---
_id: '46117'
abstract:
- lang: eng
  text: "Let $X=X_1\\times X_2$ be a product of two rank one symmetric spaces of\r\nnon-compact
    type and $\\Gamma$ a torsion-free discrete subgroup in $G_1\\times\r\nG_2$. We
    show that the spectrum of $\\Gamma \\backslash X$ is related to the\r\nasymptotic
    growth of $\\Gamma$ in the two direction defined by the two factors.\r\nWe obtain
    that $L^2(\\Gamma \\backslash G)$ is tempered for large class of\r\n$\\Gamma$."
author:
- first_name: Tobias
  full_name: Weich, Tobias
  last_name: Weich
- first_name: Lasse L.
  full_name: Wolf, Lasse L.
  last_name: Wolf
citation:
  ama: 'Weich T, Wolf LL. Temperedness of locally symmetric spaces: The product case.
    <i>arXiv:230409573</i>. Published online 2023.'
  apa: 'Weich, T., &#38; Wolf, L. L. (2023). Temperedness of locally symmetric spaces:
    The product case. In <i>arXiv:2304.09573</i>.'
  bibtex: '@article{Weich_Wolf_2023, title={Temperedness of locally symmetric spaces:
    The product case}, journal={arXiv:2304.09573}, author={Weich, Tobias and Wolf,
    Lasse L.}, year={2023} }'
  chicago: 'Weich, Tobias, and Lasse L. Wolf. “Temperedness of Locally Symmetric Spaces:
    The Product Case.” <i>ArXiv:2304.09573</i>, 2023.'
  ieee: 'T. Weich and L. L. Wolf, “Temperedness of locally symmetric spaces: The product
    case,” <i>arXiv:2304.09573</i>. 2023.'
  mla: 'Weich, Tobias, and Lasse L. Wolf. “Temperedness of Locally Symmetric Spaces:
    The Product Case.” <i>ArXiv:2304.09573</i>, 2023.'
  short: T. Weich, L.L. Wolf, ArXiv:2304.09573 (2023).
date_created: 2023-07-24T07:52:23Z
date_updated: 2023-07-24T07:53:29Z
department:
- _id: '10'
external_id:
  arxiv:
  - '2304.09573'
language:
- iso: eng
publication: arXiv:2304.09573
status: public
title: 'Temperedness of locally symmetric spaces: The product case'
type: preprint
user_id: '45027'
year: '2023'
...
---
_id: '46147'
author:
- first_name: Anian
  full_name: Brosch, Anian
  id: '75779'
  last_name: Brosch
  orcid: 0000-0003-4871-1664
- first_name: Fabio
  full_name: Tinazzi, Fabio
  last_name: Tinazzi
- first_name: Oliver
  full_name: Wallscheid, Oliver
  id: '11291'
  last_name: Wallscheid
  orcid: https://orcid.org/0000-0001-9362-8777
- first_name: Mauro
  full_name: Zigliotto, Mauro
  last_name: Zigliotto
- first_name: Joachim
  full_name: Böcker, Joachim
  id: '66'
  last_name: Böcker
  orcid: 0000-0002-8480-7295
citation:
  ama: Brosch A, Tinazzi F, Wallscheid O, Zigliotto M, Böcker J. Finite Set Sensorless
    Control With Minimum a Priori Knowledge and Tuning Effort for Interior Permanent
    Magnet Synchronous Motors. <i>IEEE Transactions on Power Electronics</i>. Published
    online 2023. doi:<a href="https://doi.org/10.1109/tpel.2023.3294557">10.1109/tpel.2023.3294557</a>
  apa: Brosch, A., Tinazzi, F., Wallscheid, O., Zigliotto, M., &#38; Böcker, J. (2023).
    Finite Set Sensorless Control With Minimum a Priori Knowledge and Tuning Effort
    for Interior Permanent Magnet Synchronous Motors. <i>IEEE Transactions on Power
    Electronics</i>. <a href="https://doi.org/10.1109/tpel.2023.3294557">https://doi.org/10.1109/tpel.2023.3294557</a>
  bibtex: '@article{Brosch_Tinazzi_Wallscheid_Zigliotto_Böcker_2023, title={Finite
    Set Sensorless Control With Minimum a Priori Knowledge and Tuning Effort for Interior
    Permanent Magnet Synchronous Motors}, DOI={<a href="https://doi.org/10.1109/tpel.2023.3294557">10.1109/tpel.2023.3294557</a>},
    journal={IEEE Transactions on Power Electronics}, publisher={Institute of Electrical
    and Electronics Engineers (IEEE)}, author={Brosch, Anian and Tinazzi, Fabio and
    Wallscheid, Oliver and Zigliotto, Mauro and Böcker, Joachim}, year={2023} }'
  chicago: Brosch, Anian, Fabio Tinazzi, Oliver Wallscheid, Mauro Zigliotto, and Joachim
    Böcker. “Finite Set Sensorless Control With Minimum a Priori Knowledge and Tuning
    Effort for Interior Permanent Magnet Synchronous Motors.” <i>IEEE Transactions
    on Power Electronics</i>, 2023. <a href="https://doi.org/10.1109/tpel.2023.3294557">https://doi.org/10.1109/tpel.2023.3294557</a>.
  ieee: 'A. Brosch, F. Tinazzi, O. Wallscheid, M. Zigliotto, and J. Böcker, “Finite
    Set Sensorless Control With Minimum a Priori Knowledge and Tuning Effort for Interior
    Permanent Magnet Synchronous Motors,” <i>IEEE Transactions on Power Electronics</i>,
    2023, doi: <a href="https://doi.org/10.1109/tpel.2023.3294557">10.1109/tpel.2023.3294557</a>.'
  mla: Brosch, Anian, et al. “Finite Set Sensorless Control With Minimum a Priori
    Knowledge and Tuning Effort for Interior Permanent Magnet Synchronous Motors.”
    <i>IEEE Transactions on Power Electronics</i>, Institute of Electrical and Electronics
    Engineers (IEEE), 2023, doi:<a href="https://doi.org/10.1109/tpel.2023.3294557">10.1109/tpel.2023.3294557</a>.
  short: A. Brosch, F. Tinazzi, O. Wallscheid, M. Zigliotto, J. Böcker, IEEE Transactions
    on Power Electronics (2023).
date_created: 2023-07-25T20:33:12Z
date_updated: 2023-07-25T20:34:51Z
department:
- _id: '52'
doi: 10.1109/tpel.2023.3294557
keyword:
- Electrical and Electronic Engineering
language:
- iso: eng
publication: IEEE Transactions on Power Electronics
publication_identifier:
  issn:
  - 0885-8993
  - 1941-0107
publication_status: published
publisher: Institute of Electrical and Electronics Engineers (IEEE)
status: public
title: Finite Set Sensorless Control With Minimum a Priori Knowledge and Tuning Effort
  for Interior Permanent Magnet Synchronous Motors
type: journal_article
user_id: '75779'
year: '2023'
...
---
_id: '38041'
abstract:
- lang: eng
  text: "<jats:p>While FPGA accelerator boards and their respective high-level design
    tools are maturing, there is still a lack of multi-FPGA applications, libraries,
    and not least, benchmarks and reference implementations towards sustained HPC
    usage of these devices. As in the early days of GPUs in HPC, for workloads that
    can reasonably be decoupled into loosely coupled working sets, multi-accelerator
    support can be achieved by using standard communication interfaces like MPI on
    the host side. However, for performance and productivity, some applications can
    profit from a tighter coupling of the accelerators. FPGAs offer unique opportunities
    here when extending the dataflow characteristics to their communication interfaces.</jats:p>\r\n
    \         <jats:p>In this work, we extend the HPCC FPGA benchmark suite by multi-FPGA
    support and three missing benchmarks that particularly characterize or stress
    inter-device communication: b_eff, PTRANS, and LINPACK. With all benchmarks implemented
    for current boards with Intel and Xilinx FPGAs, we established a baseline for
    multi-FPGA performance. Additionally, for the communication-centric benchmarks,
    we explored the potential of direct FPGA-to-FPGA communication with a circuit-switched
    inter-FPGA network that is currently only available for one of the boards. The
    evaluation with parallel execution on up to 26 FPGA boards makes use of one of
    the largest academic FPGA installations.</jats:p>"
author:
- first_name: Marius
  full_name: Meyer, Marius
  id: '40778'
  last_name: Meyer
- first_name: Tobias
  full_name: Kenter, Tobias
  id: '3145'
  last_name: Kenter
- first_name: Christian
  full_name: Plessl, Christian
  id: '16153'
  last_name: Plessl
  orcid: 0000-0001-5728-9982
citation:
  ama: Meyer M, Kenter T, Plessl C. Multi-FPGA Designs and Scaling of HPC Challenge
    Benchmarks via MPI and Circuit-Switched Inter-FPGA Networks. <i>ACM Transactions
    on Reconfigurable Technology and Systems</i>. Published online 2023. doi:<a href="https://doi.org/10.1145/3576200">10.1145/3576200</a>
  apa: Meyer, M., Kenter, T., &#38; Plessl, C. (2023). Multi-FPGA Designs and Scaling
    of HPC Challenge Benchmarks via MPI and Circuit-Switched Inter-FPGA Networks.
    <i>ACM Transactions on Reconfigurable Technology and Systems</i>. <a href="https://doi.org/10.1145/3576200">https://doi.org/10.1145/3576200</a>
  bibtex: '@article{Meyer_Kenter_Plessl_2023, title={Multi-FPGA Designs and Scaling
    of HPC Challenge Benchmarks via MPI and Circuit-Switched Inter-FPGA Networks},
    DOI={<a href="https://doi.org/10.1145/3576200">10.1145/3576200</a>}, journal={ACM
    Transactions on Reconfigurable Technology and Systems}, publisher={Association
    for Computing Machinery (ACM)}, author={Meyer, Marius and Kenter, Tobias and Plessl,
    Christian}, year={2023} }'
  chicago: Meyer, Marius, Tobias Kenter, and Christian Plessl. “Multi-FPGA Designs
    and Scaling of HPC Challenge Benchmarks via MPI and Circuit-Switched Inter-FPGA
    Networks.” <i>ACM Transactions on Reconfigurable Technology and Systems</i>, 2023.
    <a href="https://doi.org/10.1145/3576200">https://doi.org/10.1145/3576200</a>.
  ieee: 'M. Meyer, T. Kenter, and C. Plessl, “Multi-FPGA Designs and Scaling of HPC
    Challenge Benchmarks via MPI and Circuit-Switched Inter-FPGA Networks,” <i>ACM
    Transactions on Reconfigurable Technology and Systems</i>, 2023, doi: <a href="https://doi.org/10.1145/3576200">10.1145/3576200</a>.'
  mla: Meyer, Marius, et al. “Multi-FPGA Designs and Scaling of HPC Challenge Benchmarks
    via MPI and Circuit-Switched Inter-FPGA Networks.” <i>ACM Transactions on Reconfigurable
    Technology and Systems</i>, Association for Computing Machinery (ACM), 2023, doi:<a
    href="https://doi.org/10.1145/3576200">10.1145/3576200</a>.
  short: M. Meyer, T. Kenter, C. Plessl, ACM Transactions on Reconfigurable Technology
    and Systems (2023).
date_created: 2023-01-23T08:40:42Z
date_updated: 2023-07-28T08:02:05Z
department:
- _id: '27'
- _id: '518'
doi: 10.1145/3576200
keyword:
- General Computer Science
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://dl.acm.org/doi/10.1145/3576200
oa: '1'
project:
- _id: '52'
  name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
- _id: '4'
  name: 'SFB 901 - C: SFB 901 - Project Area C'
- _id: '1'
  grant_number: '160364472'
  name: 'SFB 901: SFB 901'
- _id: '14'
  grant_number: '160364472'
  name: 'SFB 901 - C2: SFB 901 - Subproject C2'
publication: ACM Transactions on Reconfigurable Technology and Systems
publication_identifier:
  issn:
  - 1936-7406
  - 1936-7414
publication_status: published
publisher: Association for Computing Machinery (ACM)
quality_controlled: '1'
status: public
title: Multi-FPGA Designs and Scaling of HPC Challenge Benchmarks via MPI and Circuit-Switched
  Inter-FPGA Networks
type: journal_article
user_id: '24135'
year: '2023'
...
---
_id: '46213'
author:
- first_name: Daniel
  full_name: Weber, Daniel
  last_name: Weber
- first_name: Maximilian
  full_name: Schenke, Maximilian
  last_name: Schenke
- first_name: Oliver
  full_name: Wallscheid, Oliver
  last_name: Wallscheid
citation:
  ama: Weber D, Schenke M, Wallscheid O. Steady-State Error Compensation for Reinforcement
    Learning-Based Control of Power Electronic Systems. <i>IEEE Access</i>. 2023;11:76524-76536.
    doi:<a href="https://doi.org/10.1109/access.2023.3297274">10.1109/access.2023.3297274</a>
  apa: Weber, D., Schenke, M., &#38; Wallscheid, O. (2023). Steady-State Error Compensation
    for Reinforcement Learning-Based Control of Power Electronic Systems. <i>IEEE
    Access</i>, <i>11</i>, 76524–76536. <a href="https://doi.org/10.1109/access.2023.3297274">https://doi.org/10.1109/access.2023.3297274</a>
  bibtex: '@article{Weber_Schenke_Wallscheid_2023, title={Steady-State Error Compensation
    for Reinforcement Learning-Based Control of Power Electronic Systems}, volume={11},
    DOI={<a href="https://doi.org/10.1109/access.2023.3297274">10.1109/access.2023.3297274</a>},
    journal={IEEE Access}, publisher={Institute of Electrical and Electronics Engineers
    (IEEE)}, author={Weber, Daniel and Schenke, Maximilian and Wallscheid, Oliver},
    year={2023}, pages={76524–76536} }'
  chicago: 'Weber, Daniel, Maximilian Schenke, and Oliver Wallscheid. “Steady-State
    Error Compensation for Reinforcement Learning-Based Control of Power Electronic
    Systems.” <i>IEEE Access</i> 11 (2023): 76524–36. <a href="https://doi.org/10.1109/access.2023.3297274">https://doi.org/10.1109/access.2023.3297274</a>.'
  ieee: 'D. Weber, M. Schenke, and O. Wallscheid, “Steady-State Error Compensation
    for Reinforcement Learning-Based Control of Power Electronic Systems,” <i>IEEE
    Access</i>, vol. 11, pp. 76524–76536, 2023, doi: <a href="https://doi.org/10.1109/access.2023.3297274">10.1109/access.2023.3297274</a>.'
  mla: Weber, Daniel, et al. “Steady-State Error Compensation for Reinforcement Learning-Based
    Control of Power Electronic Systems.” <i>IEEE Access</i>, vol. 11, Institute of
    Electrical and Electronics Engineers (IEEE), 2023, pp. 76524–36, doi:<a href="https://doi.org/10.1109/access.2023.3297274">10.1109/access.2023.3297274</a>.
  short: D. Weber, M. Schenke, O. Wallscheid, IEEE Access 11 (2023) 76524–76536.
date_created: 2023-07-31T07:04:27Z
date_updated: 2023-07-31T07:04:48Z
department:
- _id: '34'
- _id: '52'
doi: 10.1109/access.2023.3297274
intvolume: '        11'
keyword:
- General Engineering
- General Materials Science
- General Computer Science
- Electrical and Electronic Engineering
language:
- iso: eng
page: 76524-76536
publication: IEEE Access
publication_identifier:
  issn:
  - 2169-3536
publication_status: published
publisher: Institute of Electrical and Electronics Engineers (IEEE)
status: public
title: Steady-State Error Compensation for Reinforcement Learning-Based Control of
  Power Electronic Systems
type: journal_article
user_id: '24041'
volume: 11
year: '2023'
...
---
_id: '46212'
author:
- first_name: Daniel
  full_name: Weber, Daniel
  last_name: Weber
- first_name: Maximilian
  full_name: Schenke, Maximilian
  last_name: Schenke
- first_name: Oliver
  full_name: Wallscheid, Oliver
  last_name: Wallscheid
citation:
  ama: 'Weber D, Schenke M, Wallscheid O. Safe Reinforcement Learning-Based Control
    in Power Electronic Systems. In: <i>2023 International Conference on Future Energy
    Solutions (FES)</i>. IEEE; 2023. doi:<a href="https://doi.org/10.1109/fes57669.2023.10182718">10.1109/fes57669.2023.10182718</a>'
  apa: Weber, D., Schenke, M., &#38; Wallscheid, O. (2023). Safe Reinforcement Learning-Based
    Control in Power Electronic Systems. <i>2023 International Conference on Future
    Energy Solutions (FES)</i>. <a href="https://doi.org/10.1109/fes57669.2023.10182718">https://doi.org/10.1109/fes57669.2023.10182718</a>
  bibtex: '@inproceedings{Weber_Schenke_Wallscheid_2023, title={Safe Reinforcement
    Learning-Based Control in Power Electronic Systems}, DOI={<a href="https://doi.org/10.1109/fes57669.2023.10182718">10.1109/fes57669.2023.10182718</a>},
    booktitle={2023 International Conference on Future Energy Solutions (FES)}, publisher={IEEE},
    author={Weber, Daniel and Schenke, Maximilian and Wallscheid, Oliver}, year={2023}
    }'
  chicago: Weber, Daniel, Maximilian Schenke, and Oliver Wallscheid. “Safe Reinforcement
    Learning-Based Control in Power Electronic Systems.” In <i>2023 International
    Conference on Future Energy Solutions (FES)</i>. IEEE, 2023. <a href="https://doi.org/10.1109/fes57669.2023.10182718">https://doi.org/10.1109/fes57669.2023.10182718</a>.
  ieee: 'D. Weber, M. Schenke, and O. Wallscheid, “Safe Reinforcement Learning-Based
    Control in Power Electronic Systems,” 2023, doi: <a href="https://doi.org/10.1109/fes57669.2023.10182718">10.1109/fes57669.2023.10182718</a>.'
  mla: Weber, Daniel, et al. “Safe Reinforcement Learning-Based Control in Power Electronic
    Systems.” <i>2023 International Conference on Future Energy Solutions (FES)</i>,
    IEEE, 2023, doi:<a href="https://doi.org/10.1109/fes57669.2023.10182718">10.1109/fes57669.2023.10182718</a>.
  short: 'D. Weber, M. Schenke, O. Wallscheid, in: 2023 International Conference on
    Future Energy Solutions (FES), IEEE, 2023.'
date_created: 2023-07-31T07:01:22Z
date_updated: 2023-07-31T07:03:46Z
department:
- _id: '34'
- _id: '52'
doi: 10.1109/fes57669.2023.10182718
language:
- iso: eng
publication: 2023 International Conference on Future Energy Solutions (FES)
publication_status: published
publisher: IEEE
status: public
title: Safe Reinforcement Learning-Based Control in Power Electronic Systems
type: conference
user_id: '24041'
year: '2023'
...
---
_id: '46221'
author:
- first_name: N.
  full_name: N., N.
  last_name: N.
citation:
  ama: N. N. <i>Improving the End-of-Line Test of Custom-Built Geared Motors Using
    Clustering Based on Neural Networks</i>.; 2023.
  apa: N., N. (2023). <i>Improving the End-of-Line Test of Custom-Built Geared Motors
    using Clustering based on Neural Networks</i>.
  bibtex: '@book{N._2023, title={Improving the End-of-Line Test of Custom-Built Geared
    Motors using Clustering based on Neural Networks}, author={N., N.}, year={2023}
    }'
  chicago: N., N. <i>Improving the End-of-Line Test of Custom-Built Geared Motors
    Using Clustering Based on Neural Networks</i>, 2023.
  ieee: N. N., <i>Improving the End-of-Line Test of Custom-Built Geared Motors using
    Clustering based on Neural Networks</i>. 2023.
  mla: N., N. <i>Improving the End-of-Line Test of Custom-Built Geared Motors Using
    Clustering Based on Neural Networks</i>. 2023.
  short: N. N., Improving the End-of-Line Test of Custom-Built Geared Motors Using
    Clustering Based on Neural Networks, 2023.
date_created: 2023-07-31T10:49:12Z
date_updated: 2023-07-31T10:49:30Z
department:
- _id: '79'
language:
- iso: eng
status: public
supervisor:
- first_name: Christian
  full_name: Scheideler, Christian
  id: '20792'
  last_name: Scheideler
title: Improving the End-of-Line Test of Custom-Built Geared Motors using Clustering
  based on Neural Networks
type: mastersthesis
user_id: '15504'
year: '2023'
...
---
_id: '46251'
author:
- first_name: Caglar
  full_name: Demir, Caglar
  id: '43817'
  last_name: Demir
- first_name: Axel-Cyrille
  full_name: Ngonga Ngomo, Axel-Cyrille
  last_name: Ngonga Ngomo
citation:
  ama: Demir C, Ngonga Ngomo A-C. Neuro-Symbolic Class Expression Learning. <i>International
    Joint Conference on Artificial Intelligence</i>. Published online 2023.
  apa: Demir, C., &#38; Ngonga Ngomo, A.-C. (2023). Neuro-Symbolic Class Expression
    Learning. <i>International Joint Conference on Artificial Intelligence</i>. International
    Joint Conference on Artificial Intelligence IJCAI 2023, Macau.
  bibtex: '@article{Demir_Ngonga Ngomo_2023, title={Neuro-Symbolic Class Expression
    Learning}, journal={International Joint Conference on Artificial Intelligence},
    author={Demir, Caglar and Ngonga Ngomo, Axel-Cyrille}, year={2023} }'
  chicago: Demir, Caglar, and Axel-Cyrille Ngonga Ngomo. “Neuro-Symbolic Class Expression
    Learning.” <i>International Joint Conference on Artificial Intelligence</i>, 2023.
  ieee: C. Demir and A.-C. Ngonga Ngomo, “Neuro-Symbolic Class Expression Learning,”
    <i>International Joint Conference on Artificial Intelligence</i>, 2023.
  mla: Demir, Caglar, and Axel-Cyrille Ngonga Ngomo. “Neuro-Symbolic Class Expression
    Learning.” <i>International Joint Conference on Artificial Intelligence</i>, 2023.
  short: C. Demir, A.-C. Ngonga Ngomo, International Joint Conference on Artificial
    Intelligence (2023).
conference:
  location: Macau
  name: International Joint Conference on Artificial Intelligence IJCAI 2023
date_created: 2023-08-01T09:30:37Z
date_updated: 2023-08-01T09:44:30Z
ddc:
- '000'
department:
- _id: '574'
file:
- access_level: open_access
  content_type: application/pdf
  creator: cdemir
  date_created: 2023-08-01T09:30:35Z
  date_updated: 2023-08-01T09:30:35Z
  file_id: '46252'
  file_name: public.pdf
  file_size: 340865
  relation: main_file
file_date_updated: 2023-08-01T09:30:35Z
has_accepted_license: '1'
language:
- iso: eng
oa: '1'
project:
- _id: '407'
  grant_number: '101070305'
  name: 'ENEXA: Efficient Explainable Learning on Knowledge Graphs'
- _id: '410'
  name: 'KnowGraphs: KnowGraphs: Knowledge Graphs at Scale'
- _id: '285'
  grant_number: NW21-059D
  name: 'SAIL: SAIL: SustAInable Life-cycle of Intelligent Socio-Technical Systems'
publication: International Joint Conference on Artificial Intelligence
status: public
title: Neuro-Symbolic Class Expression Learning
type: journal_article
user_id: '43817'
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. <i>SIAM Journal on Discrete Mathematics</i>.
    2023;37(3):1548-1565. doi:<a href="https://doi.org/10.1137/22m1500654">10.1137/22m1500654</a>
  apa: Ma, Y., Mattiolo, D., Steffen, E., &#38; Wolf, I. H. (2023). Pairwise Disjoint
    Perfect Matchings in r-Edge-Connected r-Regular Graphs. <i>SIAM Journal on Discrete
    Mathematics</i>, <i>37</i>(3), 1548–1565. <a href="https://doi.org/10.1137/22m1500654">https://doi.org/10.1137/22m1500654</a>
  bibtex: '@article{Ma_Mattiolo_Steffen_Wolf_2023, title={Pairwise Disjoint Perfect
    Matchings in r-Edge-Connected r-Regular Graphs}, volume={37}, DOI={<a href="https://doi.org/10.1137/22m1500654">10.1137/22m1500654</a>},
    number={3}, journal={SIAM Journal on Discrete Mathematics}, publisher={Society
    for Industrial &#38; 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.” <i>SIAM
    Journal on Discrete Mathematics</i> 37, no. 3 (2023): 1548–65. <a href="https://doi.org/10.1137/22m1500654">https://doi.org/10.1137/22m1500654</a>.'
  ieee: 'Y. Ma, D. Mattiolo, E. Steffen, and I. H. Wolf, “Pairwise Disjoint Perfect
    Matchings in r-Edge-Connected r-Regular Graphs,” <i>SIAM Journal on Discrete Mathematics</i>,
    vol. 37, no. 3, pp. 1548–1565, 2023, doi: <a href="https://doi.org/10.1137/22m1500654">10.1137/22m1500654</a>.'
  mla: Ma, Yulai, et al. “Pairwise Disjoint Perfect Matchings in R-Edge-Connected
    r-Regular Graphs.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 37, no. 3,
    Society for Industrial &#38; Applied Mathematics (SIAM), 2023, pp. 1548–65, doi:<a
    href="https://doi.org/10.1137/22m1500654">10.1137/22m1500654</a>.
  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: '43228'
abstract:
- lang: eng
  text: "The computation of electron repulsion integrals (ERIs) over Gaussian-type
    orbitals (GTOs) is a challenging problem in quantum-mechanics-based atomistic
    simulations. In practical simulations, several trillions of ERIs may have to be\r\ncomputed
    for every time step.\r\nIn this work, we investigate FPGAs as accelerators for
    the ERI computation. We use template parameters, here within the Intel oneAPI
    tool flow, to create customized designs for 256 different ERI quartet classes,
    based on their orbitals. To maximize data reuse, all intermediates are buffered
    in FPGA on-chip memory with customized layout. The pre-calculation of intermediates
    also helps to overcome data dependencies caused by multi-dimensional recurrence\r\nrelations.
    The involved loop structures are partially or even fully unrolled for high throughput
    of FPGA kernels. Furthermore, a lossy compression algorithm utilizing arbitrary
    bitwidth integers is integrated in the FPGA kernels. To our\r\nbest knowledge,
    this is the first work on ERI computation on FPGAs that supports more than just
    the single most basic quartet class. Also, the integration of ERI computation
    and compression it a novelty that is not even covered by CPU or GPU libraries
    so far.\r\nOur evaluation shows that using 16-bit integer for the ERI compression,
    the fastest FPGA kernels exceed the performance of 10 GERIS ($10 \\times 10^9$
    ERIs per second) on one Intel Stratix 10 GX 2800 FPGA, with maximum absolute errors
    around $10^{-7}$ - $10^{-5}$ Hartree. The measured throughput can be accurately
    explained by a performance model. The FPGA kernels deployed on 2 FPGAs outperform
    similar computations using the widely used libint reference on a two-socket server
    with 40 Xeon Gold 6148 CPU cores of the same process technology by factors up
    to 6.0x and on a new two-socket server with 128 EPYC 7713 CPU cores by up to 1.9x."
author:
- first_name: Xin
  full_name: Wu, Xin
  id: '77439'
  last_name: Wu
- first_name: Tobias
  full_name: Kenter, Tobias
  id: '3145'
  last_name: Kenter
- first_name: Robert
  full_name: Schade, Robert
  id: '75963'
  last_name: Schade
  orcid: 0000-0002-6268-539
- first_name: Thomas
  full_name: Kühne, Thomas
  id: '49079'
  last_name: Kühne
- first_name: Christian
  full_name: Plessl, Christian
  id: '16153'
  last_name: Plessl
  orcid: 0000-0001-5728-9982
citation:
  ama: 'Wu X, Kenter T, Schade R, Kühne T, Plessl C. Computing and Compressing Electron
    Repulsion Integrals on FPGAs. In: <i>2023 IEEE 31st Annual International Symposium
    on Field-Programmable Custom Computing Machines (FCCM)</i>. ; 2023:162-173. doi:<a
    href="https://doi.org/10.1109/FCCM57271.2023.00026">10.1109/FCCM57271.2023.00026</a>'
  apa: Wu, X., Kenter, T., Schade, R., Kühne, T., &#38; Plessl, C. (2023). Computing
    and Compressing Electron Repulsion Integrals on FPGAs. <i>2023 IEEE 31st Annual
    International Symposium on Field-Programmable Custom Computing Machines (FCCM)</i>,
    162–173. <a href="https://doi.org/10.1109/FCCM57271.2023.00026">https://doi.org/10.1109/FCCM57271.2023.00026</a>
  bibtex: '@inproceedings{Wu_Kenter_Schade_Kühne_Plessl_2023, title={Computing and
    Compressing Electron Repulsion Integrals on FPGAs}, DOI={<a href="https://doi.org/10.1109/FCCM57271.2023.00026">10.1109/FCCM57271.2023.00026</a>},
    booktitle={2023 IEEE 31st Annual International Symposium on Field-Programmable
    Custom Computing Machines (FCCM)}, author={Wu, Xin and Kenter, Tobias and Schade,
    Robert and Kühne, Thomas and Plessl, Christian}, year={2023}, pages={162–173}
    }'
  chicago: Wu, Xin, Tobias Kenter, Robert Schade, Thomas Kühne, and Christian Plessl.
    “Computing and Compressing Electron Repulsion Integrals on FPGAs.” In <i>2023
    IEEE 31st Annual International Symposium on Field-Programmable Custom Computing
    Machines (FCCM)</i>, 162–73, 2023. <a href="https://doi.org/10.1109/FCCM57271.2023.00026">https://doi.org/10.1109/FCCM57271.2023.00026</a>.
  ieee: 'X. Wu, T. Kenter, R. Schade, T. Kühne, and C. Plessl, “Computing and Compressing
    Electron Repulsion Integrals on FPGAs,” in <i>2023 IEEE 31st Annual International
    Symposium on Field-Programmable Custom Computing Machines (FCCM)</i>, 2023, pp.
    162–173, doi: <a href="https://doi.org/10.1109/FCCM57271.2023.00026">10.1109/FCCM57271.2023.00026</a>.'
  mla: Wu, Xin, et al. “Computing and Compressing Electron Repulsion Integrals on
    FPGAs.” <i>2023 IEEE 31st Annual International Symposium on Field-Programmable
    Custom Computing Machines (FCCM)</i>, 2023, pp. 162–73, doi:<a href="https://doi.org/10.1109/FCCM57271.2023.00026">10.1109/FCCM57271.2023.00026</a>.
  short: 'X. Wu, T. Kenter, R. Schade, T. Kühne, C. Plessl, in: 2023 IEEE 31st Annual
    International Symposium on Field-Programmable Custom Computing Machines (FCCM),
    2023, pp. 162–173.'
date_created: 2023-03-30T11:15:40Z
date_updated: 2023-08-02T15:05:42Z
department:
- _id: '27'
- _id: '518'
doi: 10.1109/FCCM57271.2023.00026
external_id:
  arxiv:
  - '2303.13632'
language:
- iso: eng
main_file_link:
- url: https://ieeexplore.ieee.org/document/10171537
page: 162-173
project:
- _id: '52'
  name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: 2023 IEEE 31st Annual International Symposium on Field-Programmable Custom
  Computing Machines (FCCM)
quality_controlled: '1'
status: public
title: Computing and Compressing Electron Repulsion Integrals on FPGAs
type: conference
user_id: '75963'
year: '2023'
...
---
_id: '45361'
abstract:
- lang: eng
  text: <jats:p> The non-orthogonal local submatrix method applied to electronic structure–based
    molecular dynamics simulations is shown to exceed 1.1 EFLOP/s in FP16/FP32-mixed
    floating-point arithmetic when using 4400 NVIDIA A100 GPUs of the Perlmutter system.
    This is enabled by a modification of the original method that pushes the sustained
    fraction of the peak performance to about 80%. Example calculations are performed
    for SARS-CoV-2 spike proteins with up to 83 million atoms. </jats:p>
article_number: '109434202311776'
article_type: original
author:
- first_name: Robert
  full_name: Schade, Robert
  id: '75963'
  last_name: Schade
  orcid: 0000-0002-6268-539
- first_name: Tobias
  full_name: Kenter, Tobias
  id: '3145'
  last_name: Kenter
- first_name: Hossam
  full_name: Elgabarty, Hossam
  id: '60250'
  last_name: Elgabarty
  orcid: 0000-0002-4945-1481
- first_name: Michael
  full_name: Lass, Michael
  id: '24135'
  last_name: Lass
  orcid: 0000-0002-5708-7632
- first_name: Thomas
  full_name: Kühne, Thomas
  id: '49079'
  last_name: Kühne
- first_name: Christian
  full_name: Plessl, Christian
  id: '16153'
  last_name: Plessl
  orcid: 0000-0001-5728-9982
citation:
  ama: Schade R, Kenter T, Elgabarty H, Lass M, Kühne T, Plessl C. Breaking the exascale
    barrier for the electronic structure problem in ab-initio molecular dynamics.
    <i>The International Journal of High Performance Computing Applications</i>. Published
    online 2023. doi:<a href="https://doi.org/10.1177/10943420231177631">10.1177/10943420231177631</a>
  apa: Schade, R., Kenter, T., Elgabarty, H., Lass, M., Kühne, T., &#38; Plessl, C.
    (2023). Breaking the exascale barrier for the electronic structure problem in
    ab-initio molecular dynamics. <i>The International Journal of High Performance
    Computing Applications</i>, Article 109434202311776. <a href="https://doi.org/10.1177/10943420231177631">https://doi.org/10.1177/10943420231177631</a>
  bibtex: '@article{Schade_Kenter_Elgabarty_Lass_Kühne_Plessl_2023, title={Breaking
    the exascale barrier for the electronic structure problem in ab-initio molecular
    dynamics}, DOI={<a href="https://doi.org/10.1177/10943420231177631">10.1177/10943420231177631</a>},
    number={109434202311776}, journal={The International Journal of High Performance
    Computing Applications}, publisher={SAGE Publications}, author={Schade, Robert
    and Kenter, Tobias and Elgabarty, Hossam and Lass, Michael and Kühne, Thomas and
    Plessl, Christian}, year={2023} }'
  chicago: Schade, Robert, Tobias Kenter, Hossam Elgabarty, Michael Lass, Thomas Kühne,
    and Christian Plessl. “Breaking the Exascale Barrier for the Electronic Structure
    Problem in Ab-Initio Molecular Dynamics.” <i>The International Journal of High
    Performance Computing Applications</i>, 2023. <a href="https://doi.org/10.1177/10943420231177631">https://doi.org/10.1177/10943420231177631</a>.
  ieee: 'R. Schade, T. Kenter, H. Elgabarty, M. Lass, T. Kühne, and C. Plessl, “Breaking
    the exascale barrier for the electronic structure problem in ab-initio molecular
    dynamics,” <i>The International Journal of High Performance Computing Applications</i>,
    Art. no. 109434202311776, 2023, doi: <a href="https://doi.org/10.1177/10943420231177631">10.1177/10943420231177631</a>.'
  mla: Schade, Robert, et al. “Breaking the Exascale Barrier for the Electronic Structure
    Problem in Ab-Initio Molecular Dynamics.” <i>The International Journal of High
    Performance Computing Applications</i>, 109434202311776, SAGE Publications, 2023,
    doi:<a href="https://doi.org/10.1177/10943420231177631">10.1177/10943420231177631</a>.
  short: R. Schade, T. Kenter, H. Elgabarty, M. Lass, T. Kühne, C. Plessl, The International
    Journal of High Performance Computing Applications (2023).
date_created: 2023-05-30T09:19:09Z
date_updated: 2023-08-02T15:04:53Z
department:
- _id: '27'
- _id: '518'
doi: 10.1177/10943420231177631
keyword:
- Hardware and Architecture
- Theoretical Computer Science
- Software
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://journals.sagepub.com/doi/10.1177/10943420231177631
oa: '1'
project:
- _id: '52'
  name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: The International Journal of High Performance Computing Applications
publication_identifier:
  issn:
  - 1094-3420
  - 1741-2846
publication_status: published
publisher: SAGE Publications
quality_controlled: '1'
status: public
title: Breaking the exascale barrier for the electronic structure problem in ab-initio
  molecular dynamics
type: journal_article
user_id: '75963'
year: '2023'
...
---
_id: '45780'
author:
- first_name: Alexander
  full_name: Tornede, Alexander
  id: '38209'
  last_name: Tornede
citation:
  ama: 'Tornede A. <i>Advanced Algorithm Selection with Machine Learning: Handling
    Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta Level Decisions</i>.;
    2023. doi:<a href="https://doi.org/10.17619/UNIPB/1-1780 ">10.17619/UNIPB/1-1780
    </a>'
  apa: 'Tornede, A. (2023). <i>Advanced Algorithm Selection with Machine Learning:
    Handling Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta
    Level Decisions</i>. <a href="https://doi.org/10.17619/UNIPB/1-1780 ">https://doi.org/10.17619/UNIPB/1-1780
    </a>'
  bibtex: '@book{Tornede_2023, title={Advanced Algorithm Selection with Machine Learning:
    Handling Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta
    Level Decisions}, DOI={<a href="https://doi.org/10.17619/UNIPB/1-1780 ">10.17619/UNIPB/1-1780
    </a>}, author={Tornede, Alexander}, year={2023} }'
  chicago: 'Tornede, Alexander. <i>Advanced Algorithm Selection with Machine Learning:
    Handling Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta
    Level Decisions</i>, 2023. <a href="https://doi.org/10.17619/UNIPB/1-1780 ">https://doi.org/10.17619/UNIPB/1-1780
    </a>.'
  ieee: 'A. Tornede, <i>Advanced Algorithm Selection with Machine Learning: Handling
    Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta Level Decisions</i>.
    2023.'
  mla: 'Tornede, Alexander. <i>Advanced Algorithm Selection with Machine Learning:
    Handling Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta
    Level Decisions</i>. 2023, doi:<a href="https://doi.org/10.17619/UNIPB/1-1780
    ">10.17619/UNIPB/1-1780 </a>.'
  short: 'A. Tornede, Advanced Algorithm Selection with Machine Learning: Handling
    Large Algorithm Sets, Learning From Censored Data, and Simplyfing Meta Level Decisions,
    2023.'
date_created: 2023-06-27T05:20:14Z
date_updated: 2023-08-04T06:01:49Z
ddc:
- '006'
department:
- _id: '355'
doi: '10.17619/UNIPB/1-1780 '
file:
- access_level: open_access
  content_type: application/pdf
  creator: ahetzer
  date_created: 2023-07-24T08:40:35Z
  date_updated: 2023-07-24T08:42:01Z
  file_id: '46118'
  file_name: dissertation_alexander_tornede_final_publishing_compressed.pdf
  file_size: 4300633
  relation: main_file
  title: ' Advanced Algorithm Selection with Machine Learning: Handling Large Algorithm
    Sets, Learning From Censored Data, and Simplyfing Meta Level Decisions'
file_date_updated: 2023-07-24T08:42:01Z
has_accepted_license: '1'
language:
- iso: eng
oa: '1'
project:
- _id: '10'
  grant_number: '160364472'
  name: 'SFB 901 - B2: Konfiguration und Bewertung (B02)'
- _id: '3'
  name: 'SFB 901 - B: SFB 901 - Project Area B'
- _id: '1'
  grant_number: '160364472'
  name: 'SFB 901: SFB 901: On-The-Fly Computing - Individualisierte IT-Dienstleistungen
    in dynamischen Märkten '
status: public
supervisor:
- first_name: Eyke
  full_name: Hüllermeier, Eyke
  last_name: Hüllermeier
title: 'Advanced Algorithm Selection with Machine Learning: Handling Large Algorithm
  Sets, Learning From Censored Data, and Simplyfing Meta Level Decisions'
type: dissertation
user_id: '15504'
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. <i>Journal of Computational and Applied Mathematics</i>. 2023;421:114780.
    doi:<a href="https://doi.org/10.1016/j.cam.2022.114780">10.1016/j.cam.2022.114780</a>
  apa: Ober-Blöbaum, S., &#38; Offen, C. (2023). Variational Learning of Euler–Lagrange
    Dynamics from Data. <i>Journal of Computational and Applied Mathematics</i>, <i>421</i>,
    114780. <a href="https://doi.org/10.1016/j.cam.2022.114780">https://doi.org/10.1016/j.cam.2022.114780</a>
  bibtex: '@article{Ober-Blöbaum_Offen_2023, title={Variational Learning of Euler–Lagrange
    Dynamics from Data}, volume={421}, DOI={<a href="https://doi.org/10.1016/j.cam.2022.114780">10.1016/j.cam.2022.114780</a>},
    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.” <i>Journal of Computational and Applied Mathematics</i> 421
    (2023): 114780. <a href="https://doi.org/10.1016/j.cam.2022.114780">https://doi.org/10.1016/j.cam.2022.114780</a>.'
  ieee: 'S. Ober-Blöbaum and C. Offen, “Variational Learning of Euler–Lagrange Dynamics
    from Data,” <i>Journal of Computational and Applied Mathematics</i>, vol. 421,
    p. 114780, 2023, doi: <a href="https://doi.org/10.1016/j.cam.2022.114780">10.1016/j.cam.2022.114780</a>.'
  mla: Ober-Blöbaum, Sina, and Christian Offen. “Variational Learning of Euler–Lagrange
    Dynamics from Data.” <i>Journal of Computational and Applied Mathematics</i>,
    vol. 421, Elsevier, 2023, p. 114780, doi:<a href="https://doi.org/10.1016/j.cam.2022.114780">10.1016/j.cam.2022.114780</a>.
  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.
    <i>Journal of Geometric Mechanics</i>. 2023;15(1):98-115. doi:<a href="https://doi.org/10.3934/jgm.2023005">10.3934/jgm.2023005</a>
  apa: McLachlan, R., &#38; Offen, C. (2023). Backward error analysis for conjugate
    symplectic methods. <i>Journal of Geometric Mechanics</i>, <i>15</i>(1), 98–115.
    <a href="https://doi.org/10.3934/jgm.2023005">https://doi.org/10.3934/jgm.2023005</a>
  bibtex: '@article{McLachlan_Offen_2023, title={Backward error analysis for conjugate
    symplectic methods}, volume={15}, DOI={<a href="https://doi.org/10.3934/jgm.2023005">10.3934/jgm.2023005</a>},
    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.” <i>Journal of Geometric Mechanics</i> 15, no. 1 (2023): 98–115.
    <a href="https://doi.org/10.3934/jgm.2023005">https://doi.org/10.3934/jgm.2023005</a>.'
  ieee: 'R. McLachlan and C. Offen, “Backward error analysis for conjugate symplectic
    methods,” <i>Journal of Geometric Mechanics</i>, vol. 15, no. 1, pp. 98–115, 2023,
    doi: <a href="https://doi.org/10.3934/jgm.2023005">10.3934/jgm.2023005</a>.'
  mla: McLachlan, Robert, and Christian Offen. “Backward Error Analysis for Conjugate
    Symplectic Methods.” <i>Journal of Geometric Mechanics</i>, vol. 15, no. 1, AIMS
    Press, 2023, pp. 98–115, doi:<a href="https://doi.org/10.3934/jgm.2023005">10.3934/jgm.2023005</a>.
  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. <i>Chaos</i>. 2023;33(6). doi:<a href="https://doi.org/10.1063/5.0142969">10.1063/5.0142969</a>
  apa: Dierkes, E., Offen, C., Ober-Blöbaum, S., &#38; Flaßkamp, K. (2023). Hamiltonian
    Neural Networks with Automatic Symmetry Detection. <i>Chaos</i>, <i>33</i>(6),
    Article 063115. <a href="https://doi.org/10.1063/5.0142969">https://doi.org/10.1063/5.0142969</a>
  bibtex: '@article{Dierkes_Offen_Ober-Blöbaum_Flaßkamp_2023, title={Hamiltonian Neural
    Networks with Automatic Symmetry Detection}, volume={33}, DOI={<a href="https://doi.org/10.1063/5.0142969">10.1063/5.0142969</a>},
    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.” <i>Chaos</i>
    33, no. 6 (2023). <a href="https://doi.org/10.1063/5.0142969">https://doi.org/10.1063/5.0142969</a>.
  ieee: 'E. Dierkes, C. Offen, S. Ober-Blöbaum, and K. Flaßkamp, “Hamiltonian Neural
    Networks with Automatic Symmetry Detection,” <i>Chaos</i>, vol. 33, no. 6, Art.
    no. 063115, 2023, doi: <a href="https://doi.org/10.1063/5.0142969">10.1063/5.0142969</a>.'
  mla: Dierkes, Eva, et al. “Hamiltonian Neural Networks with Automatic Symmetry Detection.”
    <i>Chaos</i>, vol. 33, no. 6, 063115, AIP Publishing, 2023, doi:<a href="https://doi.org/10.1063/5.0142969">10.1063/5.0142969</a>.
  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: '46482'
abstract:
- lang: eng
  text: "Ever increasing demands on the performance of microchips are leading to ever
    more complex semiconductor technologies with ever shrinking feature sizes. Complex
    applications with high demands on safety and reliability, such as autonomous driving,
    are simultaneously driving the requirements for test and diagnosis of VLSI circuits.
    Throughout the life cycle of a microchip, uncertainties occur that affect its
    timing behavior. For example, weak circuit structures, aging effects, or process
    variations can lead to a change in the timing behavior of the circuit. While these
    uncertainties do not necessarily lead to a change of the functional behavior,
    they can lead to a reliability problem.\r\nWith modular and hybrid compaction
    two test instruments are presented in this work that can be used for X-tolerant
    test response compaction in the built-in Faster-than-At-Speed Test (FAST) which
    is used to detect uncertainties in VLSI circuits. One challenge for test response
    compaction during FAST is the high and varying X-rate at the outputs of the circuit
    under test. By dividing the circuit outputs into test groups and separately compacting
    these test groups using stochastic compactors, the modular compaction is able
    to handle these high and varying X-rates.\r\nTo deal with uncertainties on logic
    interconnects, a method for distinguishing crosstalk and process variation is
    presented. In current semiconductor technologies, the number of parasitic coupling
    capacitances between logic interconnects is growing. These coupling capacitances
    can lead to crosstalk, which causes increased current flow in the logic interconnects,
    which in turn can lead to increased electromigration. In the presented method,
    delay maps describing the timing behavior of the circuit outputs at different
    operating points are used to train artificial neural networks which classify the
    tested circuits into fault-free and faulty."
- lang: ger
  text: "Immer größere Anforderungen an die Leistungsfähigkeit von Mikrochips führen
    zu Halbleitertechnologien mit immer kleiner werdenden Strukturgrößen. Anwendungen
    mit hohen Ansprüchen an Sicherheit und Zuverlässigkeit, wie z.B. das autonome
    Fahren, treiben gleichzeitig die Anforderungen an den Test hochintegrierter Schaltungen
    an. Während des gesamten Lebenszyklus eines Mikrochips kommt es zu Unsicherheiten
    im Zeitverhalten. So können z.B. schwache Schaltungsstrukturen, Alterungseffekte
    oder Prozessvariationen zu einer Veränderung des Zeitverhaltens führen. Während
    diese Unsicherheiten nicht zu einer Veränderung des funktionalen Verhaltens führen
    müssen, können sie jedoch zu einem Zuverlässigkeitsproblem führen.\r\nMit der
    modularen und der hybriden Kompaktierung werden in dieser Arbeit zwei Testinstrumente
    vorgestellt, die für die X-tolerante Testantwortkompaktierung im eingebauten Hochgeschwindigkeitstest
    verwendet werden können. Eine Herausforderung für die Testantwortkompaktierung
    während des Hochgeschwindigkeitstests ist die hohe und variierende X-Rate an den
    Ausgängen der zu testenden Schaltung. Durch die Einteilung der Schaltungsausgänge
    in Prüfgruppen und die separierte Kompaktierung der Prüfgruppen mithilfe von stochastischen
    Kompaktierern, können die vorgestellten Verfahren diese hohen und variierenden
    X-Raten verarbeiten.\r\nFür den Umgang mit Unsicherheiten auf Verbindungsleitungen
    der Logik-Schaltung wird ein Verfahren zur Unterscheidung von Übersprechen und
    Prozessvariation vorgestellt. In aktuellen Halbleitertechnologien kommt es vermehrt
    zu parasitären Koppelkapazitäten zwischen den Verbindungsleitungen. In dem vorgestellten
    Verfahren werden künstliche neuronale Netze trainiert, um die Schaltungen in fehlerfrei
    und fehlerhaft zu klassifizieren."
author:
- first_name: Alexander
  full_name: Sprenger, Alexander
  id: '22707'
  last_name: Sprenger
  orcid: 0000-0002-0775-7677
citation:
  ama: Sprenger A. <i>Testinstrumente und Testdatenanalyse zur Verarbeitung von Unsicherheiten
    in Logikblöcken hochintegrierter Schaltungen</i>. Universität Paderborn; 2023.
    doi:<a href="https://doi.org/10.17619/UNIPB/1-1787">10.17619/UNIPB/1-1787</a>
  apa: Sprenger, A. (2023). <i>Testinstrumente und Testdatenanalyse zur Verarbeitung
    von Unsicherheiten in Logikblöcken hochintegrierter Schaltungen</i>. Universität
    Paderborn. <a href="https://doi.org/10.17619/UNIPB/1-1787">https://doi.org/10.17619/UNIPB/1-1787</a>
  bibtex: '@book{Sprenger_2023, place={Paderborn}, title={Testinstrumente und Testdatenanalyse
    zur Verarbeitung von Unsicherheiten in Logikblöcken hochintegrierter Schaltungen},
    DOI={<a href="https://doi.org/10.17619/UNIPB/1-1787">10.17619/UNIPB/1-1787</a>},
    publisher={Universität Paderborn}, author={Sprenger, Alexander}, year={2023} }'
  chicago: 'Sprenger, Alexander. <i>Testinstrumente und Testdatenanalyse zur Verarbeitung
    von Unsicherheiten in Logikblöcken hochintegrierter Schaltungen</i>. Paderborn:
    Universität Paderborn, 2023. <a href="https://doi.org/10.17619/UNIPB/1-1787">https://doi.org/10.17619/UNIPB/1-1787</a>.'
  ieee: 'A. Sprenger, <i>Testinstrumente und Testdatenanalyse zur Verarbeitung von
    Unsicherheiten in Logikblöcken hochintegrierter Schaltungen</i>. Paderborn: Universität
    Paderborn, 2023.'
  mla: Sprenger, Alexander. <i>Testinstrumente und Testdatenanalyse zur Verarbeitung
    von Unsicherheiten in Logikblöcken hochintegrierter Schaltungen</i>. Universität
    Paderborn, 2023, doi:<a href="https://doi.org/10.17619/UNIPB/1-1787">10.17619/UNIPB/1-1787</a>.
  short: A. Sprenger, Testinstrumente und Testdatenanalyse zur Verarbeitung von Unsicherheiten
    in Logikblöcken hochintegrierter Schaltungen, Universität Paderborn, Paderborn,
    2023.
date_created: 2023-08-12T09:10:38Z
date_updated: 2023-08-12T09:13:18Z
department:
- _id: '48'
doi: 10.17619/UNIPB/1-1787
extern: '1'
keyword:
- Testantwortkompaktierung
- Prozessvariation
- Silicon Lifecycle Management
language:
- iso: ger
main_file_link:
- open_access: '1'
  url: https://nbn-resolving.org/urn:nbn:de:hbz:466:2-45493
oa: '1'
page: xi, 160
place: Paderborn
publication_status: published
publisher: Universität Paderborn
status: public
supervisor:
- first_name: Sybille
  full_name: Hellebrand, Sybille
  id: '209'
  last_name: Hellebrand
  orcid: 0000-0002-3717-3939
- first_name: Marco
  full_name: Platzner, Marco
  id: '398'
  last_name: Platzner
title: Testinstrumente und Testdatenanalyse zur Verarbeitung von Unsicherheiten in
  Logikblöcken hochintegrierter Schaltungen
type: dissertation
user_id: '22707'
year: '2023'
...
---
_id: '45558'
abstract:
- lang: eng
  text: Graffiti is an urban phenomenon that is increasingly attracting the interest
    of the sciences. To the best of our knowledge, no suitable data corpora are available
    for systematic research until now. The Information System Graffiti in Germany
    project (Ingrid) closes this gap by dealing with graffiti image collections that
    have been made available to the project for public use. Within Ingrid, the graffiti
    images are collected, digitized and annotated. With this work, we aim to support
    the rapid access to a comprehensive data source on Ingrid targeted especially
    by researchers. In particular, we present IngridKG, an RDF knowledge graph of
    annotated graffiti, abides by the Linked Data and FAIR principles. We weekly update
    IngridKG by augmenting the new annotated graffiti to our knowledge graph. Our
    generation pipeline applies RDF data conversion, link discovery and data fusion
    approaches to the original data. The current version of IngridKG contains 460,640,154
    triples and is linked to 3 other knowledge graphs by over 200,000 links. In our
    use case studies, we demonstrate the usefulness of our knowledge graph for different
    applications.
author:
- first_name: Mohamed
  full_name: Sherif, Mohamed
  id: '67234'
  last_name: Sherif
  orcid: https://orcid.org/0000-0002-9927-2203
- first_name: Ana Alexandra
  full_name: Morim da Silva, Ana Alexandra
  last_name: Morim da Silva
- first_name: Svetlana
  full_name: Pestryakova, Svetlana
  last_name: Pestryakova
- first_name: Abdullah Fathi Ahmed
  full_name: Ahmed, Abdullah Fathi Ahmed
  id: '29670'
  last_name: Ahmed
- first_name: Sven
  full_name: Niemann, Sven
  id: '6593'
  last_name: Niemann
- first_name: Axel-Cyrille
  full_name: Ngonga Ngomo, Axel-Cyrille
  id: '65716'
  last_name: Ngonga Ngomo
citation:
  ama: 'Sherif M, Morim da Silva AA, Pestryakova S, Ahmed AFA, Niemann S, Ngonga Ngomo
    A-C. <i>IngridKG: A FAIR Knowledge Graph of Graffiti</i>. LibreCat University;
    2023. doi:<a href="https://doi.org/10.5281/ZENODO.7560242">10.5281/ZENODO.7560242</a>'
  apa: 'Sherif, M., Morim da Silva, A. A., Pestryakova, S., Ahmed, A. F. A., Niemann,
    S., &#38; Ngonga Ngomo, A.-C. (2023). <i>IngridKG: A FAIR Knowledge Graph of Graffiti</i>.
    LibreCat University. <a href="https://doi.org/10.5281/ZENODO.7560242">https://doi.org/10.5281/ZENODO.7560242</a>'
  bibtex: '@book{Sherif_Morim da Silva_Pestryakova_Ahmed_Niemann_Ngonga Ngomo_2023,
    title={IngridKG: A FAIR Knowledge Graph of Graffiti}, DOI={<a href="https://doi.org/10.5281/ZENODO.7560242">10.5281/ZENODO.7560242</a>},
    publisher={LibreCat University}, author={Sherif, Mohamed and Morim da Silva, Ana
    Alexandra and Pestryakova, Svetlana and Ahmed, Abdullah Fathi Ahmed and Niemann,
    Sven and Ngonga Ngomo, Axel-Cyrille}, year={2023} }'
  chicago: 'Sherif, Mohamed, Ana Alexandra Morim da Silva, Svetlana Pestryakova, Abdullah
    Fathi Ahmed Ahmed, Sven Niemann, and Axel-Cyrille Ngonga Ngomo. <i>IngridKG: A
    FAIR Knowledge Graph of Graffiti</i>. LibreCat University, 2023. <a href="https://doi.org/10.5281/ZENODO.7560242">https://doi.org/10.5281/ZENODO.7560242</a>.'
  ieee: 'M. Sherif, A. A. Morim da Silva, S. Pestryakova, A. F. A. Ahmed, S. Niemann,
    and A.-C. Ngonga Ngomo, <i>IngridKG: A FAIR Knowledge Graph of Graffiti</i>. LibreCat
    University, 2023.'
  mla: 'Sherif, Mohamed, et al. <i>IngridKG: A FAIR Knowledge Graph of Graffiti</i>.
    LibreCat University, 2023, doi:<a href="https://doi.org/10.5281/ZENODO.7560242">10.5281/ZENODO.7560242</a>.'
  short: 'M. Sherif, A.A. Morim da Silva, S. Pestryakova, A.F.A. Ahmed, S. Niemann,
    A.-C. Ngonga Ngomo, IngridKG: A FAIR Knowledge Graph of Graffiti, LibreCat University,
    2023.'
date_created: 2023-06-09T10:09:34Z
date_updated: 2023-08-16T10:23:55Z
department:
- _id: '34'
doi: 10.5281/ZENODO.7560242
project:
- _id: '104'
  grant_number: '289287267'
  name: 'INGRID: INGRID: Informationssystem Graffiti in Deutschland'
publisher: LibreCat University
status: public
title: 'IngridKG: A FAIR Knowledge Graph of Graffiti'
type: research_data
user_id: '67234'
year: '2023'
...
---
_id: '46579'
abstract:
- lang: eng
  text: "The Koopman operator has become an essential tool for data-driven analysis,
    prediction and control of complex systems, the main reason being the enormous
    potential of identifying linear function space representations of nonlinear\r\ndynamics
    from measurements. Until now, the situation where for large-scale systems, we
    (i) only have access to partial observations (i.e., measurements, as is very common
    for experimental data) or (ii) deliberately perform coarse\r\ngraining (for efficiency
    reasons) has not been treated to its full extent. In this paper, we address the
    pitfall associated with this situation, that the classical EDMD algorithm does
    not automatically provide a Koopman operator approximation for the underlying
    system if we do not carefully select the number of observables. Moreover, we show
    that symmetries in the system dynamics can be carried over to the Koopman operator,
    which allows us to massively increase the model efficiency. We also briefly draw
    a connection to domain decomposition techniques for partial differential equations
    and present numerical evidence using the Kuramoto--Sivashinsky equation."
author:
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
- first_name: Hans
  full_name: Harder, Hans
  id: '98879'
  last_name: Harder
- first_name: Feliks
  full_name: Nüske, Feliks
  last_name: Nüske
- first_name: Friedrich
  full_name: Philipp, Friedrich
  last_name: Philipp
- first_name: Manuel
  full_name: Schaller, Manuel
  last_name: Schaller
- first_name: Karl
  full_name: Worthmann, Karl
  last_name: Worthmann
citation:
  ama: Peitz S, Harder H, Nüske F, Philipp F, Schaller M, Worthmann K. Partial observations,
    coarse graining and equivariance in Koopman  operator theory for large-scale dynamical
    systems. <i>arXiv:230715325</i>. Published online 2023.
  apa: Peitz, S., Harder, H., Nüske, F., Philipp, F., Schaller, M., &#38; Worthmann,
    K. (2023). Partial observations, coarse graining and equivariance in Koopman 
    operator theory for large-scale dynamical systems. In <i>arXiv:2307.15325</i>.
  bibtex: '@article{Peitz_Harder_Nüske_Philipp_Schaller_Worthmann_2023, title={Partial
    observations, coarse graining and equivariance in Koopman  operator theory for
    large-scale dynamical systems}, journal={arXiv:2307.15325}, author={Peitz, Sebastian
    and Harder, Hans and Nüske, Feliks and Philipp, Friedrich and Schaller, Manuel
    and Worthmann, Karl}, year={2023} }'
  chicago: Peitz, Sebastian, Hans Harder, Feliks Nüske, Friedrich Philipp, Manuel
    Schaller, and Karl Worthmann. “Partial Observations, Coarse Graining and Equivariance
    in Koopman  Operator Theory for Large-Scale Dynamical Systems.” <i>ArXiv:2307.15325</i>,
    2023.
  ieee: S. Peitz, H. Harder, F. Nüske, F. Philipp, M. Schaller, and K. Worthmann,
    “Partial observations, coarse graining and equivariance in Koopman  operator theory
    for large-scale dynamical systems,” <i>arXiv:2307.15325</i>. 2023.
  mla: Peitz, Sebastian, et al. “Partial Observations, Coarse Graining and Equivariance
    in Koopman  Operator Theory for Large-Scale Dynamical Systems.” <i>ArXiv:2307.15325</i>,
    2023.
  short: S. Peitz, H. Harder, F. Nüske, F. Philipp, M. Schaller, K. Worthmann, ArXiv:2307.15325
    (2023).
date_created: 2023-08-21T05:52:24Z
date_updated: 2023-08-21T05:53:35Z
department:
- _id: '655'
external_id:
  arxiv:
  - '2307.15325'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/pdf/2307.15325
oa: '1'
publication: arXiv:2307.15325
status: public
title: Partial observations, coarse graining and equivariance in Koopman  operator
  theory for large-scale dynamical systems
type: preprint
user_id: '47427'
year: '2023'
...
---
_id: '23428'
abstract:
- lang: eng
  text: "The Koopman operator has become an essential tool for data-driven approximation
    of dynamical (control) systems in recent years, e.g., via extended dynamic mode
    decomposition. Despite its popularity, convergence results and, in particular,
    error bounds are still quite scarce. In this paper, we derive probabilistic bounds
    for the approximation error and the prediction error depending on the number of
    training data points; for both ordinary and stochastic differential equations.
    Moreover, we extend our analysis to nonlinear control-affine systems using either
    ergodic trajectories or i.i.d.\r\nsamples. Here, we exploit the linearity of the
    Koopman generator to obtain a bilinear system and, thus, circumvent the curse
    of dimensionality since we do not autonomize the system by augmenting the state
    by the control inputs. To the\r\nbest of our knowledge, this is the first finite-data
    error analysis in the stochastic and/or control setting. Finally, we demonstrate
    the effectiveness of the proposed approach by comparing it with state-of-the-art
    techniques showing its superiority whenever state and control are coupled."
article_number: '14'
author:
- first_name: Feliks
  full_name: Nüske, Feliks
  id: '81513'
  last_name: Nüske
  orcid: 0000-0003-2444-7889
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
- first_name: Friedrich
  full_name: Philipp, Friedrich
  last_name: Philipp
- first_name: Manuel
  full_name: Schaller, Manuel
  last_name: Schaller
- first_name: Karl
  full_name: Worthmann, Karl
  last_name: Worthmann
citation:
  ama: Nüske F, Peitz S, Philipp F, Schaller M, Worthmann K. Finite-data error bounds
    for Koopman-based prediction and control. <i>Journal of Nonlinear Science</i>.
    2023;33. doi:<a href="https://doi.org/10.1007/s00332-022-09862-1">10.1007/s00332-022-09862-1</a>
  apa: Nüske, F., Peitz, S., Philipp, F., Schaller, M., &#38; Worthmann, K. (2023).
    Finite-data error bounds for Koopman-based prediction and control. <i>Journal
    of Nonlinear Science</i>, <i>33</i>, Article 14. <a href="https://doi.org/10.1007/s00332-022-09862-1">https://doi.org/10.1007/s00332-022-09862-1</a>
  bibtex: '@article{Nüske_Peitz_Philipp_Schaller_Worthmann_2023, title={Finite-data
    error bounds for Koopman-based prediction and control}, volume={33}, DOI={<a href="https://doi.org/10.1007/s00332-022-09862-1">10.1007/s00332-022-09862-1</a>},
    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.”
    <i>Journal of Nonlinear Science</i> 33 (2023). <a href="https://doi.org/10.1007/s00332-022-09862-1">https://doi.org/10.1007/s00332-022-09862-1</a>.
  ieee: 'F. Nüske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann, “Finite-data
    error bounds for Koopman-based prediction and control,” <i>Journal of Nonlinear
    Science</i>, vol. 33, Art. no. 14, 2023, doi: <a href="https://doi.org/10.1007/s00332-022-09862-1">10.1007/s00332-022-09862-1</a>.'
  mla: Nüske, Feliks, et al. “Finite-Data Error Bounds for Koopman-Based Prediction
    and Control.” <i>Journal of Nonlinear Science</i>, vol. 33, 14, 2023, doi:<a href="https://doi.org/10.1007/s00332-022-09862-1">10.1007/s00332-022-09862-1</a>.
  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. <i>SIAM Journal on Scientific Computing</i>.
    2023;45(2):A579-A595. doi:<a href="https://doi.org/10.1137/21M1412682">10.1137/21M1412682</a>
  apa: Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz,
    S., &#38; Pfannschmidt, K. (2023). Efficient time stepping for numerical integration
    using reinforcement  learning. <i>SIAM Journal on Scientific Computing</i>, <i>45</i>(2),
    A579–A595. <a href="https://doi.org/10.1137/21M1412682">https://doi.org/10.1137/21M1412682</a>
  bibtex: '@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023,
    title={Efficient time stepping for numerical integration using reinforcement 
    learning}, volume={45}, DOI={<a href="https://doi.org/10.1137/21M1412682">10.1137/21M1412682</a>},
    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.” <i>SIAM Journal on Scientific
    Computing</i> 45, no. 2 (2023): A579–95. <a href="https://doi.org/10.1137/21M1412682">https://doi.org/10.1137/21M1412682</a>.'
  ieee: 'M. Dellnitz <i>et al.</i>, “Efficient time stepping for numerical integration
    using reinforcement  learning,” <i>SIAM Journal on Scientific Computing</i>, vol.
    45, no. 2, pp. A579–A595, 2023, doi: <a href="https://doi.org/10.1137/21M1412682">10.1137/21M1412682</a>.'
  mla: Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration
    Using Reinforcement  Learning.” <i>SIAM Journal on Scientific Computing</i>, vol.
    45, no. 2, 2023, pp. A579–95, doi:<a href="https://doi.org/10.1137/21M1412682">10.1137/21M1412682</a>.
  short: M. Dellnitz, E. Hüllermeier, M. Lücke, S. Ober-Blöbaum, C. Offen, S. Peitz,
    K. Pfannschmidt, SIAM Journal on Scientific Computing 45 (2023) A579–A595.
date_created: 2021-04-09T07:59:19Z
date_updated: 2023-08-25T09:24:50Z
ddc:
- '510'
department:
- _id: '101'
- _id: '636'
- _id: '355'
- _id: '655'
doi: 10.1137/21M1412682
external_id:
  arxiv:
  - arXiv:2104.03562
has_accepted_license: '1'
intvolume: '        45'
issue: '2'
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/reader/10.1137/21M1412682
page: A579-A595
publication: SIAM Journal on Scientific Computing
publication_status: published
related_material:
  link:
  - description: GitHub
    relation: software
    url: https://github.com/lueckem/quadrature-ML
status: public
title: Efficient time stepping for numerical integration using reinforcement  learning
type: journal_article
user_id: '47427'
volume: 45
year: '2023'
...
---
_id: '46739'
author:
- first_name: Somayeh
  full_name: Sadeghi-Kohan, Somayeh
  id: '78614'
  last_name: Sadeghi-Kohan
  orcid: https://orcid.org/0000-0001-7246-0610
- first_name: Sybille
  full_name: Hellebrand, Sybille
  id: '209'
  last_name: Hellebrand
  orcid: 0000-0002-3717-3939
- first_name: Hans-Joachim
  full_name: Wunderlich, Hans-Joachim
  last_name: Wunderlich
citation:
  ama: 'Sadeghi-Kohan S, Hellebrand S, Wunderlich H-J. Low Power Streaming of Sensor
    Data Using Gray Code-Based Approximate Communication. In: <i>2023 53rd Annual
    IEEE/IFIP International Conference on Dependable Systems and Networks Workshops
    (DSN-W)</i>. IEEE; 2023. doi:<a href="https://doi.org/10.1109/dsn-w58399.2023.00056">10.1109/dsn-w58399.2023.00056</a>'
  apa: Sadeghi-Kohan, S., Hellebrand, S., &#38; Wunderlich, H.-J. (2023). Low Power
    Streaming of Sensor Data Using Gray Code-Based Approximate Communication. <i>2023
    53rd Annual IEEE/IFIP International Conference on Dependable Systems and Networks
    Workshops (DSN-W)</i>. <a href="https://doi.org/10.1109/dsn-w58399.2023.00056">https://doi.org/10.1109/dsn-w58399.2023.00056</a>
  bibtex: '@inproceedings{Sadeghi-Kohan_Hellebrand_Wunderlich_2023, title={Low Power
    Streaming of Sensor Data Using Gray Code-Based Approximate Communication}, DOI={<a
    href="https://doi.org/10.1109/dsn-w58399.2023.00056">10.1109/dsn-w58399.2023.00056</a>},
    booktitle={2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems
    and Networks Workshops (DSN-W)}, publisher={IEEE}, author={Sadeghi-Kohan, Somayeh
    and Hellebrand, Sybille and Wunderlich, Hans-Joachim}, year={2023} }'
  chicago: Sadeghi-Kohan, Somayeh, Sybille Hellebrand, and Hans-Joachim Wunderlich.
    “Low Power Streaming of Sensor Data Using Gray Code-Based Approximate Communication.”
    In <i>2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems
    and Networks Workshops (DSN-W)</i>. IEEE, 2023. <a href="https://doi.org/10.1109/dsn-w58399.2023.00056">https://doi.org/10.1109/dsn-w58399.2023.00056</a>.
  ieee: 'S. Sadeghi-Kohan, S. Hellebrand, and H.-J. Wunderlich, “Low Power Streaming
    of Sensor Data Using Gray Code-Based Approximate Communication,” 2023, doi: <a
    href="https://doi.org/10.1109/dsn-w58399.2023.00056">10.1109/dsn-w58399.2023.00056</a>.'
  mla: Sadeghi-Kohan, Somayeh, et al. “Low Power Streaming of Sensor Data Using Gray
    Code-Based Approximate Communication.” <i>2023 53rd Annual IEEE/IFIP International
    Conference on Dependable Systems and Networks Workshops (DSN-W)</i>, IEEE, 2023,
    doi:<a href="https://doi.org/10.1109/dsn-w58399.2023.00056">10.1109/dsn-w58399.2023.00056</a>.
  short: 'S. Sadeghi-Kohan, S. Hellebrand, H.-J. Wunderlich, in: 2023 53rd Annual
    IEEE/IFIP International Conference on Dependable Systems and Networks Workshops
    (DSN-W), IEEE, 2023.'
date_created: 2023-08-26T10:48:31Z
date_updated: 2023-08-26T10:49:07Z
department:
- _id: '48'
doi: 10.1109/dsn-w58399.2023.00056
language:
- iso: eng
publication: 2023 53rd Annual IEEE/IFIP International Conference on Dependable Systems
  and Networks Workshops (DSN-W)
publication_status: published
publisher: IEEE
status: public
title: Low Power Streaming of Sensor Data Using Gray Code-Based Approximate Communication
type: conference
user_id: '78614'
year: '2023'
...
