---
_id: '29868'
author:
- first_name: F.
full_name: Jiménez, F.
last_name: Jiménez
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Jiménez F, Ober-Blöbaum S. Fractional Damping Through Restricted Calculus
of Variations. In: Nichtlineare Sci 31. Vol 46. J Nonlinear Sci . ; 2021.'
apa: Jiménez, F., & Ober-Blöbaum, S. (2021). Fractional Damping Through Restricted
Calculus of Variations. Nichtlineare Sci 31, 46.
bibtex: '@inproceedings{Jiménez_Ober-Blöbaum_2021, series={J Nonlinear Sci }, title={Fractional
Damping Through Restricted Calculus of Variations}, volume={46}, booktitle={Nichtlineare
Sci 31}, author={Jiménez, F. and Ober-Blöbaum, Sina}, year={2021}, collection={J
Nonlinear Sci } }'
chicago: Jiménez, F., and Sina Ober-Blöbaum. “Fractional Damping Through Restricted
Calculus of Variations.” In Nichtlineare Sci 31, Vol. 46. J Nonlinear Sci
, 2021.
ieee: F. Jiménez and S. Ober-Blöbaum, “Fractional Damping Through Restricted Calculus
of Variations,” in Nichtlineare Sci 31, 2021, vol. 46.
mla: Jiménez, F., and Sina Ober-Blöbaum. “Fractional Damping Through Restricted
Calculus of Variations.” Nichtlineare Sci 31, vol. 46, 2021.
short: 'F. Jiménez, S. Ober-Blöbaum, in: Nichtlineare Sci 31, 2021.'
date_created: 2022-02-17T07:28:47Z
date_updated: 2023-11-29T10:23:46Z
department:
- _id: '636'
intvolume: ' 46'
language:
- iso: eng
publication: Nichtlineare Sci 31
series_title: 'J Nonlinear Sci '
status: public
title: Fractional Damping Through Restricted Calculus of Variations
type: conference
user_id: '15694'
volume: 46
year: '2021'
...
---
_id: '45967'
author:
- first_name: Tim
full_name: Binz, Tim
last_name: Binz
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Binz T, Kovács B. A convergent finite element algorithm for mean curvature
flow in higher codimension. arXiv. Published online 2021.
apa: Binz, T., & Kovács, B. (2021). A convergent finite element algorithm for
mean curvature flow in higher codimension. ArXiv.
bibtex: '@article{Binz_Kovács_2021, title={A convergent finite element algorithm
for mean curvature flow in higher codimension}, journal={arXiv}, author={Binz,
Tim and Kovács, Balázs}, year={2021} }'
chicago: Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for
Mean Curvature Flow in Higher Codimension.” ArXiv, 2021.
ieee: T. Binz and B. Kovács, “A convergent finite element algorithm for mean curvature
flow in higher codimension,” arXiv, 2021.
mla: Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for Mean
Curvature Flow in Higher Codimension.” ArXiv, 2021.
short: T. Binz, B. Kovács, ArXiv (2021).
date_created: 2023-07-10T11:46:16Z
date_updated: 2024-04-03T09:16:19Z
department:
- _id: '841'
language:
- iso: eng
publication: arXiv
status: public
title: A convergent finite element algorithm for mean curvature flow in higher codimension
type: journal_article
user_id: '100441'
year: '2021'
...
---
_id: '45962'
abstract:
- lang: eng
text: "Abstract\r\n An algorithm
is proposed for generalized mean curvature flow of closed two-dimensional surfaces,
which include inverse mean curvature flow and powers of mean and inverse mean
curvature flow. Error estimates are proved for semidiscretizations and full discretizations
for the generalized flow. The algorithm proposed and studied here combines evolving
surface finite elements, whose nodes determine the discrete surface, and linearly
implicit backward difference formulae for time integration. The numerical method
is based on a system coupling the surface evolution to nonlinear second-order
parabolic evolution equations for the normal velocity and normal vector. A convergence
proof is presented in the case of finite elements of polynomial degree at least
2 and backward difference formulae of orders 2 to 5. The error analysis combines
stability estimates and consistency estimates to yield optimal-order $H^1$-norm
error bounds for the computed surface position, velocity, normal vector, normal
velocity and therefore for the mean curvature. The stability analysis is performed
in the matrix–vector formulation and is independent of geometric arguments, which
only enter the consistency analysis. Numerical experiments are presented to illustrate
the convergence results and also to report on monotone quantities, e.g. Hawking
mass for inverse mean curvature flow, and complemented by experiments for nonconvex
surfaces."
author:
- first_name: Tim
full_name: Binz, Tim
last_name: Binz
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Binz T, Kovács B. A convergent finite element algorithm for generalized mean
curvature flows of closed surfaces. IMA Journal of Numerical Analysis.
2021;42(3):2545-2588. doi:10.1093/imanum/drab043
apa: Binz, T., & Kovács, B. (2021). A convergent finite element algorithm for
generalized mean curvature flows of closed surfaces. IMA Journal of Numerical
Analysis, 42(3), 2545–2588. https://doi.org/10.1093/imanum/drab043
bibtex: '@article{Binz_Kovács_2021, title={A convergent finite element algorithm
for generalized mean curvature flows of closed surfaces}, volume={42}, DOI={10.1093/imanum/drab043}, number={3},
journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
(OUP)}, author={Binz, Tim and Kovács, Balázs}, year={2021}, pages={2545–2588}
}'
chicago: 'Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for
Generalized Mean Curvature Flows of Closed Surfaces.” IMA Journal of Numerical
Analysis 42, no. 3 (2021): 2545–88. https://doi.org/10.1093/imanum/drab043.'
ieee: 'T. Binz and B. Kovács, “A convergent finite element algorithm for generalized
mean curvature flows of closed surfaces,” IMA Journal of Numerical Analysis,
vol. 42, no. 3, pp. 2545–2588, 2021, doi: 10.1093/imanum/drab043.'
mla: Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for Generalized
Mean Curvature Flows of Closed Surfaces.” IMA Journal of Numerical Analysis,
vol. 42, no. 3, Oxford University Press (OUP), 2021, pp. 2545–88, doi:10.1093/imanum/drab043.
short: T. Binz, B. Kovács, IMA Journal of Numerical Analysis 42 (2021) 2545–2588.
date_created: 2023-07-10T11:44:41Z
date_updated: 2024-04-03T09:18:40Z
department:
- _id: '841'
doi: 10.1093/imanum/drab043
intvolume: ' 42'
issue: '3'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 2545-2588
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: A convergent finite element algorithm for generalized mean curvature flows
of closed surfaces
type: journal_article
user_id: '100441'
volume: 42
year: '2021'
...
---
_id: '45957'
abstract:
- lang: eng
text: AbstractA proof of convergence is given for
a bulk–surface finite element semidiscretisation of the Cahn–Hilliard equation
with Cahn–Hilliard-type dynamic boundary conditions in a smooth domain. The semidiscretisation
is studied in an abstract weak formulation as a second-order system. Optimal-order
uniform-in-time error estimates are shown in the $L^2$- and $H^1$-norms. The error
estimates are based on a consistency and stability analysis. The proof of stability
is performed in an abstract framework, based on energy estimates exploiting the
anti-symmetric structure of the second-order system. Numerical experiments illustrate
the theoretical results.
author:
- first_name: Paula
full_name: Harder, Paula
last_name: Harder
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Harder P, Kovács B. Error estimates for the Cahn–Hilliard equation with dynamic
boundary conditions. IMA Journal of Numerical Analysis. 2021;42(3):2589-2620.
doi:10.1093/imanum/drab045
apa: Harder, P., & Kovács, B. (2021). Error estimates for the Cahn–Hilliard
equation with dynamic boundary conditions. IMA Journal of Numerical Analysis,
42(3), 2589–2620. https://doi.org/10.1093/imanum/drab045
bibtex: '@article{Harder_Kovács_2021, title={Error estimates for the Cahn–Hilliard
equation with dynamic boundary conditions}, volume={42}, DOI={10.1093/imanum/drab045},
number={3}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University
Press (OUP)}, author={Harder, Paula and Kovács, Balázs}, year={2021}, pages={2589–2620}
}'
chicago: 'Harder, Paula, and Balázs Kovács. “Error Estimates for the Cahn–Hilliard
Equation with Dynamic Boundary Conditions.” IMA Journal of Numerical Analysis
42, no. 3 (2021): 2589–2620. https://doi.org/10.1093/imanum/drab045.'
ieee: 'P. Harder and B. Kovács, “Error estimates for the Cahn–Hilliard equation
with dynamic boundary conditions,” IMA Journal of Numerical Analysis, vol.
42, no. 3, pp. 2589–2620, 2021, doi: 10.1093/imanum/drab045.'
mla: Harder, Paula, and Balázs Kovács. “Error Estimates for the Cahn–Hilliard Equation
with Dynamic Boundary Conditions.” IMA Journal of Numerical Analysis, vol.
42, no. 3, Oxford University Press (OUP), 2021, pp. 2589–620, doi:10.1093/imanum/drab045.
short: P. Harder, B. Kovács, IMA Journal of Numerical Analysis 42 (2021) 2589–2620.
date_created: 2023-07-10T11:43:28Z
date_updated: 2024-04-03T09:20:15Z
department:
- _id: '841'
doi: 10.1093/imanum/drab045
intvolume: ' 42'
issue: '3'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 2589-2620
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions
type: journal_article
user_id: '100441'
volume: 42
year: '2021'
...
---
_id: '45961'
author:
- first_name: Jörg
full_name: Nick, Jörg
last_name: Nick
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Christian
full_name: Lubich, Christian
last_name: Lubich
citation:
ama: 'Nick J, Kovács B, Lubich C. Correction to: Stable and convergent fully discrete
interior–exterior coupling of Maxwell’s equations. Numerische Mathematik.
2021;147(4):997-1000. doi:10.1007/s00211-021-01196-6'
apa: 'Nick, J., Kovács, B., & Lubich, C. (2021). Correction to: Stable and convergent
fully discrete interior–exterior coupling of Maxwell’s equations. Numerische
Mathematik, 147(4), 997–1000. https://doi.org/10.1007/s00211-021-01196-6'
bibtex: '@article{Nick_Kovács_Lubich_2021, title={Correction to: Stable and convergent
fully discrete interior–exterior coupling of Maxwell’s equations}, volume={147},
DOI={10.1007/s00211-021-01196-6},
number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business
Media LLC}, author={Nick, Jörg and Kovács, Balázs and Lubich, Christian}, year={2021},
pages={997–1000} }'
chicago: 'Nick, Jörg, Balázs Kovács, and Christian Lubich. “Correction to: Stable
and Convergent Fully Discrete Interior–Exterior Coupling of Maxwell’s Equations.”
Numerische Mathematik 147, no. 4 (2021): 997–1000. https://doi.org/10.1007/s00211-021-01196-6.'
ieee: 'J. Nick, B. Kovács, and C. Lubich, “Correction to: Stable and convergent
fully discrete interior–exterior coupling of Maxwell’s equations,” Numerische
Mathematik, vol. 147, no. 4, pp. 997–1000, 2021, doi: 10.1007/s00211-021-01196-6.'
mla: 'Nick, Jörg, et al. “Correction to: Stable and Convergent Fully Discrete Interior–Exterior
Coupling of Maxwell’s Equations.” Numerische Mathematik, vol. 147, no.
4, Springer Science and Business Media LLC, 2021, pp. 997–1000, doi:10.1007/s00211-021-01196-6.'
short: J. Nick, B. Kovács, C. Lubich, Numerische Mathematik 147 (2021) 997–1000.
date_created: 2023-07-10T11:44:25Z
date_updated: 2024-04-03T09:18:52Z
department:
- _id: '841'
doi: 10.1007/s00211-021-01196-6
intvolume: ' 147'
issue: '4'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 997-1000
publication: Numerische Mathematik
publication_identifier:
issn:
- 0029-599X
- 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: 'Correction to: Stable and convergent fully discrete interior–exterior coupling
of Maxwell’s equations'
type: journal_article
user_id: '100441'
volume: 147
year: '2021'
...
---
_id: '45959'
author:
- first_name: Balázs
full_name: Kovács, Balázs
last_name: Kovács
- first_name: Buyang
full_name: Li, Buyang
last_name: Li
- first_name: Christian
full_name: Lubich, Christian
last_name: Lubich
citation:
ama: Kovács B, Li B, Lubich C. A convergent evolving finite element algorithm for
Willmore flow of closed surfaces. Numerische Mathematik. 2021;149(3):595-643.
doi:10.1007/s00211-021-01238-z
apa: Kovács, B., Li, B., & Lubich, C. (2021). A convergent evolving finite element
algorithm for Willmore flow of closed surfaces. Numerische Mathematik,
149(3), 595–643. https://doi.org/10.1007/s00211-021-01238-z
bibtex: '@article{Kovács_Li_Lubich_2021, title={A convergent evolving finite element
algorithm for Willmore flow of closed surfaces}, volume={149}, DOI={10.1007/s00211-021-01238-z},
number={3}, journal={Numerische Mathematik}, publisher={Springer Science and Business
Media LLC}, author={Kovács, Balázs and Li, Buyang and Lubich, Christian}, year={2021},
pages={595–643} }'
chicago: 'Kovács, Balázs, Buyang Li, and Christian Lubich. “A Convergent Evolving
Finite Element Algorithm for Willmore Flow of Closed Surfaces.” Numerische
Mathematik 149, no. 3 (2021): 595–643. https://doi.org/10.1007/s00211-021-01238-z.'
ieee: 'B. Kovács, B. Li, and C. Lubich, “A convergent evolving finite element algorithm
for Willmore flow of closed surfaces,” Numerische Mathematik, vol. 149,
no. 3, pp. 595–643, 2021, doi: 10.1007/s00211-021-01238-z.'
mla: Kovács, Balázs, et al. “A Convergent Evolving Finite Element Algorithm for
Willmore Flow of Closed Surfaces.” Numerische Mathematik, vol. 149, no.
3, Springer Science and Business Media LLC, 2021, pp. 595–643, doi:10.1007/s00211-021-01238-z.
short: B. Kovács, B. Li, C. Lubich, Numerische Mathematik 149 (2021) 595–643.
date_created: 2023-07-10T11:43:59Z
date_updated: 2024-04-03T09:19:20Z
department:
- _id: '841'
doi: 10.1007/s00211-021-01238-z
intvolume: ' 149'
issue: '3'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 595-643
publication: Numerische Mathematik
publication_identifier:
issn:
- 0029-599X
- 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A convergent evolving finite element algorithm for Willmore flow of closed
surfaces
type: journal_article
user_id: '100441'
volume: 149
year: '2021'
...
---
_id: '55290'
author:
- first_name: St.
full_name: Baier, St.
last_name: Baier
- first_name: D.
full_name: Mazumder, D.
last_name: Mazumder
- first_name: Marc
full_name: Technau, Marc
id: '106108'
last_name: Technau
orcid: 0000-0001-9650-2459
citation:
ama: Baier St, Mazumder D, Technau M. On the distribution of αp modulo one in quadratic
number fields. Unif Distrib Theory. 2021;16(2):1–48. doi:10.2478/udt-2021-0006
apa: Baier, St., Mazumder, D., & Technau, M. (2021). On the distribution of
αp modulo one in quadratic number fields. Unif. Distrib. Theory, 16(2),
1–48. https://doi.org/10.2478/udt-2021-0006
bibtex: '@article{Baier_Mazumder_Technau_2021, title={On the distribution of αp
modulo one in quadratic number fields}, volume={16}, DOI={10.2478/udt-2021-0006},
number={2}, journal={Unif. Distrib. Theory}, author={Baier, St. and Mazumder,
D. and Technau, Marc}, year={2021}, pages={1–48} }'
chicago: 'Baier, St., D. Mazumder, and Marc Technau. “On the Distribution of Αp
modulo One in Quadratic Number Fields.” Unif. Distrib. Theory 16, no. 2
(2021): 1–48. https://doi.org/10.2478/udt-2021-0006.'
ieee: 'St. Baier, D. Mazumder, and M. Technau, “On the distribution of αp modulo
one in quadratic number fields,” Unif. Distrib. Theory, vol. 16, no. 2,
pp. 1–48, 2021, doi: 10.2478/udt-2021-0006.'
mla: Baier, St., et al. “On the Distribution of Αp modulo One in Quadratic Number
Fields.” Unif. Distrib. Theory, vol. 16, no. 2, 2021, pp. 1–48, doi:10.2478/udt-2021-0006.
short: St. Baier, D. Mazumder, M. Technau, Unif. Distrib. Theory 16 (2021) 1–48.
date_created: 2024-07-16T11:09:03Z
date_updated: 2024-07-24T07:23:43Z
department:
- _id: '102'
doi: 10.2478/udt-2021-0006
extern: '1'
intvolume: ' 16'
issue: '2'
language:
- iso: eng
page: 1–48
publication: Unif. Distrib. Theory
status: public
title: On the distribution of αp modulo one in quadratic number fields
type: journal_article
user_id: '106108'
volume: 16
year: '2021'
...
---
_id: '55289'
author:
- first_name: Marc
full_name: Technau, Marc
id: '106108'
last_name: Technau
orcid: 0000-0001-9650-2459
- first_name: A.
full_name: Zafeiropoulos, A.
last_name: Zafeiropoulos
citation:
ama: Technau M, Zafeiropoulos A. Metric results on summatory arithmetic functions
on Beatty sets. Acta Arith. 2021;197(1):93–104. doi:10.4064/aa200128-10-6
apa: Technau, M., & Zafeiropoulos, A. (2021). Metric results on summatory arithmetic
functions on Beatty sets. Acta Arith., 197(1), 93–104. https://doi.org/10.4064/aa200128-10-6
bibtex: '@article{Technau_Zafeiropoulos_2021, title={Metric results on summatory
arithmetic functions on Beatty sets}, volume={197}, DOI={10.4064/aa200128-10-6},
number={1}, journal={Acta Arith.}, author={Technau, Marc and Zafeiropoulos, A.},
year={2021}, pages={93–104} }'
chicago: 'Technau, Marc, and A. Zafeiropoulos. “Metric Results on Summatory Arithmetic
Functions on Beatty Sets.” Acta Arith. 197, no. 1 (2021): 93–104. https://doi.org/10.4064/aa200128-10-6.'
ieee: 'M. Technau and A. Zafeiropoulos, “Metric results on summatory arithmetic
functions on Beatty sets,” Acta Arith., vol. 197, no. 1, pp. 93–104, 2021,
doi: 10.4064/aa200128-10-6.'
mla: Technau, Marc, and A. Zafeiropoulos. “Metric Results on Summatory Arithmetic
Functions on Beatty Sets.” Acta Arith., vol. 197, no. 1, 2021, pp. 93–104,
doi:10.4064/aa200128-10-6.
short: M. Technau, A. Zafeiropoulos, Acta Arith. 197 (2021) 93–104.
date_created: 2024-07-16T11:09:03Z
date_updated: 2024-07-24T07:25:48Z
department:
- _id: '102'
doi: 10.4064/aa200128-10-6
extern: '1'
intvolume: ' 197'
issue: '1'
language:
- iso: eng
page: 93–104
publication: Acta Arith.
status: public
title: Metric results on summatory arithmetic functions on Beatty sets
type: journal_article
user_id: '106108'
volume: 197
year: '2021'
...
---
_id: '34840'
abstract:
- lang: eng
text: 'In this paper we obtain a complete list of imaginary n-quadratic fields with
class groups of exponent 3 and 5 under ERH for every positive integer n where
an n-quadratic field is a number field of degree 2ⁿ represented as the composite
of n quadratic fields. '
author:
- first_name: Jürgen
full_name: Klüners, Jürgen
id: '21202'
last_name: Klüners
- first_name: Toru
full_name: Komatsu, Toru
last_name: Komatsu
citation:
ama: Klüners J, Komatsu T. Imaginary multiquadratic number fields with class group
of exponent $3$ and $5$. Mathematics of Computation. 2021;90(329):1483-1497.
doi:10.1090/mcom/3609
apa: Klüners, J., & Komatsu, T. (2021). Imaginary multiquadratic number fields
with class group of exponent $3$ and $5$. Mathematics of Computation, 90(329),
1483–1497. https://doi.org/10.1090/mcom/3609
bibtex: '@article{Klüners_Komatsu_2021, title={Imaginary multiquadratic number fields
with class group of exponent $3$ and $5$}, volume={90}, DOI={10.1090/mcom/3609},
number={329}, journal={Mathematics of Computation}, publisher={American Mathematical
Society (AMS)}, author={Klüners, Jürgen and Komatsu, Toru}, year={2021}, pages={1483–1497}
}'
chicago: 'Klüners, Jürgen, and Toru Komatsu. “Imaginary Multiquadratic Number Fields
with Class Group of Exponent $3$ and $5$.” Mathematics of Computation 90,
no. 329 (2021): 1483–97. https://doi.org/10.1090/mcom/3609.'
ieee: 'J. Klüners and T. Komatsu, “Imaginary multiquadratic number fields with class
group of exponent $3$ and $5$,” Mathematics of Computation, vol. 90, no.
329, pp. 1483–1497, 2021, doi: 10.1090/mcom/3609.'
mla: Klüners, Jürgen, and Toru Komatsu. “Imaginary Multiquadratic Number Fields
with Class Group of Exponent $3$ and $5$.” Mathematics of Computation,
vol. 90, no. 329, American Mathematical Society (AMS), 2021, pp. 1483–97, doi:10.1090/mcom/3609.
short: J. Klüners, T. Komatsu, Mathematics of Computation 90 (2021) 1483–1497.
date_created: 2022-12-22T10:48:44Z
date_updated: 2023-03-06T08:57:45Z
department:
- _id: '102'
doi: 10.1090/mcom/3609
external_id:
arxiv:
- 2004.03308v2
intvolume: ' 90'
issue: '329'
keyword:
- Applied Mathematics
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 1483-1497
publication: Mathematics of Computation
publication_identifier:
issn:
- 0025-5718
- 1088-6842
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: Imaginary multiquadratic number fields with class group of exponent $3$ and
$5$
type: journal_article
user_id: '93826'
volume: 90
year: '2021'
...
---
_id: '34912'
abstract:
- lang: eng
text: 'Let E be an ordinary elliptic curve over a finite field and g be a positive
integer. Under some technical assumptions, we give an algorithm to span the isomorphism
classes of principally polarized abelian varieties in the isogeny class of E⁹
. The varieties are first described as hermitian lattices over (not necessarily
maximal) quadratic orders and then geometrically in terms of their algebraic theta
null point. We also show how to algebraically compute Siegel modular forms of
even weight given as polynomials in the theta constants by a careful choice of
an affine lift of the theta null point. We then use these results to give an algebraic
computation of Serre’s obstruction for principally polarized abelian threefolds
isogenous to E³ and of the Igusa modular form in dimension 4. We illustrate our
algorithms with examples of curves with many rational points over finite fields. '
author:
- first_name: Markus
full_name: Kirschmer, Markus
id: '82258'
last_name: Kirschmer
- first_name: Fabien
full_name: Narbonne, Fabien
last_name: Narbonne
- first_name: Christophe
full_name: Ritzenthaler, Christophe
last_name: Ritzenthaler
- first_name: Damien
full_name: Robert, Damien
last_name: Robert
citation:
ama: Kirschmer M, Narbonne F, Ritzenthaler C, Robert D. Spanning the isogeny class
of a power of an elliptic curve. Mathematics of Computation. 2021;91(333):401-449.
doi:10.1090/mcom/3672
apa: Kirschmer, M., Narbonne, F., Ritzenthaler, C., & Robert, D. (2021). Spanning
the isogeny class of a power of an elliptic curve. Mathematics of Computation,
91(333), 401–449. https://doi.org/10.1090/mcom/3672
bibtex: '@article{Kirschmer_Narbonne_Ritzenthaler_Robert_2021, title={Spanning the
isogeny class of a power of an elliptic curve}, volume={91}, DOI={10.1090/mcom/3672},
number={333}, journal={Mathematics of Computation}, publisher={American Mathematical
Society (AMS)}, author={Kirschmer, Markus and Narbonne, Fabien and Ritzenthaler,
Christophe and Robert, Damien}, year={2021}, pages={401–449} }'
chicago: 'Kirschmer, Markus, Fabien Narbonne, Christophe Ritzenthaler, and Damien
Robert. “Spanning the Isogeny Class of a Power of an Elliptic Curve.” Mathematics
of Computation 91, no. 333 (2021): 401–49. https://doi.org/10.1090/mcom/3672.'
ieee: 'M. Kirschmer, F. Narbonne, C. Ritzenthaler, and D. Robert, “Spanning the
isogeny class of a power of an elliptic curve,” Mathematics of Computation,
vol. 91, no. 333, pp. 401–449, 2021, doi: 10.1090/mcom/3672.'
mla: Kirschmer, Markus, et al. “Spanning the Isogeny Class of a Power of an Elliptic
Curve.” Mathematics of Computation, vol. 91, no. 333, American Mathematical
Society (AMS), 2021, pp. 401–49, doi:10.1090/mcom/3672.
short: M. Kirschmer, F. Narbonne, C. Ritzenthaler, D. Robert, Mathematics of Computation
91 (2021) 401–449.
date_created: 2022-12-23T11:02:02Z
date_updated: 2023-04-04T07:52:43Z
department:
- _id: '102'
doi: 10.1090/mcom/3672
intvolume: ' 91'
issue: '333'
keyword:
- Applied Mathematics
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 401-449
publication: Mathematics of Computation
publication_identifier:
issn:
- 0025-5718
- 1088-6842
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: Spanning the isogeny class of a power of an elliptic curve
type: journal_article
user_id: '93826'
volume: 91
year: '2021'
...
---
_id: '19938'
abstract:
- lang: eng
text: 'We show that symplectic integrators preserve bifurcations of Hamiltonian
boundary value problems and that nonsymplectic integrators do not. We provide
a universal description of the breaking of umbilic bifurcations by nonysmplectic
integrators. We discover extra structure induced from certain types of boundary
value problems, including classical Dirichlet problems, that is useful to locate
bifurcations. Geodesics connecting two points are an example of a Hamiltonian
boundary value problem, and we introduce the jet-RATTLE method, a symplectic integrator
that easily computes geodesics and their bifurcations. Finally, we study the periodic
pitchfork bifurcation, a codimension-1 bifurcation arising in integrable Hamiltonian
systems. It is not preserved by either symplectic on nonsymplectic integrators,
but in some circumstances symplecticity greatly reduces the error. '
article_type: original
author:
- first_name: Robert I
full_name: McLachlan, Robert I
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
citation:
ama: McLachlan RI, Offen C. Preservation of Bifurcations of Hamiltonian Boundary
Value Problems Under Discretisation. Foundations of Computational Mathematics.
2020;20(6):1363-1400. doi:10.1007/s10208-020-09454-z
apa: McLachlan, R. I., & Offen, C. (2020). Preservation of Bifurcations of Hamiltonian
Boundary Value Problems Under Discretisation. Foundations of Computational
Mathematics, 20(6), 1363–1400. https://doi.org/10.1007/s10208-020-09454-z
bibtex: '@article{McLachlan_Offen_2020, title={Preservation of Bifurcations of Hamiltonian
Boundary Value Problems Under Discretisation}, volume={20}, DOI={10.1007/s10208-020-09454-z},
number={6}, journal={Foundations of Computational Mathematics}, author={McLachlan,
Robert I and Offen, Christian}, year={2020}, pages={1363–1400} }'
chicago: 'McLachlan, Robert I, and Christian Offen. “Preservation of Bifurcations
of Hamiltonian Boundary Value Problems Under Discretisation.” Foundations of
Computational Mathematics 20, no. 6 (2020): 1363–1400. https://doi.org/10.1007/s10208-020-09454-z.'
ieee: R. I. McLachlan and C. Offen, “Preservation of Bifurcations of Hamiltonian
Boundary Value Problems Under Discretisation,” Foundations of Computational
Mathematics, vol. 20, no. 6, pp. 1363–1400, 2020.
mla: McLachlan, Robert I., and Christian Offen. “Preservation of Bifurcations of
Hamiltonian Boundary Value Problems Under Discretisation.” Foundations of Computational
Mathematics, vol. 20, no. 6, 2020, pp. 1363–400, doi:10.1007/s10208-020-09454-z.
short: R.I. McLachlan, C. Offen, Foundations of Computational Mathematics 20 (2020)
1363–1400.
date_created: 2020-10-06T16:31:46Z
date_updated: 2022-01-06T06:54:14Z
department:
- _id: '636'
doi: 10.1007/s10208-020-09454-z
extern: '1'
intvolume: ' 20'
issue: '6'
language:
- iso: eng
main_file_link:
- url: https://rdcu.be/b79aB
page: 1363-1400
publication: Foundations of Computational Mathematics
publication_status: published
status: public
title: Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation
type: journal_article
user_id: '85279'
volume: 20
year: '2020'
...
---
_id: '19939'
article_type: original
author:
- first_name: Lisa Maria
full_name: Kreusser, Lisa Maria
last_name: Kreusser
- first_name: Robert I
full_name: McLachlan, Robert I
last_name: McLachlan
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: https://orcid.org/0000-0002-5940-8057
citation:
ama: Kreusser LM, McLachlan RI, Offen C. Detection of high codimensional bifurcations
in variational PDEs. Nonlinearity. 2020;33(5):2335-2363. doi:10.1088/1361-6544/ab7293
apa: Kreusser, L. M., McLachlan, R. I., & Offen, C. (2020). Detection of high
codimensional bifurcations in variational PDEs. Nonlinearity, 33(5),
2335–2363. https://doi.org/10.1088/1361-6544/ab7293
bibtex: '@article{Kreusser_McLachlan_Offen_2020, title={Detection of high codimensional
bifurcations in variational PDEs}, volume={33}, DOI={10.1088/1361-6544/ab7293},
number={5}, journal={Nonlinearity}, author={Kreusser, Lisa Maria and McLachlan,
Robert I and Offen, Christian}, year={2020}, pages={2335–2363} }'
chicago: 'Kreusser, Lisa Maria, Robert I McLachlan, and Christian Offen. “Detection
of High Codimensional Bifurcations in Variational PDEs.” Nonlinearity 33,
no. 5 (2020): 2335–63. https://doi.org/10.1088/1361-6544/ab7293.'
ieee: L. M. Kreusser, R. I. McLachlan, and C. Offen, “Detection of high codimensional
bifurcations in variational PDEs,” Nonlinearity, vol. 33, no. 5, pp. 2335–2363,
2020.
mla: Kreusser, Lisa Maria, et al. “Detection of High Codimensional Bifurcations
in Variational PDEs.” Nonlinearity, vol. 33, no. 5, 2020, pp. 2335–63,
doi:10.1088/1361-6544/ab7293.
short: L.M. Kreusser, R.I. McLachlan, C. Offen, Nonlinearity 33 (2020) 2335–2363.
date_created: 2020-10-06T16:32:04Z
date_updated: 2022-01-06T06:54:14Z
department:
- _id: '636'
doi: 10.1088/1361-6544/ab7293
extern: '1'
intvolume: ' 33'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1088/1361-6544/ab7293
oa: '1'
page: 2335-2363
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: Detection of high codimensional bifurcations in variational PDEs
type: journal_article
user_id: '85279'
volume: 33
year: '2020'
...
---
_id: '17411'
abstract:
- lang: eng
text: Many dynamical systems possess symmetries, e.g. rotational and translational
invariances of mechanical systems. These can be beneficially exploited in the
design of numerical optimal control methods. We present a model predictive control
scheme which is based on a library of precomputed motion primitives. The primitives
are equivalence classes w.r.t. the symmetry of the optimal control problems. Trim
primitives as relative equilibria w.r.t. this symmetry, play a crucial role in
the algorithm. The approach is illustrated using an academic mobile robot example.
author:
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: 'Flaßkamp K, Ober-Blöbaum S, Peitz S. Symmetry in Optimal Control: A Multiobjective
Model Predictive Control Approach. In: Junge O, Schütze O, Froyland G, Ober-Blöbaum
S, Padberg-Gehle K, eds. Advances in Dynamics, Optimization and Computation.
Cham: Springer; 2020. doi:10.1007/978-3-030-51264-4_9'
apa: 'Flaßkamp, K., Ober-Blöbaum, S., & Peitz, S. (2020). Symmetry in Optimal
Control: A Multiobjective Model Predictive Control Approach. In O. Junge, O. Schütze,
G. Froyland, S. Ober-Blöbaum, & K. Padberg-Gehle (Eds.), Advances in Dynamics,
Optimization and Computation. Cham: Springer. https://doi.org/10.1007/978-3-030-51264-4_9'
bibtex: '@inbook{Flaßkamp_Ober-Blöbaum_Peitz_2020, place={Cham}, title={Symmetry
in Optimal Control: A Multiobjective Model Predictive Control Approach}, DOI={10.1007/978-3-030-51264-4_9},
booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer},
author={Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Peitz, Sebastian}, editor={Junge,
Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle,
KathrinEditors}, year={2020} }'
chicago: 'Flaßkamp, Kathrin, Sina Ober-Blöbaum, and Sebastian Peitz. “Symmetry in
Optimal Control: A Multiobjective Model Predictive Control Approach.” In Advances
in Dynamics, Optimization and Computation, edited by Oliver Junge, Oliver
Schütze, Gary Froyland, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle. Cham: Springer,
2020. https://doi.org/10.1007/978-3-030-51264-4_9.'
ieee: 'K. Flaßkamp, S. Ober-Blöbaum, and S. Peitz, “Symmetry in Optimal Control:
A Multiobjective Model Predictive Control Approach,” in Advances in Dynamics,
Optimization and Computation, O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum,
and K. Padberg-Gehle, Eds. Cham: Springer, 2020.'
mla: 'Flaßkamp, Kathrin, et al. “Symmetry in Optimal Control: A Multiobjective Model
Predictive Control Approach.” Advances in Dynamics, Optimization and Computation,
edited by Oliver Junge et al., Springer, 2020, doi:10.1007/978-3-030-51264-4_9.'
short: 'K. Flaßkamp, S. Ober-Blöbaum, S. Peitz, in: O. Junge, O. Schütze, G. Froyland,
S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and
Computation, Springer, Cham, 2020.'
date_created: 2020-07-27T09:50:19Z
date_updated: 2022-01-06T06:53:11Z
department:
- _id: '101'
doi: 10.1007/978-3-030-51264-4_9
editor:
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Kathrin
full_name: Padberg-Gehle, Kathrin
last_name: Padberg-Gehle
language:
- iso: eng
place: Cham
publication: Advances in Dynamics, Optimization and Computation
publication_identifier:
isbn:
- '9783030512637'
- '9783030512644'
issn:
- 2198-4182
- 2198-4190
publication_status: published
publisher: Springer
status: public
title: 'Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach'
type: book_chapter
user_id: '47427'
year: '2020'
...
---
_id: '21819'
abstract:
- lang: eng
text: Many dimensionality and model reduction techniques rely on estimating
dominant eigenfunctions of associated dynamical operators from data. Important
examples include the Koopman operator and its generator, but also the Schrödinger
operator. We propose a kernel-based method for the approximation of differential
operators in reproducing kernel Hilbert spaces and show how eigenfunctions can
be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms
are applied to molecular dynamics and quantum chemistry examples. Furthermore,
we exploit that, under certain conditions, the Schrödinger operator can be transformed
into a Kolmogorov backward operator corresponding to a drift-diffusion process
and vice versa. This allows us to apply methods developed for the analysis of
high-dimensional stochastic differential equations to quantum mechanical systems.
article_number: '722'
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Boumediene
full_name: Hamzi, Boumediene
last_name: Hamzi
citation:
ama: Klus S, Nüske F, Hamzi B. Kernel-Based Approximation of the Koopman Generator
and Schrödinger Operator. Entropy. 2020. doi:10.3390/e22070722
apa: Klus, S., Nüske, F., & Hamzi, B. (2020). Kernel-Based Approximation of
the Koopman Generator and Schrödinger Operator. Entropy. https://doi.org/10.3390/e22070722
bibtex: '@article{Klus_Nüske_Hamzi_2020, title={Kernel-Based Approximation of the
Koopman Generator and Schrödinger Operator}, DOI={10.3390/e22070722},
number={722}, journal={Entropy}, author={Klus, Stefan and Nüske, Feliks and Hamzi,
Boumediene}, year={2020} }'
chicago: Klus, Stefan, Feliks Nüske, and Boumediene Hamzi. “Kernel-Based Approximation
of the Koopman Generator and Schrödinger Operator.” Entropy, 2020. https://doi.org/10.3390/e22070722.
ieee: S. Klus, F. Nüske, and B. Hamzi, “Kernel-Based Approximation of the Koopman
Generator and Schrödinger Operator,” Entropy, 2020.
mla: Klus, Stefan, et al. “Kernel-Based Approximation of the Koopman Generator and
Schrödinger Operator.” Entropy, 722, 2020, doi:10.3390/e22070722.
short: S. Klus, F. Nüske, B. Hamzi, Entropy (2020).
date_created: 2021-04-28T18:06:35Z
date_updated: 2022-01-06T06:55:16Z
department:
- _id: '101'
doi: 10.3390/e22070722
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.mdpi.com/1099-4300/22/7/722
oa: '1'
publication: Entropy
publication_identifier:
issn:
- 1099-4300
publication_status: published
status: public
title: Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator
type: journal_article
user_id: '81513'
year: '2020'
...
---
_id: '10596'
abstract:
- lang: eng
text: Multi-objective optimization is an active field of research that has many
applications. Owing to its success and because decision-making processes are becoming
more and more complex, there is a recent trend for incorporating many objectives
into such problems. The challenge with such problems, however, is that the dimensions
of the solution sets—the so-called Pareto sets and fronts—grow with the number
of objectives. It is thus no longer possible to compute or to approximate the
entire solution set of a given problem that contains many (e.g. more than three)
objectives. On the other hand, the computation of single solutions (e.g. via scalarization
methods) leads to unsatisfying results in many cases, even if user preferences
are incorporated. In this article, the Pareto Explorer tool is presented—a global/local
exploration tool for the treatment of many-objective optimization problems (MaOPs).
In the first step, a solution of the problem is computed via a global search algorithm
that ideally already includes user preferences. In the second step, a local search
along the Pareto set/front of the given MaOP is performed in user specified directions.
For this, several continuation-like procedures are proposed that can incorporate
preferences defined in decision, objective, or in weight space. The applicability
and usefulness of Pareto Explorer is demonstrated on benchmark problems as well
as on an application from industrial laundry design.
article_type: original
author:
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Oliver
full_name: Cuate, Oliver
last_name: Cuate
- first_name: Adanay
full_name: Martín, Adanay
last_name: Martín
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Schütze O, Cuate O, Martín A, Peitz S, Dellnitz M. Pareto Explorer: a global/local
exploration tool for many-objective optimization problems. Engineering Optimization.
2020;52(5):832-855. doi:10.1080/0305215x.2019.1617286'
apa: 'Schütze, O., Cuate, O., Martín, A., Peitz, S., & Dellnitz, M. (2020).
Pareto Explorer: a global/local exploration tool for many-objective optimization
problems. Engineering Optimization, 52(5), 832–855. https://doi.org/10.1080/0305215x.2019.1617286'
bibtex: '@article{Schütze_Cuate_Martín_Peitz_Dellnitz_2020, title={Pareto Explorer:
a global/local exploration tool for many-objective optimization problems}, volume={52},
DOI={10.1080/0305215x.2019.1617286},
number={5}, journal={Engineering Optimization}, author={Schütze, Oliver and Cuate,
Oliver and Martín, Adanay and Peitz, Sebastian and Dellnitz, Michael}, year={2020},
pages={832–855} }'
chicago: 'Schütze, Oliver, Oliver Cuate, Adanay Martín, Sebastian Peitz, and Michael
Dellnitz. “Pareto Explorer: A Global/Local Exploration Tool for Many-Objective
Optimization Problems.” Engineering Optimization 52, no. 5 (2020): 832–55.
https://doi.org/10.1080/0305215x.2019.1617286.'
ieee: 'O. Schütze, O. Cuate, A. Martín, S. Peitz, and M. Dellnitz, “Pareto Explorer:
a global/local exploration tool for many-objective optimization problems,” Engineering
Optimization, vol. 52, no. 5, pp. 832–855, 2020.'
mla: 'Schütze, Oliver, et al. “Pareto Explorer: A Global/Local Exploration Tool
for Many-Objective Optimization Problems.” Engineering Optimization, vol.
52, no. 5, 2020, pp. 832–55, doi:10.1080/0305215x.2019.1617286.'
short: O. Schütze, O. Cuate, A. Martín, S. Peitz, M. Dellnitz, Engineering Optimization
52 (2020) 832–855.
date_created: 2019-07-10T08:14:39Z
date_updated: 2022-01-06T06:50:46Z
department:
- _id: '101'
doi: 10.1080/0305215x.2019.1617286
intvolume: ' 52'
issue: '5'
language:
- iso: eng
page: 832-855
publication: Engineering Optimization
publication_identifier:
issn:
- 0305-215X
- 1029-0273
publication_status: published
status: public
title: 'Pareto Explorer: a global/local exploration tool for many-objective optimization
problems'
type: journal_article
user_id: '47427'
volume: 52
year: '2020'
...
---
_id: '16288'
abstract:
- lang: eng
text: We derive a data-driven method for the approximation of the Koopman generator
called gEDMD, which can be regarded as a straightforward extension of EDMD (extended
dynamic mode decomposition). This approach is applicable to deterministic and
stochastic dynamical systems. It can be used for computing eigenvalues, eigenfunctions,
and modes of the generator and for system identification. In addition to learning
the governing equations of deterministic systems, which then reduces to SINDy
(sparse identification of nonlinear dynamics), it is possible to identify the
drift and diffusion terms of stochastic differential equations from data. Moreover,
we apply gEDMD to derive coarse-grained models of high-dimensional systems, and
also to determine efficient model predictive control strategies. We highlight
relationships with other methods and demonstrate the efficacy of the proposed
methods using several guiding examples and prototypical molecular dynamics problems.
article_number: '132416'
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Jan-Hendrik
full_name: Niemann, Jan-Hendrik
last_name: Niemann
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
- first_name: Christof
full_name: Schütte, Christof
last_name: Schütte
citation:
ama: 'Klus S, Nüske F, Peitz S, Niemann J-H, Clementi C, Schütte C. Data-driven
approximation of the Koopman generator: Model reduction, system identification,
and control. Physica D: Nonlinear Phenomena. 2020;406. doi:10.1016/j.physd.2020.132416'
apa: 'Klus, S., Nüske, F., Peitz, S., Niemann, J.-H., Clementi, C., & Schütte,
C. (2020). Data-driven approximation of the Koopman generator: Model reduction,
system identification, and control. Physica D: Nonlinear Phenomena, 406.
https://doi.org/10.1016/j.physd.2020.132416'
bibtex: '@article{Klus_Nüske_Peitz_Niemann_Clementi_Schütte_2020, title={Data-driven
approximation of the Koopman generator: Model reduction, system identification,
and control}, volume={406}, DOI={10.1016/j.physd.2020.132416},
number={132416}, journal={Physica D: Nonlinear Phenomena}, author={Klus, Stefan
and Nüske, Feliks and Peitz, Sebastian and Niemann, Jan-Hendrik and Clementi,
Cecilia and Schütte, Christof}, year={2020} }'
chicago: 'Klus, Stefan, Feliks Nüske, Sebastian Peitz, Jan-Hendrik Niemann, Cecilia
Clementi, and Christof Schütte. “Data-Driven Approximation of the Koopman Generator:
Model Reduction, System Identification, and Control.” Physica D: Nonlinear
Phenomena 406 (2020). https://doi.org/10.1016/j.physd.2020.132416.'
ieee: 'S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, and C. Schütte,
“Data-driven approximation of the Koopman generator: Model reduction, system identification,
and control,” Physica D: Nonlinear Phenomena, vol. 406, 2020.'
mla: 'Klus, Stefan, et al. “Data-Driven Approximation of the Koopman Generator:
Model Reduction, System Identification, and Control.” Physica D: Nonlinear
Phenomena, vol. 406, 132416, 2020, doi:10.1016/j.physd.2020.132416.'
short: 'S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, C. Schütte, Physica
D: Nonlinear Phenomena 406 (2020).'
date_created: 2020-03-13T12:35:40Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1016/j.physd.2020.132416
intvolume: ' 406'
language:
- iso: eng
publication: 'Physica D: Nonlinear Phenomena'
publication_identifier:
issn:
- 0167-2789
publication_status: published
status: public
title: 'Data-driven approximation of the Koopman generator: Model reduction, system
identification, and control'
type: journal_article
user_id: '47427'
volume: 406
year: '2020'
...
---
_id: '16289'
abstract:
- lang: eng
text: In the development of model predictive controllers for PDE-constrained problems,
the use of reduced order models is essential to enable real-time applicability.
Besides local linearization approaches, proper orthogonal decomposition (POD)
has been most widely used in the past in order to derive such models. Due to the
huge advances concerning both theory as well as the numerical approximation, a
very promising alternative based on the Koopman operator has recently emerged.
In this chapter, we present two control strategies for model predictive control
of nonlinear PDEs using data-efficient approximations of the Koopman operator.
In the first one, the dynamic control system is replaced by a small number of
autonomous systems with different yet constant inputs. The control problem is
consequently transformed into a switching problem. In the second approach, a bilinear
surrogate model is obtained via a convex combination of these autonomous systems.
Using a recent convergence result for extended dynamic mode decomposition (EDMD),
convergence of the reduced objective function can be shown. We study the properties
of these two strategies with respect to solution quality, data requirements, and
complexity of the resulting optimization problem using the 1-dimensional Burgers
equation and the 2-dimensional Navier–Stokes equations as examples. Finally, an
extension for online adaptivity is presented.
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
citation:
ama: 'Peitz S, Klus S. Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced
Order Models Based on the Koopman Operator. In: Lecture Notes in Control and
Information Sciences. Vol 484. Lecture Notes in Control and Information Sciences.
Cham: Springer; 2020:257-282. doi:10.1007/978-3-030-35713-9_10'
apa: 'Peitz, S., & Klus, S. (2020). Feedback Control of Nonlinear PDEs Using
Data-Efficient Reduced Order Models Based on the Koopman Operator. In Lecture
Notes in Control and Information Sciences (Vol. 484, pp. 257–282). Cham: Springer.
https://doi.org/10.1007/978-3-030-35713-9_10'
bibtex: '@inbook{Peitz_Klus_2020, place={Cham}, series={Lecture Notes in Control
and Information Sciences}, title={Feedback Control of Nonlinear PDEs Using Data-Efficient
Reduced Order Models Based on the Koopman Operator}, volume={484}, DOI={10.1007/978-3-030-35713-9_10},
booktitle={Lecture Notes in Control and Information Sciences}, publisher={Springer},
author={Peitz, Sebastian and Klus, Stefan}, year={2020}, pages={257–282}, collection={Lecture
Notes in Control and Information Sciences} }'
chicago: 'Peitz, Sebastian, and Stefan Klus. “Feedback Control of Nonlinear PDEs
Using Data-Efficient Reduced Order Models Based on the Koopman Operator.” In Lecture
Notes in Control and Information Sciences, 484:257–82. Lecture Notes in Control
and Information Sciences. Cham: Springer, 2020. https://doi.org/10.1007/978-3-030-35713-9_10.'
ieee: 'S. Peitz and S. Klus, “Feedback Control of Nonlinear PDEs Using Data-Efficient
Reduced Order Models Based on the Koopman Operator,” in Lecture Notes in Control
and Information Sciences, vol. 484, Cham: Springer, 2020, pp. 257–282.'
mla: Peitz, Sebastian, and Stefan Klus. “Feedback Control of Nonlinear PDEs Using
Data-Efficient Reduced Order Models Based on the Koopman Operator.” Lecture
Notes in Control and Information Sciences, vol. 484, Springer, 2020, pp. 257–82,
doi:10.1007/978-3-030-35713-9_10.
short: 'S. Peitz, S. Klus, in: Lecture Notes in Control and Information Sciences,
Springer, Cham, 2020, pp. 257–282.'
date_created: 2020-03-13T12:38:52Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1007/978-3-030-35713-9_10
intvolume: ' 484'
language:
- iso: eng
page: 257-282
place: Cham
publication: Lecture Notes in Control and Information Sciences
publication_identifier:
isbn:
- '9783030357122'
- '9783030357139'
issn:
- 0170-8643
- 1610-7411
publication_status: published
publisher: Springer
series_title: Lecture Notes in Control and Information Sciences
status: public
title: Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models
Based on the Koopman Operator
type: book_chapter
user_id: '47427'
volume: 484
year: '2020'
...
---
_id: '16290'
abstract:
- lang: eng
text: The control of complex systems is of critical importance in many branches
of science, engineering, and industry, many of which are governed by nonlinear
partial differential equations. Controlling an unsteady fluid flow is particularly
important, as flow control is a key enabler for technologies in energy (e.g.,
wind, tidal, and combustion), transportation (e.g., planes, trains, and automobiles),
security (e.g., tracking airborne contamination), and health (e.g., artificial
hearts and artificial respiration). However, the high-dimensional, nonlinear,
and multi-scale dynamics make real-time feedback control infeasible. Fortunately,
these high- dimensional systems exhibit dominant, low-dimensional patterns of
activity that can be exploited for effective control in the sense that knowledge
of the entire state of a system is not required. Advances in machine learning
have the potential to revolutionize flow control given its ability to extract
principled, low-rank feature spaces characterizing such complex systems.We present
a novel deep learning modelpredictive control framework that exploits low-rank
features of the flow in order to achieve considerable improvements to control
performance. Instead of predicting the entire fluid state, we use a recurrent
neural network (RNN) to accurately predict the control relevant quantities of
the system, which are then embedded into an MPC framework to construct a feedback
loop. In order to lower the data requirements and to improve the prediction accuracy
and thus the control performance, incoming sensor data are used to update the
RNN online. The results are validated using varying fluid flow examples of increasing
complexity.
article_type: original
author:
- 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: https://orcid.org/0000-0002-3389-793X
- first_name: Steven L.
full_name: Brunton, Steven L.
last_name: Brunton
- first_name: J. Nathan
full_name: Kutz, J. Nathan
last_name: Kutz
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Bieker K, Peitz S, Brunton SL, Kutz JN, Dellnitz M. Deep model predictive flow
control with limited sensor data and online learning. Theoretical and Computational
Fluid Dynamics. 2020;34:577–591. doi:10.1007/s00162-020-00520-4
apa: Bieker, K., Peitz, S., Brunton, S. L., Kutz, J. N., & Dellnitz, M. (2020).
Deep model predictive flow control with limited sensor data and online learning.
Theoretical and Computational Fluid Dynamics, 34, 577–591. https://doi.org/10.1007/s00162-020-00520-4
bibtex: '@article{Bieker_Peitz_Brunton_Kutz_Dellnitz_2020, title={Deep model predictive
flow control with limited sensor data and online learning}, volume={34}, DOI={10.1007/s00162-020-00520-4},
journal={Theoretical and Computational Fluid Dynamics}, author={Bieker, Katharina
and Peitz, Sebastian and Brunton, Steven L. and Kutz, J. Nathan and Dellnitz,
Michael}, year={2020}, pages={577–591} }'
chicago: 'Bieker, Katharina, Sebastian Peitz, Steven L. Brunton, J. Nathan Kutz,
and Michael Dellnitz. “Deep Model Predictive Flow Control with Limited Sensor
Data and Online Learning.” Theoretical and Computational Fluid Dynamics
34 (2020): 577–591. https://doi.org/10.1007/s00162-020-00520-4.'
ieee: K. Bieker, S. Peitz, S. L. Brunton, J. N. Kutz, and M. Dellnitz, “Deep model
predictive flow control with limited sensor data and online learning,” Theoretical
and Computational Fluid Dynamics, vol. 34, pp. 577–591, 2020.
mla: Bieker, Katharina, et al. “Deep Model Predictive Flow Control with Limited
Sensor Data and Online Learning.” Theoretical and Computational Fluid Dynamics,
vol. 34, 2020, pp. 577–591, doi:10.1007/s00162-020-00520-4.
short: K. Bieker, S. Peitz, S.L. Brunton, J.N. Kutz, M. Dellnitz, Theoretical and
Computational Fluid Dynamics 34 (2020) 577–591.
date_created: 2020-03-13T12:40:09Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1007/s00162-020-00520-4
intvolume: ' 34'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s00162-020-00520-4.pdf
oa: '1'
page: 577–591
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: Theoretical and Computational Fluid Dynamics
publication_identifier:
issn:
- 0935-4964
- 1432-2250
publication_status: published
status: public
title: Deep model predictive flow control with limited sensor data and online learning
type: journal_article
user_id: '47427'
volume: 34
year: '2020'
...
---
_id: '16309'
abstract:
- lang: eng
text: "In recent years, the success of the Koopman operator in dynamical systems\r\nanalysis
has also fueled the development of Koopman operator-based control\r\nframeworks.
In order to preserve the relatively low data requirements for an\r\napproximation
via Dynamic Mode Decomposition, a quantization approach was\r\nrecently proposed
in [Peitz & Klus, Automatica 106, 2019]. This way, control\r\nof nonlinear dynamical
systems can be realized by means of switched systems\r\ntechniques, using only
a finite set of autonomous Koopman operator-based\r\nreduced models. These individual
systems can be approximated very efficiently\r\nfrom data. The main idea is to
transform a control system into a set of\r\nautonomous systems for which the optimal
switching sequence has to be computed.\r\nIn this article, we extend these results
to continuous control inputs using\r\nrelaxation. This way, we combine the advantages
of the data efficiency of\r\napproximating a finite set of autonomous systems
with continuous controls. We\r\nshow that when using the Koopman generator, this
relaxation --- realized by\r\nlinear interpolation between two operators --- does
not introduce any error for\r\ncontrol affine systems. This allows us to control
high-dimensional nonlinear\r\nsystems using bilinear, low-dimensional surrogate
models. The efficiency of the\r\nproposed approach is demonstrated using several
examples with increasing\r\ncomplexity, from the Duffing oscillator to the chaotic
fluidic pinball."
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Samuel E.
full_name: Otto, Samuel E.
last_name: Otto
- first_name: Clarence W.
full_name: Rowley, Clarence W.
last_name: Rowley
citation:
ama: Peitz S, Otto SE, Rowley CW. Data-Driven Model Predictive Control using Interpolated
Koopman Generators. SIAM Journal on Applied Dynamical Systems. 2020;19(3):2162-2193.
doi:10.1137/20M1325678
apa: Peitz, S., Otto, S. E., & Rowley, C. W. (2020). Data-Driven Model Predictive
Control using Interpolated Koopman Generators. SIAM Journal on Applied Dynamical
Systems, 19(3), 2162–2193. https://doi.org/10.1137/20M1325678
bibtex: '@article{Peitz_Otto_Rowley_2020, title={Data-Driven Model Predictive Control
using Interpolated Koopman Generators}, volume={19}, DOI={10.1137/20M1325678},
number={3}, journal={SIAM Journal on Applied Dynamical Systems}, author={Peitz,
Sebastian and Otto, Samuel E. and Rowley, Clarence W.}, year={2020}, pages={2162–2193}
}'
chicago: 'Peitz, Sebastian, Samuel E. Otto, and Clarence W. Rowley. “Data-Driven
Model Predictive Control Using Interpolated Koopman Generators.” SIAM Journal
on Applied Dynamical Systems 19, no. 3 (2020): 2162–93. https://doi.org/10.1137/20M1325678.'
ieee: S. Peitz, S. E. Otto, and C. W. Rowley, “Data-Driven Model Predictive Control
using Interpolated Koopman Generators,” SIAM Journal on Applied Dynamical
Systems, vol. 19, no. 3, pp. 2162–2193, 2020.
mla: Peitz, Sebastian, et al. “Data-Driven Model Predictive Control Using Interpolated
Koopman Generators.” SIAM Journal on Applied Dynamical Systems, vol. 19,
no. 3, 2020, pp. 2162–93, doi:10.1137/20M1325678.
short: S. Peitz, S.E. Otto, C.W. Rowley, SIAM Journal on Applied Dynamical Systems
19 (2020) 2162–2193.
date_created: 2020-03-17T09:53:01Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1137/20M1325678
intvolume: ' 19'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/pdf/10.1137/20M1325678
page: 2162-2193
publication: SIAM Journal on Applied Dynamical Systems
status: public
title: Data-Driven Model Predictive Control using Interpolated Koopman Generators
type: journal_article
user_id: '47427'
volume: 19
year: '2020'
...
---
_id: '29399'
author:
- first_name: D. J. N.
full_name: Limebeer, D. J. N.
last_name: Limebeer
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: F. H.
full_name: Farshi, F. H.
last_name: Farshi
citation:
ama: Limebeer DJN, Ober-Blöbaum S, Farshi FH. Variational integrators for dissipative
systems. IEEE Transactions on Automatic Control. 2020;65(4):1381-1396.
apa: Limebeer, D. J. N., Ober-Blöbaum, S., & Farshi, F. H. (2020). Variational
integrators for dissipative systems. IEEE Transactions on Automatic Control,
65(4), 1381–1396.
bibtex: '@article{Limebeer_Ober-Blöbaum_Farshi_2020, title={Variational integrators
for dissipative systems}, volume={65(4)}, journal={IEEE Transactions on Automatic
Control}, author={Limebeer, D. J. N. and Ober-Blöbaum, Sina and Farshi, F. H.},
year={2020}, pages={1381–1396} }'
chicago: 'Limebeer, D. J. N., Sina Ober-Blöbaum, and F. H. Farshi. “Variational
Integrators for Dissipative Systems.” IEEE Transactions on Automatic Control
65(4) (2020): 1381–96.'
ieee: D. J. N. Limebeer, S. Ober-Blöbaum, and F. H. Farshi, “Variational integrators
for dissipative systems,” IEEE Transactions on Automatic Control, vol.
65(4), pp. 1381–1396, 2020.
mla: Limebeer, D. J. N., et al. “Variational Integrators for Dissipative Systems.”
IEEE Transactions on Automatic Control, vol. 65(4), 2020, pp. 1381–96.
short: D.J.N. Limebeer, S. Ober-Blöbaum, F.H. Farshi, IEEE Transactions on Automatic
Control 65(4) (2020) 1381–1396.
date_created: 2022-01-18T11:17:25Z
date_updated: 2022-01-21T08:26:46Z
department:
- _id: '636'
language:
- iso: eng
page: 1381-1396
publication: IEEE Transactions on Automatic Control
status: public
title: Variational integrators for dissipative systems
type: journal_article
user_id: '15694'
volume: 65(4)
year: '2020'
...