngeneral case, the regularization path is piecewise
smooth. Moreover, our theory\r\nallows for a classification of the nonsmooth features
that occur in between\r\nsmooth parts. This is demonstrated in two applications,
namely support-vector\r\nmachines and exact penalty methods."
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Katharina
full_name: Bieker, Katharina
id: '32829'
last_name: Bieker
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Gebken B, Bieker K, Peitz S. On the structure of regularization paths for piecewise
differentiable regularization terms. Journal of Global Optimization. 2023;85(3):709-741.
doi:10.1007/s10898-022-01223-2
apa: Gebken, B., Bieker, K., & Peitz, S. (2023). On the structure of regularization
paths for piecewise differentiable regularization terms. Journal of Global
Optimization, 85(3), 709–741. https://doi.org/10.1007/s10898-022-01223-2
bibtex: '@article{Gebken_Bieker_Peitz_2023, title={On the structure of regularization
paths for piecewise differentiable regularization terms}, volume={85}, DOI={10.1007/s10898-022-01223-2},
number={3}, journal={Journal of Global Optimization}, author={Gebken, Bennet and
Bieker, Katharina and Peitz, Sebastian}, year={2023}, pages={709–741} }'
chicago: 'Gebken, Bennet, Katharina Bieker, and Sebastian Peitz. “On the Structure
of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal
of Global Optimization 85, no. 3 (2023): 709–41. https://doi.org/10.1007/s10898-022-01223-2.'
ieee: 'B. Gebken, K. Bieker, and S. Peitz, “On the structure of regularization paths
for piecewise differentiable regularization terms,” Journal of Global Optimization,
vol. 85, no. 3, pp. 709–741, 2023, doi: 10.1007/s10898-022-01223-2.'
mla: Gebken, Bennet, et al. “On the Structure of Regularization Paths for Piecewise
Differentiable Regularization Terms.” Journal of Global Optimization, vol.
85, no. 3, 2023, pp. 709–41, doi:10.1007/s10898-022-01223-2.
short: B. Gebken, K. Bieker, S. Peitz, Journal of Global Optimization 85 (2023)
709–741.
date_created: 2021-11-15T09:24:59Z
date_updated: 2023-03-11T17:16:33Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s10898-022-01223-2
intvolume: ' 85'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf
oa: '1'
page: 709-741
publication: Journal of Global Optimization
status: public
title: On the structure of regularization paths for piecewise differentiable regularization
terms
type: journal_article
user_id: '47427'
volume: 85
year: '2023'
...
---
_id: '44501'
abstract:
- lang: eng
text: "Extending the notion of maxcut, the study of the frustration index of signed
graphs is one of the basic questions in the theory of signed graphs. Recently
two of the authors initiated the study of critically frustrated signed graphs.
That is a signed graph whose frustration index decreases with the removal of any
edge. The main focus of this study is on critical signed graphs which are not
edge-disjoint unions of critically frustrated signed graphs (namely non-decomposable
signed graphs) and which are not built from other critically frustrated signed
graphs by subdivision. We conjecture that for any given k there are only finitely
many critically k-frustrated signed graphs of this kind.\r\nProviding support
for this conjecture we show that there are only two of such critically 3-frustrated
signed graphs where there is no pair of edge-disjoint negative cycles. Similarly,
we show that there are exactly ten critically 3-frustrated signed planar graphs
that are neither decomposable nor subdivisions of other critically frustrated
signed graphs. We present a method for building non-decomposable critically frustrated
signed graphs based on two given such signed graphs. We also show that the condition
of being non-decomposable is necessary for our conjecture. "
author:
- first_name: Chiara
full_name: Cappello, Chiara
id: '72874'
last_name: Cappello
- first_name: Reza
full_name: Naserasr, Reza
last_name: Naserasr
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
- first_name: Zhouningxin
full_name: Wang, Zhouningxin
last_name: Wang
citation:
ama: Cappello C, Naserasr R, Steffen E, Wang Z. Critically 3-frustrated signed graphs.
arXiv:230410243. Published online 2023.
apa: Cappello, C., Naserasr, R., Steffen, E., & Wang, Z. (2023). Critically
3-frustrated signed graphs. In arXiv:2304.10243.
bibtex: '@article{Cappello_Naserasr_Steffen_Wang_2023, title={Critically 3-frustrated
signed graphs}, journal={arXiv:2304.10243}, author={Cappello, Chiara and Naserasr,
Reza and Steffen, Eckhard and Wang, Zhouningxin}, year={2023} }'
chicago: Cappello, Chiara, Reza Naserasr, Eckhard Steffen, and Zhouningxin Wang.
“Critically 3-Frustrated Signed Graphs.” ArXiv:2304.10243, 2023.
ieee: C. Cappello, R. Naserasr, E. Steffen, and Z. Wang, “Critically 3-frustrated
signed graphs,” arXiv:2304.10243. 2023.
mla: Cappello, Chiara, et al. “Critically 3-Frustrated Signed Graphs.” ArXiv:2304.10243,
2023.
short: C. Cappello, R. Naserasr, E. Steffen, Z. Wang, ArXiv:2304.10243 (2023).
date_created: 2023-05-05T06:52:39Z
date_updated: 2023-05-05T06:53:47Z
department:
- _id: '542'
external_id:
arxiv:
- '2304.10243'
language:
- iso: eng
publication: arXiv:2304.10243
status: public
title: Critically 3-frustrated signed graphs
type: preprint
user_id: '15540'
year: '2023'
...
---
_id: '44857'
abstract:
- lang: eng
text: Ancestral reconstruction is a classic task in comparative genomics. Here,
we study the genome median problem, a related computational problem which, given
a set of three or more genomes, asks to find a new genome that minimizes the sum
of pairwise distances between it and the given genomes. The distance stands for
the amount of evolution observed at the genome level, for which we determine the
minimum number of rearrangement operations necessary to transform one genome into
the other. For almost all rearrangement operations the median problem is NP-hard,
with the exception of the breakpoint median that can be constructed efficiently
for multichromosomal circular and mixed genomes. In this work, we study the median
problem under a restricted rearrangement measure called c4-distance, which is
closely related to the breakpoint and the DCJ distance. We identify tight bounds
and decomposers of the c4-median and develop algorithms for its construction,
one exact ILP-based and three combinatorial heuristics. Subsequently, we perform
experiments on simulated data sets. Our results suggest that the c4-distance is
useful for the study the genome median problem, from theoretical and practical
perspectives.
author:
- first_name: Helmuth O.M.
full_name: Silva, Helmuth O.M.
last_name: Silva
- first_name: Diego P.
full_name: Rubert, Diego P.
last_name: Rubert
- first_name: Eloi
full_name: Araujo, Eloi
last_name: Araujo
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
- first_name: Daniel
full_name: Doerr, Daniel
last_name: Doerr
- first_name: Fábio V.
full_name: Martinez, Fábio V.
last_name: Martinez
citation:
ama: Silva HOM, Rubert DP, Araujo E, Steffen E, Doerr D, Martinez FV. Algorithms
for the genome median under a restricted measure of rearrangement. RAIRO -
Operations Research. 2023;57(3):1045-1058. doi:10.1051/ro/2023052
apa: Silva, H. O. M., Rubert, D. P., Araujo, E., Steffen, E., Doerr, D., & Martinez,
F. V. (2023). Algorithms for the genome median under a restricted measure of rearrangement.
RAIRO - Operations Research, 57(3), 1045–1058. https://doi.org/10.1051/ro/2023052
bibtex: '@article{Silva_Rubert_Araujo_Steffen_Doerr_Martinez_2023, title={Algorithms
for the genome median under a restricted measure of rearrangement}, volume={57},
DOI={10.1051/ro/2023052}, number={3},
journal={RAIRO - Operations Research}, publisher={EDP Sciences}, author={Silva,
Helmuth O.M. and Rubert, Diego P. and Araujo, Eloi and Steffen, Eckhard and Doerr,
Daniel and Martinez, Fábio V.}, year={2023}, pages={1045–1058} }'
chicago: 'Silva, Helmuth O.M., Diego P. Rubert, Eloi Araujo, Eckhard Steffen, Daniel
Doerr, and Fábio V. Martinez. “Algorithms for the Genome Median under a Restricted
Measure of Rearrangement.” RAIRO - Operations Research 57, no. 3 (2023):
1045–58. https://doi.org/10.1051/ro/2023052.'
ieee: 'H. O. M. Silva, D. P. Rubert, E. Araujo, E. Steffen, D. Doerr, and F. V.
Martinez, “Algorithms for the genome median under a restricted measure of rearrangement,”
RAIRO - Operations Research, vol. 57, no. 3, pp. 1045–1058, 2023, doi:
10.1051/ro/2023052.'
mla: Silva, Helmuth O. M., et al. “Algorithms for the Genome Median under a Restricted
Measure of Rearrangement.” RAIRO - Operations Research, vol. 57, no. 3,
EDP Sciences, 2023, pp. 1045–58, doi:10.1051/ro/2023052.
short: H.O.M. Silva, D.P. Rubert, E. Araujo, E. Steffen, D. Doerr, F.V. Martinez,
RAIRO - Operations Research 57 (2023) 1045–1058.
date_created: 2023-05-16T08:48:22Z
date_updated: 2023-05-16T08:49:30Z
department:
- _id: '542'
doi: 10.1051/ro/2023052
intvolume: ' 57'
issue: '3'
keyword:
- Management Science and Operations Research
- Computer Science Applications
- Theoretical Computer Science
language:
- iso: eng
page: 1045-1058
publication: RAIRO - Operations Research
publication_identifier:
issn:
- 0399-0559
- 2804-7303
publication_status: published
publisher: EDP Sciences
status: public
title: Algorithms for the genome median under a restricted measure of rearrangement
type: journal_article
user_id: '15540'
volume: 57
year: '2023'
...
---
_id: '44859'
author:
- first_name: Yulai
full_name: Ma, Yulai
id: '92748'
last_name: Ma
- first_name: Davide
full_name: Mattiolo, Davide
last_name: Mattiolo
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
- first_name: Isaak Hieronymus
full_name: Wolf, Isaak Hieronymus
id: '88145'
last_name: Wolf
citation:
ama: Ma Y, Mattiolo D, Steffen E, Wolf IH. Sets of r-graphs that color all r-graphs.
arXiv:230508619. Published online 2023.
apa: Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Sets of r-graphs
that color all r-graphs. In arXiv:2305.08619.
bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Sets of r-graphs that color
all r-graphs}, journal={arXiv:2305.08619}, author={Ma, Yulai and Mattiolo, Davide
and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023} }'
chicago: Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf.
“Sets of R-Graphs That Color All r-Graphs.” ArXiv:2305.08619, 2023.
ieee: Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Sets of r-graphs that color
all r-graphs,” arXiv:2305.08619. 2023.
mla: Ma, Yulai, et al. “Sets of R-Graphs That Color All r-Graphs.” ArXiv:2305.08619,
2023.
short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, ArXiv:2305.08619 (2023).
date_created: 2023-05-16T10:07:47Z
date_updated: 2023-05-16T11:17:26Z
department:
- _id: '542'
external_id:
arxiv:
- '2305.08619'
language:
- iso: eng
publication: arXiv:2305.08619
status: public
title: Sets of r-graphs that color all r-graphs
type: preprint
user_id: '15540'
year: '2023'
...
---
_id: '45498'
abstract:
- lang: eng
text: "We present a novel method for high-order phase reduction in networks of\r\nweakly
coupled oscillators and, more generally, perturbations of reducible\r\nnormally
hyperbolic (quasi-)periodic tori. Our method works by computing an\r\nasymptotic
expansion for an embedding of the perturbed invariant torus, as well\r\nas for
the reduced phase dynamics in local coordinates. Both can be determined\r\nto
arbitrary degrees of accuracy, and we show that the phase dynamics may\r\ndirectly
be obtained in normal form. We apply the method to predict remote\r\nsynchronisation
in a chain of coupled Stuart-Landau oscillators."
author:
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Eddie
full_name: Nijholt, Eddie
last_name: Nijholt
- first_name: Bob
full_name: Rink, Bob
last_name: Rink
citation:
ama: von der Gracht S, Nijholt E, Rink B. A parametrisation method for high-order
phase reduction in coupled oscillator networks. arXiv:230603320.
apa: von der Gracht, S., Nijholt, E., & Rink, B. (n.d.). A parametrisation method
for high-order phase reduction in coupled oscillator networks. In arXiv:2306.03320.
bibtex: '@article{von der Gracht_Nijholt_Rink, title={A parametrisation method for
high-order phase reduction in coupled oscillator networks}, journal={arXiv:2306.03320},
author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob} }'
chicago: Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “A Parametrisation
Method for High-Order Phase Reduction in Coupled Oscillator Networks.” ArXiv:2306.03320,
n.d.
ieee: S. von der Gracht, E. Nijholt, and B. Rink, “A parametrisation method for
high-order phase reduction in coupled oscillator networks,” arXiv:2306.03320.
.
mla: von der Gracht, Sören, et al. “A Parametrisation Method for High-Order Phase
Reduction in Coupled Oscillator Networks.” ArXiv:2306.03320.
short: S. von der Gracht, E. Nijholt, B. Rink, ArXiv:2306.03320 (n.d.).
date_created: 2023-06-07T07:57:28Z
date_updated: 2023-06-07T07:59:06Z
department:
- _id: '101'
external_id:
arxiv:
- '2306.03320'
language:
- iso: eng
main_file_link:
- url: https://arxiv.org/pdf/2306.03320
page: '29'
publication: arXiv:2306.03320
publication_status: submitted
status: public
title: A parametrisation method for high-order phase reduction in coupled oscillator
networks
type: preprint
user_id: '97359'
year: '2023'
...
---
_id: '46256'
author:
- first_name: Yulai
full_name: Ma, Yulai
id: '92748'
last_name: Ma
- first_name: Davide
full_name: Mattiolo, Davide
last_name: Mattiolo
- first_name: Eckhard
full_name: Steffen, Eckhard
id: '15548'
last_name: Steffen
orcid: 0000-0002-9808-7401
- first_name: Isaak Hieronymus
full_name: Wolf, Isaak Hieronymus
id: '88145'
last_name: Wolf
citation:
ama: Ma Y, Mattiolo D, Steffen E, Wolf IH. Pairwise Disjoint Perfect Matchings in
r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete Mathematics.
2023;37(3):1548-1565. doi:10.1137/22m1500654
apa: Ma, Y., Mattiolo, D., Steffen, E., & Wolf, I. H. (2023). Pairwise Disjoint
Perfect Matchings in r-Edge-Connected r-Regular Graphs. SIAM Journal on Discrete
Mathematics, 37(3), 1548–1565. https://doi.org/10.1137/22m1500654
bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Pairwise Disjoint Perfect
Matchings in r-Edge-Connected r-Regular Graphs}, volume={37}, DOI={10.1137/22m1500654},
number={3}, journal={SIAM Journal on Discrete Mathematics}, publisher={Society
for Industrial & Applied Mathematics (SIAM)}, author={Ma, Yulai and Mattiolo,
Davide and Steffen, Eckhard and Wolf, Isaak Hieronymus}, year={2023}, pages={1548–1565}
}'
chicago: 'Ma, Yulai, Davide Mattiolo, Eckhard Steffen, and Isaak Hieronymus Wolf.
“Pairwise Disjoint Perfect Matchings in R-Edge-Connected r-Regular Graphs.” SIAM
Journal on Discrete Mathematics 37, no. 3 (2023): 1548–65. https://doi.org/10.1137/22m1500654.'
ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Pairwise Disjoint Perfect
Matchings in r-Edge-Connected r-Regular Graphs,” SIAM Journal on Discrete Mathematics,
vol. 37, no. 3, pp. 1548–1565, 2023, doi: 10.1137/22m1500654.'
mla: Ma, Yulai, et al. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected
r-Regular Graphs.” SIAM Journal on Discrete Mathematics, vol. 37, no. 3,
Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 1548–65, doi:10.1137/22m1500654.
short: Y. Ma, D. Mattiolo, E. Steffen, I.H. Wolf, SIAM Journal on Discrete Mathematics
37 (2023) 1548–1565.
date_created: 2023-08-01T10:08:32Z
date_updated: 2023-08-01T10:09:35Z
department:
- _id: '542'
doi: 10.1137/22m1500654
intvolume: ' 37'
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
page: 1548-1565
publication: SIAM Journal on Discrete Mathematics
publication_identifier:
issn:
- 0895-4801
- 1095-7146
publication_status: published
publisher: Society for Industrial & Applied Mathematics (SIAM)
status: public
title: Pairwise Disjoint Perfect Matchings in r-Edge-Connected r-Regular Graphs
type: journal_article
user_id: '15540'
volume: 37
year: '2023'
...
---
_id: '42163'
abstract:
- lang: eng
text: 'The article shows how to learn models of dynamical systems from data which
are governed by an unknown variational PDE. Rather than employing reduction techniques,
we learn a discrete field theory governed by a discrete Lagrangian density $L_d$
that is modelled as a neural network. Careful regularisation of the loss function
for training $L_d$ is necessary to obtain a field theory that is suitable for
numerical computations: we derive a regularisation term which optimises the solvability
of the discrete Euler--Lagrange equations. Secondly, we develop a method to find
solutions to machine learned discrete field theories which constitute travelling
waves of the underlying continuous PDE.'
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Offen C, Ober-Blöbaum S. Learning discrete Lagrangians for variational PDEs
from data and detection of travelling waves. In: Nielsen F, Barbaresco F, eds.
Geometric Science of Information. Vol 14071. Lecture Notes in Computer
Science (LNCS). Springer, Cham.; 2023:569-579. doi:10.1007/978-3-031-38271-0_57'
apa: Offen, C., & Ober-Blöbaum, S. (2023). Learning discrete Lagrangians for
variational PDEs from data and detection of travelling waves. In F. Nielsen &
F. Barbaresco (Eds.), Geometric Science of Information (Vol. 14071, pp.
569–579). Springer, Cham. https://doi.org/10.1007/978-3-031-38271-0_57
bibtex: '@inproceedings{Offen_Ober-Blöbaum_2023, series={Lecture Notes in Computer
Science (LNCS)}, title={Learning discrete Lagrangians for variational PDEs from
data and detection of travelling waves}, volume={14071}, DOI={10.1007/978-3-031-38271-0_57},
booktitle={Geometric Science of Information}, publisher={Springer, Cham.}, author={Offen,
Christian and Ober-Blöbaum, Sina}, editor={Nielsen, F and Barbaresco, F}, year={2023},
pages={569–579}, collection={Lecture Notes in Computer Science (LNCS)} }'
chicago: Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians
for Variational PDEs from Data and Detection of Travelling Waves.” In Geometric
Science of Information, edited by F Nielsen and F Barbaresco, 14071:569–79.
Lecture Notes in Computer Science (LNCS). Springer, Cham., 2023. https://doi.org/10.1007/978-3-031-38271-0_57.
ieee: 'C. Offen and S. Ober-Blöbaum, “Learning discrete Lagrangians for variational
PDEs from data and detection of travelling waves,” in Geometric Science of
Information, Saint-Malo, Palais du Grand Large, France, 2023, vol. 14071,
pp. 569–579, doi: 10.1007/978-3-031-38271-0_57.'
mla: Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for
Variational PDEs from Data and Detection of Travelling Waves.” Geometric Science
of Information, edited by F Nielsen and F Barbaresco, vol. 14071, Springer,
Cham., 2023, pp. 569–79, doi:10.1007/978-3-031-38271-0_57.
short: 'C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric
Science of Information, Springer, Cham., 2023, pp. 569–579.'
conference:
end_date: 2023-09-01
location: Saint-Malo, Palais du Grand Large, France
name: ' GSI''23 6th International Conference on Geometric Science of Information'
start_date: 2023-08-30
date_created: 2023-02-16T11:32:48Z
date_updated: 2023-08-10T08:34:04Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1007/978-3-031-38271-0_57
editor:
- first_name: F
full_name: Nielsen, F
last_name: Nielsen
- first_name: F
full_name: Barbaresco, F
last_name: Barbaresco
external_id:
arxiv:
- '2302.08232 '
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2023-08-02T12:04:17Z
date_updated: 2023-08-02T12:04:17Z
description: |-
The article shows how to learn models of dynamical systems
from data which are governed by an unknown variational PDE. Rather
than employing reduction techniques, we learn a discrete field theory
governed by a discrete Lagrangian density Ld that is modelled as a neural network. Careful regularisation of the loss function for training Ld is
necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of
the discrete Euler–Lagrange equations. Secondly, we develop a method to
find solutions to machine learned discrete field theories which constitute
travelling waves of the underlying continuous PDE.
file_id: '46273'
file_name: LDensityLearning.pdf
file_size: 1938962
relation: main_file
title: Learning discrete Lagrangians for variational PDEs from data and detection
of travelling waves
file_date_updated: 2023-08-02T12:04:17Z
has_accepted_license: '1'
intvolume: ' 14071'
keyword:
- System identification
- discrete Lagrangians
- travelling waves
language:
- iso: eng
oa: '1'
page: 569-579
publication: Geometric Science of Information
publication_identifier:
eisbn:
- 978-3-031-38271-0
publication_status: published
publisher: Springer, Cham.
quality_controlled: '1'
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Christian-Offen/LagrangianDensityML
series_title: Lecture Notes in Computer Science (LNCS)
status: public
title: Learning discrete Lagrangians for variational PDEs from data and detection
of travelling waves
type: conference
user_id: '85279'
volume: 14071
year: '2023'
...
---
_id: '29240'
abstract:
- lang: eng
text: "The principle of least action is one of the most fundamental physical principle.
It says that among all possible motions connecting two points in a phase space,
the system will exhibit those motions which extremise an action functional. Many
qualitative features of dynamical systems, such as the presence of conservation
laws and energy balance equations, are related to the existence of an action functional.
Incorporating variational structure into learning algorithms for dynamical systems
is, therefore, crucial in order to make sure that the learned model shares important
features with the exact physical system. In this paper we show how to incorporate
variational principles into trajectory predictions of learned dynamical systems.
The novelty of this work is that (1) our technique relies only on discrete position
data of observed trajectories. Velocities or conjugate momenta do not need to
be observed or approximated and no prior knowledge about the form of the variational
principle is assumed. Instead, they are recovered using backward error analysis.
(2) Moreover, our technique compensates discretisation errors when trajectories
are computed from the learned system. This is important when moderate to large
step-sizes are used and high accuracy is required. For this,\r\nwe introduce and
rigorously analyse the concept of inverse modified Lagrangians by developing an
inverse version of variational backward error analysis. (3) Finally, we introduce
a method to perform system identification from position observations only, based
on variational backward error analysis."
article_type: original
author:
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
citation:
ama: Ober-Blöbaum S, Offen C. Variational Learning of Euler–Lagrange Dynamics from
Data. Journal of Computational and Applied Mathematics. 2023;421:114780.
doi:10.1016/j.cam.2022.114780
apa: Ober-Blöbaum, S., & Offen, C. (2023). Variational Learning of Euler–Lagrange
Dynamics from Data. Journal of Computational and Applied Mathematics, 421,
114780. https://doi.org/10.1016/j.cam.2022.114780
bibtex: '@article{Ober-Blöbaum_Offen_2023, title={Variational Learning of Euler–Lagrange
Dynamics from Data}, volume={421}, DOI={10.1016/j.cam.2022.114780},
journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier},
author={Ober-Blöbaum, Sina and Offen, Christian}, year={2023}, pages={114780}
}'
chicago: 'Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange
Dynamics from Data.” Journal of Computational and Applied Mathematics 421
(2023): 114780. https://doi.org/10.1016/j.cam.2022.114780.'
ieee: 'S. Ober-Blöbaum and C. Offen, “Variational Learning of Euler–Lagrange Dynamics
from Data,” Journal of Computational and Applied Mathematics, vol. 421,
p. 114780, 2023, doi: 10.1016/j.cam.2022.114780.'
mla: Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange
Dynamics from Data.” Journal of Computational and Applied Mathematics,
vol. 421, Elsevier, 2023, p. 114780, doi:10.1016/j.cam.2022.114780.
short: S. Ober-Blöbaum, C. Offen, Journal of Computational and Applied Mathematics
421 (2023) 114780.
date_created: 2022-01-11T13:24:00Z
date_updated: 2023-08-10T08:42:39Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1016/j.cam.2022.114780
external_id:
arxiv:
- '2112.12619'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2022-06-28T15:25:50Z
date_updated: 2022-06-28T15:25:50Z
description: |-
The principle of least action is one of the most fundamental physical principle. It says that among all possible motions
connecting two points in a phase space, the system will exhibit those motions which extremise an action functional.
Many qualitative features of dynamical systems, such as the presence of conservation laws and energy balance equa-
tions, are related to the existence of an action functional. Incorporating variational structure into learning algorithms
for dynamical systems is, therefore, crucial in order to make sure that the learned model shares important features
with the exact physical system. In this paper we show how to incorporate variational principles into trajectory predic-
tions of learned dynamical systems. The novelty of this work is that (1) our technique relies only on discrete position
data of observed trajectories. Velocities or conjugate momenta do not need to be observed or approximated and no
prior knowledge about the form of the variational principle is assumed. Instead, they are recovered using backward
error analysis. (2) Moreover, our technique compensates discretisation errors when trajectories are computed from the
learned system. This is important when moderate to large step-sizes are used and high accuracy is required. For this,
we introduce and rigorously analyse the concept of inverse modified Lagrangians by developing an inverse version of
variational backward error analysis. (3) Finally, we introduce a method to perform system identification from position
observations only, based on variational backward error analysis.
file_id: '32274'
file_name: ShadowLagrangian_revision1_journal_style_arxiv.pdf
file_size: 3640770
relation: main_file
title: Variational Learning of Euler–Lagrange Dynamics from Data
file_date_updated: 2022-06-28T15:25:50Z
has_accepted_license: '1'
intvolume: ' 421'
keyword:
- Lagrangian learning
- variational backward error analysis
- modified Lagrangian
- variational integrators
- physics informed learning
language:
- iso: eng
oa: '1'
page: '114780'
publication: Journal of Computational and Applied Mathematics
publication_identifier:
issn:
- 0377-0427
publication_status: epub_ahead
publisher: Elsevier
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/Christian-Offen/LagrangianShadowIntegration
status: public
title: Variational Learning of Euler–Lagrange Dynamics from Data
type: journal_article
user_id: '85279'
volume: 421
year: '2023'
...
---
_id: '29236'
abstract:
- lang: eng
text: The numerical solution of an ordinary differential equation can be interpreted
as the exact solution of a nearby modified equation. Investigating the behaviour
of numerical solutions by analysing the modified equation is known as backward
error analysis. If the original and modified equation share structural properties,
then the exact and approximate solution share geometric features such as the existence
of conserved quantities. Conjugate symplectic methods preserve a modified symplectic
form and a modified Hamiltonian when applied to a Hamiltonian system. We show
how a blended version of variational and symplectic techniques can be used to
compute modified symplectic and Hamiltonian structures. In contrast to other approaches,
our backward error analysis method does not rely on an ansatz but computes the
structures systematically, provided that a variational formulation of the method
is known. The technique is illustrated on the example of symmetric linear multistep
methods with matrix coefficients.
article_type: original
author:
- first_name: Robert
full_name: McLachlan, Robert
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
citation:
ama: McLachlan R, Offen C. Backward error analysis for conjugate symplectic methods.
Journal of Geometric Mechanics. 2023;15(1):98-115. doi:10.3934/jgm.2023005
apa: McLachlan, R., & Offen, C. (2023). Backward error analysis for conjugate
symplectic methods. Journal of Geometric Mechanics, 15(1), 98–115.
https://doi.org/10.3934/jgm.2023005
bibtex: '@article{McLachlan_Offen_2023, title={Backward error analysis for conjugate
symplectic methods}, volume={15}, DOI={10.3934/jgm.2023005},
number={1}, journal={Journal of Geometric Mechanics}, publisher={AIMS Press},
author={McLachlan, Robert and Offen, Christian}, year={2023}, pages={98–115} }'
chicago: 'McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate
Symplectic Methods.” Journal of Geometric Mechanics 15, no. 1 (2023): 98–115.
https://doi.org/10.3934/jgm.2023005.'
ieee: 'R. McLachlan and C. Offen, “Backward error analysis for conjugate symplectic
methods,” Journal of Geometric Mechanics, vol. 15, no. 1, pp. 98–115, 2023,
doi: 10.3934/jgm.2023005.'
mla: McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate
Symplectic Methods.” Journal of Geometric Mechanics, vol. 15, no. 1, AIMS
Press, 2023, pp. 98–115, doi:10.3934/jgm.2023005.
short: R. McLachlan, C. Offen, Journal of Geometric Mechanics 15 (2023) 98–115.
date_created: 2022-01-11T12:48:39Z
date_updated: 2023-08-10T08:40:30Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.3934/jgm.2023005
external_id:
arxiv:
- '2201.03911'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2022-08-12T16:48:59Z
date_updated: 2022-08-12T16:48:59Z
description: The numerical solution of an ordinary differential equation can be
interpreted as the exact solution of a nearby modified equation. Investigating
the behaviour of numerical solutions by analysing the modified equation is known
as backward error analysis. If the original and modified equation share structural
properties, then the exact and approximate solution share geometric features such
as the existence of conserved quantities. Conjugate symplectic methods preserve
a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian
system. We show how a blended version of variational and symplectic techniques
can be used to compute modified symplectic and Hamiltonian structures. In contrast
to other approaches, our backward error analysis method does not rely on an ansatz
but computes the structures systematically, provided that a variational formulation
of the method is known. The technique is illustrated on the example of symmetric
linear multistep methods with matrix coefficients.
file_id: '32801'
file_name: BEA_MultiStep_Matrix.pdf
file_size: 827030
relation: main_file
title: Backward error analysis for conjugate symplectic methods
file_date_updated: 2022-08-12T16:48:59Z
has_accepted_license: '1'
intvolume: ' 15'
issue: '1'
keyword:
- variational integrators
- backward error analysis
- Euler--Lagrange equations
- multistep methods
- conjugate symplectic methods
language:
- iso: eng
oa: '1'
page: 98-115
publication: Journal of Geometric Mechanics
publication_status: published
publisher: AIMS Press
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/Christian-Offen/BEAConjugateSymplectic
status: public
title: Backward error analysis for conjugate symplectic methods
type: journal_article
user_id: '85279'
volume: 15
year: '2023'
...
---
_id: '37654'
abstract:
- lang: eng
text: "Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate
prior physical knowledge when\r\nlearning the dynamical equations of Hamiltonian
systems. Hereby, the symplectic system structure is preserved despite\r\nthe data-driven
modeling approach. However, preserving symmetries requires additional attention.
In this research, we\r\nenhance the HNN with a Lie algebra framework to detect
and embed symmetries in the neural network. This approach\r\nallows to simultaneously
learn the symmetry group action and the total energy of the system. As illustrating
examples,\r\na pendulum on a cart and a two-body problem from astrodynamics are
considered."
article_number: '063115'
article_type: original
author:
- first_name: Eva
full_name: Dierkes, Eva
last_name: Dierkes
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
citation:
ama: Dierkes E, Offen C, Ober-Blöbaum S, Flaßkamp K. Hamiltonian Neural Networks
with Automatic Symmetry Detection. Chaos. 2023;33(6). doi:10.1063/5.0142969
apa: Dierkes, E., Offen, C., Ober-Blöbaum, S., & Flaßkamp, K. (2023). Hamiltonian
Neural Networks with Automatic Symmetry Detection. Chaos, 33(6),
Article 063115. https://doi.org/10.1063/5.0142969
bibtex: '@article{Dierkes_Offen_Ober-Blöbaum_Flaßkamp_2023, title={Hamiltonian Neural
Networks with Automatic Symmetry Detection}, volume={33}, DOI={10.1063/5.0142969},
number={6063115}, journal={Chaos}, publisher={AIP Publishing}, author={Dierkes,
Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}, year={2023}
}'
chicago: Dierkes, Eva, Christian Offen, Sina Ober-Blöbaum, and Kathrin Flaßkamp.
“Hamiltonian Neural Networks with Automatic Symmetry Detection.” Chaos
33, no. 6 (2023). https://doi.org/10.1063/5.0142969.
ieee: 'E. Dierkes, C. Offen, S. Ober-Blöbaum, and K. Flaßkamp, “Hamiltonian Neural
Networks with Automatic Symmetry Detection,” Chaos, vol. 33, no. 6, Art.
no. 063115, 2023, doi: 10.1063/5.0142969.'
mla: Dierkes, Eva, et al. “Hamiltonian Neural Networks with Automatic Symmetry Detection.”
Chaos, vol. 33, no. 6, 063115, AIP Publishing, 2023, doi:10.1063/5.0142969.
short: E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023).
date_created: 2023-01-20T09:10:06Z
date_updated: 2023-08-10T08:37:01Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1063/5.0142969
external_id:
arxiv:
- '2301.07928'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2023-04-26T16:20:56Z
date_updated: 2023-04-26T16:20:56Z
description: |-
Incorporating physical system knowledge into data-driven
system identification has been shown to be beneficial. The
approach presented in this article combines learning of an
energy-conserving model from data with detecting a Lie
group representation of the unknown system symmetry.
The proposed approach can improve the learned model
and reveal underlying symmetry simultaneously.
file_id: '44205'
file_name: JournalPaper_main.pdf
file_size: 5200111
relation: main_file
title: Hamiltonian Neural Networks with Automatic Symmetry Detection
file_date_updated: 2023-04-26T16:20:56Z
has_accepted_license: '1'
intvolume: ' 33'
issue: '6'
language:
- iso: eng
oa: '1'
publication: Chaos
publication_identifier:
issn:
- 1054-1500
publication_status: published
publisher: AIP Publishing
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/eva-dierkes/HNN_withSymmetries
status: public
title: Hamiltonian Neural Networks with Automatic Symmetry Detection
type: journal_article
user_id: '85279'
volume: 33
year: '2023'
...
---
_id: '23428'
abstract:
- lang: eng
text: "The Koopman operator has become an essential tool for data-driven approximation
of dynamical (control) systems in recent years, e.g., via extended dynamic mode
decomposition. Despite its popularity, convergence results and, in particular,
error bounds are still quite scarce. In this paper, we derive probabilistic bounds
for the approximation error and the prediction error depending on the number of
training data points; for both ordinary and stochastic differential equations.
Moreover, we extend our analysis to nonlinear control-affine systems using either
ergodic trajectories or i.i.d.\r\nsamples. Here, we exploit the linearity of the
Koopman generator to obtain a bilinear system and, thus, circumvent the curse
of dimensionality since we do not autonomize the system by augmenting the state
by the control inputs. To the\r\nbest of our knowledge, this is the first finite-data
error analysis in the stochastic and/or control setting. Finally, we demonstrate
the effectiveness of the proposed approach by comparing it with state-of-the-art
techniques showing its superiority whenever state and control are coupled."
article_number: '14'
author:
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Friedrich
full_name: Philipp, Friedrich
last_name: Philipp
- first_name: Manuel
full_name: Schaller, Manuel
last_name: Schaller
- first_name: Karl
full_name: Worthmann, Karl
last_name: Worthmann
citation:
ama: Nüske F, Peitz S, Philipp F, Schaller M, Worthmann K. Finite-data error bounds
for Koopman-based prediction and control. Journal of Nonlinear Science.
2023;33. doi:10.1007/s00332-022-09862-1
apa: Nüske, F., Peitz, S., Philipp, F., Schaller, M., & Worthmann, K. (2023).
Finite-data error bounds for Koopman-based prediction and control. Journal
of Nonlinear Science, 33, Article 14. https://doi.org/10.1007/s00332-022-09862-1
bibtex: '@article{Nüske_Peitz_Philipp_Schaller_Worthmann_2023, title={Finite-data
error bounds for Koopman-based prediction and control}, volume={33}, DOI={10.1007/s00332-022-09862-1},
number={14}, journal={Journal of Nonlinear Science}, author={Nüske, Feliks and
Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl},
year={2023} }'
chicago: Nüske, Feliks, Sebastian Peitz, Friedrich Philipp, Manuel Schaller, and
Karl Worthmann. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.”
Journal of Nonlinear Science 33 (2023). https://doi.org/10.1007/s00332-022-09862-1.
ieee: 'F. Nüske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann, “Finite-data
error bounds for Koopman-based prediction and control,” Journal of Nonlinear
Science, vol. 33, Art. no. 14, 2023, doi: 10.1007/s00332-022-09862-1.'
mla: Nüske, Feliks, et al. “Finite-Data Error Bounds for Koopman-Based Prediction
and Control.” Journal of Nonlinear Science, vol. 33, 14, 2023, doi:10.1007/s00332-022-09862-1.
short: F. Nüske, S. Peitz, F. Philipp, M. Schaller, K. Worthmann, Journal of Nonlinear
Science 33 (2023).
date_created: 2021-08-17T12:25:09Z
date_updated: 2023-08-24T07:50:12Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s00332-022-09862-1
intvolume: ' 33'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf
oa: '1'
publication: Journal of Nonlinear Science
publication_status: published
status: public
title: Finite-data error bounds for Koopman-based prediction and control
type: journal_article
user_id: '47427'
volume: 33
year: '2023'
...
---
_id: '21600'
abstract:
- lang: eng
text: Many problems in science and engineering require an efficient numerical approximation
of integrals or solutions to differential equations. For systems with rapidly
changing dynamics, an equidistant discretization is often inadvisable as it results
in prohibitively large errors or computational effort. To this end, adaptive schemes,
such as solvers based on Runge–Kutta pairs, have been developed which adapt the
step size based on local error estimations at each step. While the classical schemes
apply very generally and are highly efficient on regular systems, they can behave
suboptimally when an inefficient step rejection mechanism is triggered by structurally
complex systems such as chaotic systems. To overcome these issues, we propose
a method to tailor numerical schemes to the problem class at hand. This is achieved
by combining simple, classical quadrature rules or ODE solvers with data-driven
time-stepping controllers. Compared with learning solution operators to ODEs directly,
it generalizes better to unseen initial data as our approach employs classical
numerical schemes as base methods. At the same time it can make use of identified
structures of a problem class and, therefore, outperforms state-of-the-art adaptive
schemes. Several examples demonstrate superior efficiency. Source code is available
at https://github.com/lueckem/quadrature-ML.
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Eyke
full_name: Hüllermeier, Eyke
id: '48129'
last_name: Hüllermeier
- first_name: Marvin
full_name: Lücke, Marvin
last_name: Lücke
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Karlson
full_name: Pfannschmidt, Karlson
id: '13472'
last_name: Pfannschmidt
orcid: 0000-0001-9407-7903
citation:
ama: Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical
integration using reinforcement learning. SIAM Journal on Scientific Computing.
2023;45(2):A579-A595. doi:10.1137/21M1412682
apa: Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz,
S., & Pfannschmidt, K. (2023). Efficient time stepping for numerical integration
using reinforcement learning. SIAM Journal on Scientific Computing, 45(2),
A579–A595. https://doi.org/10.1137/21M1412682
bibtex: '@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023,
title={Efficient time stepping for numerical integration using reinforcement
learning}, volume={45}, DOI={10.1137/21M1412682},
number={2}, journal={SIAM Journal on Scientific Computing}, author={Dellnitz,
Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen,
Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, year={2023}, pages={A579–A595}
}'
chicago: 'Dellnitz, Michael, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum,
Christian Offen, Sebastian Peitz, and Karlson Pfannschmidt. “Efficient Time Stepping
for Numerical Integration Using Reinforcement Learning.” SIAM Journal on Scientific
Computing 45, no. 2 (2023): A579–95. https://doi.org/10.1137/21M1412682.'
ieee: 'M. Dellnitz et al., “Efficient time stepping for numerical integration
using reinforcement learning,” SIAM Journal on Scientific Computing, vol.
45, no. 2, pp. A579–A595, 2023, doi: 10.1137/21M1412682.'
mla: Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration
Using Reinforcement Learning.” SIAM Journal on Scientific Computing, vol.
45, no. 2, 2023, pp. A579–95, doi:10.1137/21M1412682.
short: M. Dellnitz, E. Hüllermeier, M. Lücke, S. Ober-Blöbaum, C. Offen, S. Peitz,
K. Pfannschmidt, SIAM Journal on Scientific Computing 45 (2023) A579–A595.
date_created: 2021-04-09T07:59:19Z
date_updated: 2023-08-25T09:24:50Z
ddc:
- '510'
department:
- _id: '101'
- _id: '636'
- _id: '355'
- _id: '655'
doi: 10.1137/21M1412682
external_id:
arxiv:
- arXiv:2104.03562
has_accepted_license: '1'
intvolume: ' 45'
issue: '2'
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/reader/10.1137/21M1412682
page: A579-A595
publication: SIAM Journal on Scientific Computing
publication_status: published
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/lueckem/quadrature-ML
status: public
title: Efficient time stepping for numerical integration using reinforcement learning
type: journal_article
user_id: '47427'
volume: 45
year: '2023'
...