---
_id: '6445'
article_number: '30'
article_type: original
author:
- first_name: Bernhard
  full_name: Bachmann, Bernhard
  id: '33931'
  last_name: Bachmann
  orcid: 0000-0002-4339-0438
  orcid_put_code_url: https://api.orcid.org/v2.0/0000-0002-4339-0438/work/202504183
- first_name: Luca
  full_name: Bonaventura, Luca
  last_name: Bonaventura
- first_name: Francesco
  full_name: Casella, Francesco
  last_name: Casella
- first_name: Soledad
  full_name: Fernández-García, Soledad
  last_name: Fernández-García
- first_name: Macarena
  full_name: Gómez-Mármol, Macarena
  last_name: Gómez-Mármol
- first_name: Philip
  full_name: Hannebohm, Philip
  id: '221456'
  last_name: Hannebohm
  orcid: 0009-0003-8902-9079
  orcid_put_code_url: https://api.orcid.org/v2.0/0009-0003-8902-9079/work/202504184
citation:
  alphadin: '<span style="font-variant:small-caps;">Bachmann, Bernhard</span> ; <span
    style="font-variant:small-caps;">Bonaventura, Luca</span> ; <span style="font-variant:small-caps;">Casella,
    Francesco</span> ; <span style="font-variant:small-caps;">Fernández-García, Soledad</span>
    ; <span style="font-variant:small-caps;">Gómez-Mármol, Macarena</span> ; <span
    style="font-variant:small-caps;">Hannebohm, Philip</span>: Self-Adjusting Multi-Rate
    Runge-Kutta Methods: Analysis and Efficient Implementation in An Open Source Framework.
    In: <i>Journal of Scientific Computing</i> Bd. 105, Springer Science and Business
    Media LLC (2025), Nr. 1'
  ama: 'Bachmann B, Bonaventura L, Casella F, Fernández-García S, Gómez-Mármol M,
    Hannebohm P. Self-Adjusting Multi-Rate Runge-Kutta Methods: Analysis and Efficient
    Implementation in An Open Source Framework. <i>Journal of Scientific Computing</i>.
    2025;105(1). doi:<a href="https://doi.org/10.1007/s10915-025-03049-y">10.1007/s10915-025-03049-y</a>'
  apa: 'Bachmann, B., Bonaventura, L., Casella, F., Fernández-García, S., Gómez-Mármol,
    M., &#38; Hannebohm, P. (2025). Self-Adjusting Multi-Rate Runge-Kutta Methods:
    Analysis and Efficient Implementation in An Open Source Framework. <i>Journal
    of Scientific Computing</i>, <i>105</i>(1). <a href="https://doi.org/10.1007/s10915-025-03049-y">https://doi.org/10.1007/s10915-025-03049-y</a>'
  bibtex: '@article{Bachmann_Bonaventura_Casella_Fernández-García_Gómez-Mármol_Hannebohm_2025,
    title={Self-Adjusting Multi-Rate Runge-Kutta Methods: Analysis and Efficient Implementation
    in An Open Source Framework}, volume={105}, DOI={<a href="https://doi.org/10.1007/s10915-025-03049-y">10.1007/s10915-025-03049-y</a>},
    number={130}, journal={Journal of Scientific Computing}, publisher={Springer Science
    and Business Media LLC}, author={Bachmann, Bernhard and Bonaventura, Luca and
    Casella, Francesco and Fernández-García, Soledad and Gómez-Mármol, Macarena and
    Hannebohm, Philip}, year={2025} }'
  chicago: 'Bachmann, Bernhard, Luca Bonaventura, Francesco Casella, Soledad Fernández-García,
    Macarena Gómez-Mármol, and Philip Hannebohm. “Self-Adjusting Multi-Rate Runge-Kutta
    Methods: Analysis and Efficient Implementation in An Open Source Framework.” <i>Journal
    of Scientific Computing</i> 105, no. 1 (2025). <a href="https://doi.org/10.1007/s10915-025-03049-y">https://doi.org/10.1007/s10915-025-03049-y</a>.'
  ieee: 'B. Bachmann, L. Bonaventura, F. Casella, S. Fernández-García, M. Gómez-Mármol,
    and P. Hannebohm, “Self-Adjusting Multi-Rate Runge-Kutta Methods: Analysis and
    Efficient Implementation in An Open Source Framework,” <i>Journal of Scientific
    Computing</i>, vol. 105, no. 1, 2025.'
  mla: 'Bachmann, Bernhard, et al. “Self-Adjusting Multi-Rate Runge-Kutta Methods:
    Analysis and Efficient Implementation in An Open Source Framework.” <i>Journal
    of Scientific Computing</i>, vol. 105, no. 1, 30, Springer Science and Business
    Media LLC, 2025, doi:<a href="https://doi.org/10.1007/s10915-025-03049-y">10.1007/s10915-025-03049-y</a>.'
  short: B. Bachmann, L. Bonaventura, F. Casella, S. Fernández-García, M. Gómez-Mármol,
    P. Hannebohm, Journal of Scientific Computing 105 (2025).
date_created: 2026-01-14T16:03:23Z
date_updated: 2026-03-17T15:29:30Z
doi: 10.1007/s10915-025-03049-y
intvolume: '       105'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
publication: Journal of Scientific Computing
publication_identifier:
  eissn:
  - 1573-7691
  issn:
  - 0885-7474
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: 'Self-Adjusting Multi-Rate Runge-Kutta Methods: Analysis and Efficient Implementation
  in An Open Source Framework'
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: '263827'
volume: 105
year: '2025'
...
---
_id: '6448'
author:
- first_name: Felix
  full_name: Brandt, Felix
  last_name: Brandt
- first_name: Andreas
  full_name: Heuermann, Andreas
  last_name: Heuermann
- first_name: Philip
  full_name: Hannebohm, Philip
  id: '221456'
  last_name: Hannebohm
  orcid: 0009-0003-8902-9079
  orcid_put_code_url: https://api.orcid.org/v2.0/0009-0003-8902-9079/work/202504693
- first_name: Bernhard
  full_name: Bachmann, Bernhard
  id: '33931'
  last_name: Bachmann
  orcid: 0000-0002-4339-0438
  orcid_put_code_url: https://api.orcid.org/v2.0/0000-0002-4339-0438/work/202504694
citation:
  alphadin: '<span style="font-variant:small-caps;">Brandt, Felix</span> ; <span style="font-variant:small-caps;">Heuermann,
    Andreas</span> ; <span style="font-variant:small-caps;">Hannebohm, Philip</span>
    ; <span style="font-variant:small-caps;">Bachmann, Bernhard</span>: Residual-Informed
    Learning of Solutions to Algebraic Loops. In: <i>arXiv:2510.09317</i> (2025)'
  ama: Brandt F, Heuermann A, Hannebohm P, Bachmann B. Residual-Informed Learning
    of Solutions to Algebraic Loops. <i>arXiv:251009317</i>. 2025.
  apa: Brandt, F., Heuermann, A., Hannebohm, P., &#38; Bachmann, B. (2025). Residual-Informed
    Learning of Solutions to Algebraic Loops. <i>ArXiv:2510.09317</i>.
  bibtex: '@article{Brandt_Heuermann_Hannebohm_Bachmann_2025, title={Residual-Informed
    Learning of Solutions to Algebraic Loops}, journal={arXiv:2510.09317}, author={Brandt,
    Felix and Heuermann, Andreas and Hannebohm, Philip and Bachmann, Bernhard}, year={2025}
    }'
  chicago: Brandt, Felix, Andreas Heuermann, Philip Hannebohm, and Bernhard Bachmann.
    “Residual-Informed Learning of Solutions to Algebraic Loops.” <i>ArXiv:2510.09317</i>,
    2025.
  ieee: F. Brandt, A. Heuermann, P. Hannebohm, and B. Bachmann, “Residual-Informed
    Learning of Solutions to Algebraic Loops,” <i>arXiv:2510.09317</i>. 2025.
  mla: Brandt, Felix, et al. “Residual-Informed Learning of Solutions to Algebraic
    Loops.” <i>ArXiv:2510.09317</i>, 2025.
  short: F. Brandt, A. Heuermann, P. Hannebohm, B. Bachmann, ArXiv:2510.09317 (2025).
date_created: 2026-01-14T16:09:00Z
date_updated: 2026-03-17T15:29:30Z
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
publication: arXiv:2510.09317
status: public
title: Residual-Informed Learning of Solutions to Algebraic Loops
type: preprint
user_id: '263827'
year: '2025'
...
---
_id: '6449'
author:
- first_name: Francesco
  full_name: Casella, Francesco
  last_name: Casella
- first_name: Bernhard
  full_name: Bachmann, Bernhard
  id: '33931'
  last_name: Bachmann
  orcid: 0000-0002-4339-0438
  orcid_put_code_url: https://api.orcid.org/v2.0/0000-0002-4339-0438/work/202504612
- first_name: Karim
  full_name: Abdelhak, Karim
  last_name: Abdelhak
- first_name: Philip
  full_name: Hannebohm, Philip
  id: '221456'
  last_name: Hannebohm
  orcid: 0009-0003-8902-9079
  orcid_put_code_url: https://api.orcid.org/v2.0/0009-0003-8902-9079/work/202504613
- first_name: Teus
  full_name: Van der Stelt, Teus
  last_name: Van der Stelt
citation:
  alphadin: '<span style="font-variant:small-caps;">Casella, Francesco</span> ; <span
    style="font-variant:small-caps;">Bachmann, Bernhard</span> ; <span style="font-variant:small-caps;">Abdelhak,
    Karim</span> ; <span style="font-variant:small-caps;">Hannebohm, Philip</span>
    ; <span style="font-variant:small-caps;">Van der Stelt, Teus</span>: Diagnosing
    Newton’s Solver Convergence Failures in the Initialization of Modelica Models.
    In: <i>Proceedings of the 16th International Modelica&#38;FMI Conference, September
    8 – 10, 2025, Lucerne University of Applied Sciences and Arts (HSLU)</i>, <i>Linköping
    Electronic Conference Proceedings</i>. Bd. 218 : Linköping University Electronic
    Press, 2025'
  ama: 'Casella F, Bachmann B, Abdelhak K, Hannebohm P, Van der Stelt T. Diagnosing
    Newton’s Solver Convergence Failures in the Initialization of Modelica Models.
    In: <i>Proceedings of the 16th International Modelica&#38;FMI Conference, September
    8 – 10, 2025, Lucerne University of Applied Sciences and Arts (HSLU)</i>. Vol
    218. Linköping Electronic Conference Proceedings. Linköping University Electronic
    Press; 2025. doi:<a href="https://doi.org/10.3384/ecp218109">10.3384/ecp218109</a>'
  apa: Casella, F., Bachmann, B., Abdelhak, K., Hannebohm, P., &#38; Van der Stelt,
    T. (2025). Diagnosing Newton’s Solver Convergence Failures in the Initialization
    of Modelica Models. In <i>Proceedings of the 16th International Modelica&#38;FMI
    Conference, September 8 – 10, 2025, Lucerne University of Applied Sciences and
    Arts (HSLU)</i> (Vol. 218). Linköping University Electronic Press. <a href="https://doi.org/10.3384/ecp218109">https://doi.org/10.3384/ecp218109</a>
  bibtex: '@inproceedings{Casella_Bachmann_Abdelhak_Hannebohm_Van der Stelt_2025,
    series={Linköping Electronic Conference Proceedings}, title={Diagnosing Newton’s
    Solver Convergence Failures in the Initialization of Modelica Models}, volume={218},
    DOI={<a href="https://doi.org/10.3384/ecp218109">10.3384/ecp218109</a>}, booktitle={Proceedings
    of the 16th International Modelica&#38;FMI Conference, September 8 – 10, 2025,
    Lucerne University of Applied Sciences and Arts (HSLU)}, publisher={Linköping
    University Electronic Press}, author={Casella, Francesco and Bachmann, Bernhard
    and Abdelhak, Karim and Hannebohm, Philip and Van der Stelt, Teus}, year={2025},
    collection={Linköping Electronic Conference Proceedings} }'
  chicago: Casella, Francesco, Bernhard Bachmann, Karim Abdelhak, Philip Hannebohm,
    and Teus Van der Stelt. “Diagnosing Newton’s Solver Convergence Failures in the
    Initialization of Modelica Models.” In <i>Proceedings of the 16th International
    Modelica&#38;FMI Conference, September 8 – 10, 2025, Lucerne University of Applied
    Sciences and Arts (HSLU)</i>, Vol. 218. Linköping Electronic Conference Proceedings.
    Linköping University Electronic Press, 2025. <a href="https://doi.org/10.3384/ecp218109">https://doi.org/10.3384/ecp218109</a>.
  ieee: F. Casella, B. Bachmann, K. Abdelhak, P. Hannebohm, and T. Van der Stelt,
    “Diagnosing Newton’s Solver Convergence Failures in the Initialization of Modelica
    Models,” in <i>Proceedings of the 16th International Modelica&#38;FMI Conference,
    September 8 – 10, 2025, Lucerne University of Applied Sciences and Arts (HSLU)</i>,
    2025, vol. 218.
  mla: Casella, Francesco, et al. “Diagnosing Newton’s Solver Convergence Failures
    in the Initialization of Modelica Models.” <i>Proceedings of the 16th International
    Modelica&#38;FMI Conference, September 8 – 10, 2025, Lucerne University of Applied
    Sciences and Arts (HSLU)</i>, vol. 218, Linköping University Electronic Press,
    2025, doi:<a href="https://doi.org/10.3384/ecp218109">10.3384/ecp218109</a>.
  short: 'F. Casella, B. Bachmann, K. Abdelhak, P. Hannebohm, T. Van der Stelt, in:
    Proceedings of the 16th International Modelica&#38;FMI Conference, September 8
    – 10, 2025, Lucerne University of Applied Sciences and Arts (HSLU), Linköping
    University Electronic Press, 2025.'
conference:
  name: The 16th International Modelica&FMI Conference, September 8 – 10, 2025, Lucerne
    University of Applied Sciences and Arts (HSLU)
date_created: 2026-01-14T16:10:30Z
date_updated: 2026-03-17T15:29:30Z
doi: 10.3384/ecp218109
intvolume: '       218'
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
publication: Proceedings of the 16th International Modelica&FMI Conference, September
  8 – 10, 2025, Lucerne University of Applied Sciences and Arts (HSLU)
publication_identifier:
  eisbn:
  - 978-91-8118-266-8
publication_status: published
publisher: Linköping University Electronic Press
series_title: Linköping Electronic Conference Proceedings
status: public
title: Diagnosing Newton’s Solver Convergence Failures in the Initialization of Modelica
  Models
type: conference
user_id: '263827'
volume: 218
year: '2025'
...
---
_id: '6357'
author:
- first_name: Philip
  full_name: Hannebohm, Philip
  id: '221456'
  last_name: Hannebohm
  orcid: 0009-0003-8902-9079
  orcid_put_code_url: https://api.orcid.org/v2.0/0009-0003-8902-9079/work/198431201
- first_name: Bernhard
  full_name: Bachmann, Bernhard
  id: '33931'
  last_name: Bachmann
  orcid: 0000-0002-4339-0438
  orcid_put_code_url: https://api.orcid.org/v2.0/0000-0002-4339-0438/work/198431202
citation:
  alphadin: '<span style="font-variant:small-caps;">Hannebohm, Philip</span> ; <span
    style="font-variant:small-caps;">Bachmann, Bernhard</span>: Selective Evaluation
    of RHS during Multi-Rate Simulation. In: <span style="font-variant:small-caps;">Zimmer,
    D.</span> ; <span style="font-variant:small-caps;">Müller, U. C.</span> (Hrsg.):
    <i>Proceedings of the 16th International Modelica&#38;FMI Conference</i>, <i>Linköping
    Electronic Conference Proceedings</i>. Bd. 218 : Linköping University Electronic
    Press, 2025, S. 943–947'
  ama: 'Hannebohm P, Bachmann B. Selective Evaluation of RHS during Multi-Rate Simulation.
    In: Zimmer D, Müller UC, eds. <i>Proceedings of the 16th International Modelica&#38;FMI
    Conference</i>. Vol 218. Linköping Electronic Conference Proceedings. Linköping
    University Electronic Press; 2025:943–947. doi:<a href="https://doi.org/10.3384/ecp218943">10.3384/ecp218943</a>'
  apa: 'Hannebohm, P., &#38; Bachmann, B. (2025). Selective Evaluation of RHS during
    Multi-Rate Simulation. In D. Zimmer &#38; U. C. Müller (Eds.), <i>Proceedings
    of the 16th International Modelica&#38;FMI Conference</i> (Vol. 218, pp. 943–947).
    Lucerne: Linköping University Electronic Press. <a href="https://doi.org/10.3384/ecp218943">https://doi.org/10.3384/ecp218943</a>'
  bibtex: '@inproceedings{Hannebohm_Bachmann_2025, series={Linköping Electronic Conference
    Proceedings}, title={Selective Evaluation of RHS during Multi-Rate Simulation},
    volume={218}, DOI={<a href="https://doi.org/10.3384/ecp218943">10.3384/ecp218943</a>},
    booktitle={Proceedings of the 16th International Modelica&#38;FMI Conference},
    publisher={Linköping University Electronic Press}, author={Hannebohm, Philip and
    Bachmann, Bernhard}, editor={Zimmer, Dirk and Müller, Ulf ChristianEditors}, year={2025},
    pages={943–947}, collection={Linköping Electronic Conference Proceedings} }'
  chicago: Hannebohm, Philip, and Bernhard Bachmann. “Selective Evaluation of RHS
    during Multi-Rate Simulation.” In <i>Proceedings of the 16th International Modelica&#38;FMI
    Conference</i>, edited by Dirk Zimmer and Ulf Christian Müller, 218:943–947. Linköping
    Electronic Conference Proceedings. Linköping University Electronic Press, 2025.
    <a href="https://doi.org/10.3384/ecp218943">https://doi.org/10.3384/ecp218943</a>.
  ieee: P. Hannebohm and B. Bachmann, “Selective Evaluation of RHS during Multi-Rate
    Simulation,” in <i>Proceedings of the 16th International Modelica&#38;FMI Conference</i>,
    Lucerne, 2025, vol. 218, pp. 943–947.
  mla: Hannebohm, Philip, and Bernhard Bachmann. “Selective Evaluation of RHS during
    Multi-Rate Simulation.” <i>Proceedings of the 16th International Modelica&#38;FMI
    Conference</i>, edited by Dirk Zimmer and Ulf Christian Müller, vol. 218, Linköping
    University Electronic Press, 2025, pp. 943–947, doi:<a href="https://doi.org/10.3384/ecp218943">10.3384/ecp218943</a>.
  short: 'P. Hannebohm, B. Bachmann, in: D. Zimmer, U.C. Müller (Eds.), Proceedings
    of the 16th International Modelica&#38;FMI Conference, Linköping University Electronic
    Press, 2025, pp. 943–947.'
conference:
  end_date: 2025-09-10
  location: Lucerne
  name: The 16th International Modelica&FMI Conference
  start_date: 2025-09-08
date_created: 2025-12-01T13:48:57Z
date_updated: 2026-03-17T15:29:29Z
department:
- _id: '103'
doi: 10.3384/ecp218943
editor:
- first_name: Dirk
  full_name: Zimmer, Dirk
  last_name: Zimmer
- first_name: Ulf Christian
  full_name: Müller, Ulf Christian
  last_name: Müller
file:
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  creator: phannebohm
  date_created: 2025-12-01T13:55:19Z
  date_updated: 2025-12-01T13:55:19Z
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  file_name: paper.pdf
  file_size: 149702
  relation: main_file
  success: 1
file_date_updated: 2025-12-01T13:55:19Z
has_accepted_license: '1'
intvolume: '       218'
keyword:
- Equation-based modelling
- Multi-rate simulation
- Structural analysis
language:
- iso: eng
oa: '1'
page: 943–947
publication: Proceedings of the 16th International Modelica&FMI Conference
publication_identifier:
  eisbn:
  - 978-91-8118-266-8
publication_status: published
publisher: Linköping University Electronic Press
quality_controlled: '1'
series_title: Linköping Electronic Conference Proceedings
status: public
title: Selective Evaluation of RHS during Multi-Rate Simulation
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference_abstract
urn: urn:nbn:de:hbz:bi10-63570
user_id: '263827'
volume: 218
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...
---
_id: '6359'
author:
- first_name: Linus
  full_name: Langenkamp, Linus
  id: '240430'
  last_name: Langenkamp
  orcid: 0009-0009-7517-4842
  orcid_put_code_url: https://api.orcid.org/v2.0/0009-0009-7517-4842/work/198540284
- first_name: Philip
  full_name: Hannebohm, Philip
  id: '221456'
  last_name: Hannebohm
  orcid: 0009-0003-8902-9079
  orcid_put_code_url: https://api.orcid.org/v2.0/0009-0003-8902-9079/work/198540286
- first_name: Bernhard
  full_name: Bachmann, Bernhard
  id: '33931'
  last_name: Bachmann
  orcid: 0000-0002-4339-0438
  orcid_put_code_url: https://api.orcid.org/v2.0/0000-0002-4339-0438/work/198540287
citation:
  alphadin: '<span style="font-variant:small-caps;">Langenkamp, Linus</span> ; <span
    style="font-variant:small-caps;">Hannebohm, Philip</span> ; <span style="font-variant:small-caps;">Bachmann,
    Bernhard</span>: Efficient Training of Physics-enhanced Neural ODEs via Direct
    Collocation and Nonlinear Programming. In: <span style="font-variant:small-caps;">Zimmer,
    D.</span> ; <span style="font-variant:small-caps;">Müller, U. C.</span> (Hrsg.):
    <i>Proceedings of the 16th International Modelica&#38;FMI Conference</i>. Bd.
    218 : Linköping University Electronic Press, 2025, S. 445–457'
  ama: 'Langenkamp L, Hannebohm P, Bachmann B. Efficient Training of Physics-enhanced
    Neural ODEs via Direct Collocation and Nonlinear Programming. In: Zimmer D, Müller
    UC, eds. <i>Proceedings of the 16th International Modelica&#38;FMI Conference</i>.
    Vol 218. Linköping University Electronic Press; 2025:445-457. doi:<a href="https://doi.org/10.3384/ecp218445">10.3384/ecp218445</a>'
  apa: 'Langenkamp, L., Hannebohm, P., &#38; Bachmann, B. (2025). Efficient Training
    of Physics-enhanced Neural ODEs via Direct Collocation and Nonlinear Programming.
    In D. Zimmer &#38; U. C. Müller (Eds.), <i>Proceedings of the 16th International
    Modelica&#38;FMI Conference</i> (Vol. 218, pp. 445–457). Luzern: Linköping University
    Electronic Press. <a href="https://doi.org/10.3384/ecp218445">https://doi.org/10.3384/ecp218445</a>'
  bibtex: '@inproceedings{Langenkamp_Hannebohm_Bachmann_2025, title={Efficient Training
    of Physics-enhanced Neural ODEs via Direct Collocation and Nonlinear Programming},
    volume={218}, DOI={<a href="https://doi.org/10.3384/ecp218445">10.3384/ecp218445</a>},
    booktitle={Proceedings of the 16th International Modelica&#38;FMI Conference},
    publisher={Linköping University Electronic Press}, author={Langenkamp, Linus and
    Hannebohm, Philip and Bachmann, Bernhard}, editor={Zimmer, Dirk and Müller, Ulf
    ChristianEditors}, year={2025}, pages={445–457} }'
  chicago: Langenkamp, Linus, Philip Hannebohm, and Bernhard Bachmann. “Efficient
    Training of Physics-Enhanced Neural ODEs via Direct Collocation and Nonlinear
    Programming.” In <i>Proceedings of the 16th International Modelica&#38;FMI Conference</i>,
    edited by Dirk Zimmer and Ulf Christian Müller, 218:445–57. Linköping University
    Electronic Press, 2025. <a href="https://doi.org/10.3384/ecp218445">https://doi.org/10.3384/ecp218445</a>.
  ieee: L. Langenkamp, P. Hannebohm, and B. Bachmann, “Efficient Training of Physics-enhanced
    Neural ODEs via Direct Collocation and Nonlinear Programming,” in <i>Proceedings
    of the 16th International Modelica&#38;FMI Conference</i>, Luzern, 2025, vol.
    218, pp. 445–457.
  mla: Langenkamp, Linus, et al. “Efficient Training of Physics-Enhanced Neural ODEs
    via Direct Collocation and Nonlinear Programming.” <i>Proceedings of the 16th
    International Modelica&#38;FMI Conference</i>, edited by Dirk Zimmer and Ulf Christian
    Müller, vol. 218, Linköping University Electronic Press, 2025, pp. 445–57, doi:<a
    href="https://doi.org/10.3384/ecp218445">10.3384/ecp218445</a>.
  short: 'L. Langenkamp, P. Hannebohm, B. Bachmann, in: D. Zimmer, U.C. Müller (Eds.),
    Proceedings of the 16th International Modelica&#38;FMI Conference, Linköping University
    Electronic Press, 2025, pp. 445–457.'
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  name: The 16th International Modelica&FMI Conference
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keyword:
- Physics-enhanced Neural ODEs
- Dynamic Optimization
- Nonlinear Programming
- Modelica
- NeuralODEs
- Universal Differential Equations
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title: Efficient Training of Physics-enhanced Neural ODEs via Direct Collocation and
  Nonlinear Programming
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  full_name: Schäfer, Matthias
  last_name: Schäfer
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citation:
  alphadin: '<span style="font-variant:small-caps;">Heuermann, Andreas</span> ; <span
    style="font-variant:small-caps;">Hannebohm, Philip</span> ; <span style="font-variant:small-caps;">Schäfer,
    Matthias</span> ; <span style="font-variant:small-caps;">Bachmann, Bernhard</span>:
    Accelerating the simulation of equation-based models by replacing non-linear algebraic
    loops with error-controlled machine learning surrogates. In: <span style="font-variant:small-caps;">Müller,
    D.</span> ; <span style="font-variant:small-caps;">Monti, A.</span> ; <span style="font-variant:small-caps;">Benigni,
    A.</span> (Hrsg.): <i>Proceedings of the 15th International Modelica Conference
    2023, Aachen, October 9-11</i>, <i>Linköping Electronic Conference Proceedings</i>.
    Bd. 204 : Linköping University Electronic Press, 2023, S. 275–284'
  ama: 'Heuermann A, Hannebohm P, Schäfer M, Bachmann B. Accelerating the simulation
    of equation-based models by replacing non-linear algebraic loops with error-controlled
    machine learning surrogates. In: Müller D, Monti A, Benigni A, eds. <i>Proceedings
    of the 15th International Modelica Conference 2023, Aachen, October 9-11</i>.
    Vol 204. Linköping Electronic Conference Proceedings. Linköping University Electronic
    Press; 2023:275-284. doi:<a href="https://doi.org/10.3384/ecp204275">10.3384/ecp204275</a>'
  apa: 'Heuermann, A., Hannebohm, P., Schäfer, M., &#38; Bachmann, B. (2023). Accelerating
    the simulation of equation-based models by replacing non-linear algebraic loops
    with error-controlled machine learning surrogates. In D. Müller, A. Monti, &#38;
    A. Benigni (Eds.), <i>Proceedings of the 15th International Modelica Conference
    2023, Aachen, October 9-11</i> (Vol. 204, pp. 275–284). Aachen: Linköping University
    Electronic Press. <a href="https://doi.org/10.3384/ecp204275">https://doi.org/10.3384/ecp204275</a>'
  bibtex: '@inproceedings{Heuermann_Hannebohm_Schäfer_Bachmann_2023, series={Linköping
    Electronic Conference Proceedings}, title={Accelerating the simulation of equation-based
    models by replacing non-linear algebraic loops with error-controlled machine learning
    surrogates}, volume={204}, DOI={<a href="https://doi.org/10.3384/ecp204275">10.3384/ecp204275</a>},
    booktitle={Proceedings of the 15th International Modelica Conference 2023, Aachen,
    October 9-11}, publisher={Linköping University Electronic Press}, author={Heuermann,
    Andreas and Hannebohm, Philip and Schäfer, Matthias and Bachmann, Bernhard}, editor={Müller,
    Dirk  and Monti, Antonello  and Benigni, Andrea Editors}, year={2023}, pages={275–284},
    collection={Linköping Electronic Conference Proceedings} }'
  chicago: Heuermann, Andreas, Philip Hannebohm, Matthias Schäfer, and Bernhard Bachmann.
    “Accelerating the Simulation of Equation-Based Models by Replacing Non-Linear
    Algebraic Loops with Error-Controlled Machine Learning Surrogates.” In <i>Proceedings
    of the 15th International Modelica Conference 2023, Aachen, October 9-11</i>,
    edited by Dirk  Müller, Antonello  Monti, and Andrea  Benigni, 204:275–84. Linköping
    Electronic Conference Proceedings. Linköping University Electronic Press, 2023.
    <a href="https://doi.org/10.3384/ecp204275">https://doi.org/10.3384/ecp204275</a>.
  ieee: A. Heuermann, P. Hannebohm, M. Schäfer, and B. Bachmann, “Accelerating the
    simulation of equation-based models by replacing non-linear algebraic loops with
    error-controlled machine learning surrogates,” in <i>Proceedings of the 15th International
    Modelica Conference 2023, Aachen, October 9-11</i>, Aachen, 2023, vol. 204, pp.
    275–284.
  mla: Heuermann, Andreas, et al. “Accelerating the Simulation of Equation-Based Models
    by Replacing Non-Linear Algebraic Loops with Error-Controlled Machine Learning
    Surrogates.” <i>Proceedings of the 15th International Modelica Conference 2023,
    Aachen, October 9-11</i>, edited by Dirk  Müller et al., vol. 204, Linköping University
    Electronic Press, 2023, pp. 275–84, doi:<a href="https://doi.org/10.3384/ecp204275">10.3384/ecp204275</a>.
  short: 'A. Heuermann, P. Hannebohm, M. Schäfer, B. Bachmann, in: D. Müller, A. Monti,
    A. Benigni (Eds.), Proceedings of the 15th International Modelica Conference 2023,
    Aachen, October 9-11, Linköping University Electronic Press, 2023, pp. 275–284.'
conference:
  end_date: 2023-10-11
  location: Aachen
  name: 15th International Modelica Conference 2023
  start_date: 2023-10-09
date_created: 2024-05-29T10:04:12Z
date_updated: 2026-03-17T15:29:03Z
doi: 10.3384/ecp204275
editor:
- first_name: 'Dirk '
  full_name: 'Müller, Dirk '
  last_name: Müller
- first_name: 'Antonello '
  full_name: 'Monti, Antonello '
  last_name: Monti
- first_name: 'Andrea '
  full_name: 'Benigni, Andrea '
  last_name: Benigni
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title: Accelerating the simulation of equation-based models by replacing non-linear
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author:
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- first_name: Matthias
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citation:
  alphadin: '<span style="font-variant:small-caps;">Heuermann, Andreas</span> ; <span
    style="font-variant:small-caps;">Hannebohm, Philip</span> ; <span style="font-variant:small-caps;">Schäfer,
    Matthias</span> ; <span style="font-variant:small-caps;">Bachmann, Bernhard</span>:
    Fehlerkontrollierte ML-Surrogate zur beschleunigten Simulation nichtlinearer Gleichungssysteme
    in Modelica. In:  : Unpublished, 2023'
  ama: 'Heuermann A, Hannebohm P, Schäfer M, Bachmann B. Fehlerkontrollierte ML-Surrogate
    zur beschleunigten Simulation nichtlinearer Gleichungssysteme in Modelica. In:
    Unpublished; 2023. doi:<a href="https://doi.org/10.13140/RG.2.2.11838.70729">10.13140/RG.2.2.11838.70729</a>'
  apa: 'Heuermann, A., Hannebohm, P., Schäfer, M., &#38; Bachmann, B. (2023). Fehlerkontrollierte
    ML-Surrogate zur beschleunigten Simulation nichtlinearer Gleichungssysteme in
    Modelica. Presented at the KI@HSBI 2023 Kongress, Bielefeld: Unpublished. <a href="https://doi.org/10.13140/RG.2.2.11838.70729">https://doi.org/10.13140/RG.2.2.11838.70729</a>'
  bibtex: '@inproceedings{Heuermann_Hannebohm_Schäfer_Bachmann_2023, title={Fehlerkontrollierte
    ML-Surrogate zur beschleunigten Simulation nichtlinearer Gleichungssysteme in
    Modelica}, DOI={<a href="https://doi.org/10.13140/RG.2.2.11838.70729">10.13140/RG.2.2.11838.70729</a>},
    publisher={Unpublished}, author={Heuermann, Andreas and Hannebohm, Philip and
    Schäfer, Matthias and Bachmann, Bernhard}, year={2023} }'
  chicago: Heuermann, Andreas, Philip Hannebohm, Matthias Schäfer, and Bernhard Bachmann.
    “Fehlerkontrollierte ML-Surrogate Zur Beschleunigten Simulation Nichtlinearer
    Gleichungssysteme in Modelica.” Unpublished, 2023. <a href="https://doi.org/10.13140/RG.2.2.11838.70729">https://doi.org/10.13140/RG.2.2.11838.70729</a>.
  ieee: A. Heuermann, P. Hannebohm, M. Schäfer, and B. Bachmann, “Fehlerkontrollierte
    ML-Surrogate zur beschleunigten Simulation nichtlinearer Gleichungssysteme in
    Modelica,” presented at the KI@HSBI 2023 Kongress, Bielefeld, 2023.
  mla: Heuermann, Andreas, et al. <i>Fehlerkontrollierte ML-Surrogate Zur Beschleunigten
    Simulation Nichtlinearer Gleichungssysteme in Modelica</i>. Unpublished, 2023,
    doi:<a href="https://doi.org/10.13140/RG.2.2.11838.70729">10.13140/RG.2.2.11838.70729</a>.
  short: 'A. Heuermann, P. Hannebohm, M. Schäfer, B. Bachmann, in: Unpublished, 2023.'
conference:
  end_date: 2023-11-30
  location: Bielefeld
  name: KI@HSBI 2023 Kongress
  start_date: 2023-11-30
date_created: 2024-05-29T10:06:06Z
date_updated: 2026-03-17T15:29:03Z
doi: 10.13140/RG.2.2.11838.70729
file:
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project:
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  name: Institute for Data Science Solutions
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status: public
title: Fehlerkontrollierte ML-Surrogate zur beschleunigten Simulation nichtlinearer
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