---
_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.'
conference:
  end_date: 2025-09-10
  location: Luzern
  name: The 16th International Modelica&FMI Conference
  start_date: 2025-09-08
date_created: 2025-12-02T13:49:45Z
date_updated: 2026-03-17T15:29:29Z
department:
- _id: '103'
doi: 10.3384/ecp218445
editor:
- first_name: Dirk
  full_name: Zimmer, Dirk
  last_name: Zimmer
- first_name: Ulf Christian
  full_name: Müller, Ulf Christian
  last_name: Müller
file:
- access_level: open_access
  content_type: application/pdf
  creator: llangenkamp
  date_created: 2025-12-02T13:48:28Z
  date_updated: 2025-12-02T13:48:28Z
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  file_name: paper.pdf
  file_size: 11486460
  relation: main_file
  success: 1
file_date_updated: 2025-12-02T13:48:28Z
has_accepted_license: '1'
intvolume: '       218'
keyword:
- Physics-enhanced Neural ODEs
- Dynamic Optimization
- Nonlinear Programming
- Modelica
- NeuralODEs
- Universal Differential Equations
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
page: 445 - 457
publication: Proceedings of the 16th International Modelica&FMI Conference
publication_status: published
publisher: Linköping University Electronic Press
status: public
title: Efficient Training of Physics-enhanced Neural ODEs via Direct Collocation and
  Nonlinear Programming
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  short: CC BY (4.0)
type: conference
urn: urn:nbn:de:hbz:bi10-63592
user_id: '240430'
volume: 218
year: '2025'
...
---
_id: '6361'
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/198561013
- 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/198561014
citation:
  alphadin: '<span style="font-variant:small-caps;">Langenkamp, Linus</span> ; <span
    style="font-variant:small-caps;">Bachmann, Bernhard</span>: Enhancing Collocation-Based
    Dynamic Optimization through Adaptive Mesh Refinement. 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. 127–138'
  ama: 'Langenkamp L, Bachmann B. Enhancing Collocation-Based Dynamic Optimization
    through Adaptive Mesh Refinement. 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; 2025:127-138.
    doi:<a href="https://doi.org/10.3384/ecp218127">10.3384/ecp218127</a>'
  apa: 'Langenkamp, L., &#38; Bachmann, B. (2025). Enhancing Collocation-Based Dynamic
    Optimization through Adaptive Mesh Refinement. In D. Zimmer &#38; U. C. Müller
    (Eds.), <i>Proceedings of the 16th International Modelica&#38;FMI Conference</i>
    (Vol. 218, pp. 127–138). Luzern: Linköping University Electronic Press. <a href="https://doi.org/10.3384/ecp218127">https://doi.org/10.3384/ecp218127</a>'
  bibtex: '@inproceedings{Langenkamp_Bachmann_2025, series={Linköping Electronic Conference
    Proceedings}, title={Enhancing Collocation-Based Dynamic Optimization through
    Adaptive Mesh Refinement}, volume={218}, DOI={<a href="https://doi.org/10.3384/ecp218127">10.3384/ecp218127</a>},
    booktitle={Proceedings of the 16th International Modelica&#38;FMI Conference},
    publisher={Linköping University Electronic Press}, author={Langenkamp, Linus and
    Bachmann, Bernhard}, editor={Zimmer, Dirk and Müller, Ulf ChristianEditors}, year={2025},
    pages={127–138}, collection={Linköping Electronic Conference Proceedings} }'
  chicago: Langenkamp, Linus, and Bernhard Bachmann. “Enhancing Collocation-Based
    Dynamic Optimization through Adaptive Mesh Refinement.” In <i>Proceedings of the
    16th International Modelica&#38;FMI Conference</i>, edited by Dirk Zimmer and
    Ulf Christian Müller, 218:127–38. Linköping Electronic Conference Proceedings.
    Linköping University Electronic Press, 2025. <a href="https://doi.org/10.3384/ecp218127">https://doi.org/10.3384/ecp218127</a>.
  ieee: L. Langenkamp and B. Bachmann, “Enhancing Collocation-Based Dynamic Optimization
    through Adaptive Mesh Refinement,” in <i>Proceedings of the 16th International
    Modelica&#38;FMI Conference</i>, Luzern, 2025, vol. 218, pp. 127–138.
  mla: Langenkamp, Linus, and Bernhard Bachmann. “Enhancing Collocation-Based Dynamic
    Optimization through Adaptive Mesh Refinement.” <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. 127–38, doi:<a href="https://doi.org/10.3384/ecp218127">10.3384/ecp218127</a>.
  short: 'L. Langenkamp, B. Bachmann, in: D. Zimmer, U.C. Müller (Eds.), Proceedings
    of the 16th International Modelica&#38;FMI Conference, Linköping University Electronic
    Press, 2025, pp. 127–138.'
conference:
  end_date: 2025-09-10
  location: Luzern
  name: The 16th International Modelica&FMI Conference
  start_date: 2025-09-08
date_created: 2025-12-02T17:57:34Z
date_updated: 2026-03-17T15:29:29Z
department:
- _id: '103'
doi: 10.3384/ecp218127
editor:
- first_name: Dirk
  full_name: Zimmer, Dirk
  last_name: Zimmer
- first_name: Ulf Christian
  full_name: Müller, Ulf Christian
  last_name: Müller
file:
- access_level: open_access
  content_type: application/pdf
  creator: llangenkamp
  date_created: 2025-12-02T17:59:17Z
  date_updated: 2025-12-02T17:59:17Z
  file_id: '6362'
  file_name: paper.pdf
  file_size: 615701
  relation: main_file
  success: 1
file_date_updated: 2025-12-02T17:59:17Z
has_accepted_license: '1'
intvolume: '       218'
keyword:
- Dynamic Optimization
- Direct Collocation
- Adaptive Mesh Refinement
- Nonlinear Programming
language:
- iso: eng
oa: '1'
page: 127 - 138
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
series_title: Linköping Electronic Conference Proceedings
status: public
title: Enhancing Collocation-Based Dynamic Optimization through Adaptive Mesh Refinement
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
urn: urn:nbn:de:hbz:bi10-63618
user_id: '220548'
volume: 218
year: '2025'
...
---
_id: '4551'
author:
- first_name: Ronald H. W.
  full_name: Hoppe, Ronald H. W.
  last_name: Hoppe
- first_name: Svetozara
  full_name: Petrova, Svetozara
  id: '201871'
  last_name: Petrova
citation:
  alphadin: '<span style="font-variant:small-caps;">Hoppe, Ronald H. W.</span> ; <span
    style="font-variant:small-caps;">Petrova, Svetozara</span>: Applications of Primal-dual
    Interior Methods in Structural Optimization. In: <i>Computational Methods in Applied
    Mathematics</i> Bd. 3, Walter de Gruyter GmbH (2003), Nr. 1, S. 159–176'
  ama: Hoppe RHW, Petrova S. Applications of Primal-dual Interior Methods in Structural
    Optimization. <i>Computational Methods in Applied Mathematics</i>. 2003;3(1):159-176.
    doi:<a href="https://doi.org/10.2478/cmam-2003-0011">10.2478/cmam-2003-0011</a>
  apa: Hoppe, R. H. W., &#38; Petrova, S. (2003). Applications of Primal-dual Interior
    Methods in Structural Optimization. <i>Computational Methods in Applied Mathematics</i>,
    <i>3</i>(1), 159–176. <a href="https://doi.org/10.2478/cmam-2003-0011">https://doi.org/10.2478/cmam-2003-0011</a>
  bibtex: '@article{Hoppe_Petrova_2003, title={Applications of Primal-dual Interior
    Methods in Structural Optimization}, volume={3}, DOI={<a href="https://doi.org/10.2478/cmam-2003-0011">10.2478/cmam-2003-0011</a>},
    number={1}, journal={Computational Methods in Applied Mathematics}, publisher={Walter
    de Gruyter GmbH}, author={Hoppe, Ronald H. W. and Petrova, Svetozara}, year={2003},
    pages={159–176} }'
  chicago: 'Hoppe, Ronald H. W., and Svetozara Petrova. “Applications of Primal-Dual
    Interior Methods in Structural Optimization.” <i>Computational Methods in Applied
    Mathematics</i> 3, no. 1 (2003): 159–76. <a href="https://doi.org/10.2478/cmam-2003-0011">https://doi.org/10.2478/cmam-2003-0011</a>.'
  ieee: R. H. W. Hoppe and S. Petrova, “Applications of Primal-dual Interior Methods
    in Structural Optimization,” <i>Computational Methods in Applied Mathematics</i>,
    vol. 3, no. 1, pp. 159–176, 2003.
  mla: Hoppe, Ronald H. W., and Svetozara Petrova. “Applications of Primal-Dual Interior
    Methods in Structural Optimization.” <i>Computational Methods in Applied Mathematics</i>,
    vol. 3, no. 1, Walter de Gruyter GmbH, 2003, pp. 159–76, doi:<a href="https://doi.org/10.2478/cmam-2003-0011">10.2478/cmam-2003-0011</a>.
  short: R.H.W. Hoppe, S. Petrova, Computational Methods in Applied Mathematics 3
    (2003) 159–176.
date_created: 2024-04-25T13:14:17Z
date_updated: 2026-03-17T15:29:02Z
doi: 10.2478/cmam-2003-0011
intvolume: '         3'
issue: '1'
keyword:
- structural optimization
- nonlinear programming
- primal-dual interior-point methods
- eddy current equations
- elasticity equations
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
page: 159-176
project:
- _id: f432a2ee-bceb-11ed-a251-a83585c5074d
  name: Institute for Data Science Solutions
publication: Computational Methods in Applied Mathematics
publication_identifier:
  eissn:
  - 1609-9389
  issn:
  - 1609-4840
publication_status: published
publisher: Walter de Gruyter GmbH
status: public
title: Applications of Primal-dual Interior Methods in Structural Optimization
tmp:
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  legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
  name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
    (CC BY-NC-ND 4.0)
  short: CC BY-NC-ND (4.0)
type: journal_article
user_id: '220548'
volume: 3
year: '2003'
...
---
_id: '4545'
author:
- first_name: R.H.W.
  full_name: Hoppe, R.H.W.
  last_name: Hoppe
- first_name: Svetozara
  full_name: Petrova, Svetozara
  id: '201871'
  last_name: Petrova
- first_name: V.
  full_name: Schulz, V.
  last_name: Schulz
citation:
  alphadin: '<span style="font-variant:small-caps;">Hoppe, R.H.W.</span> ; <span style="font-variant:small-caps;">Petrova,
    Svetozara</span> ; <span style="font-variant:small-caps;">Schulz, V.</span>: Primal-Dual
    Newton-Type Interior-Point Method for Topology Optimization. In: <i>Journal of
    Optimization Theory and Applications</i> Bd. 114, Springer Science and Business
    Media LLC (2002), Nr. 3, S. 545–571'
  ama: Hoppe RHW, Petrova S, Schulz V. Primal-Dual Newton-Type Interior-Point Method
    for Topology Optimization. <i>Journal of Optimization Theory and Applications</i>.
    2002;114(3):545-571. doi:<a href="https://doi.org/10.1023/A:1016070928600">10.1023/A:1016070928600</a>
  apa: Hoppe, R. H. W., Petrova, S., &#38; Schulz, V. (2002). Primal-Dual Newton-Type
    Interior-Point Method for Topology Optimization. <i>Journal of Optimization Theory
    and Applications</i>, <i>114</i>(3), 545–571. <a href="https://doi.org/10.1023/A:1016070928600">https://doi.org/10.1023/A:1016070928600</a>
  bibtex: '@article{Hoppe_Petrova_Schulz_2002, title={Primal-Dual Newton-Type Interior-Point
    Method for Topology Optimization}, volume={114}, DOI={<a href="https://doi.org/10.1023/A:1016070928600">10.1023/A:1016070928600</a>},
    number={3}, journal={Journal of Optimization Theory and Applications}, publisher={Springer
    Science and Business Media LLC}, author={Hoppe, R.H.W. and Petrova, Svetozara
    and Schulz, V.}, year={2002}, pages={545–571} }'
  chicago: 'Hoppe, R.H.W., Svetozara Petrova, and V. Schulz. “Primal-Dual Newton-Type
    Interior-Point Method for Topology Optimization.” <i>Journal of Optimization Theory
    and Applications</i> 114, no. 3 (2002): 545–71. <a href="https://doi.org/10.1023/A:1016070928600">https://doi.org/10.1023/A:1016070928600</a>.'
  ieee: R. H. W. Hoppe, S. Petrova, and V. Schulz, “Primal-Dual Newton-Type Interior-Point
    Method for Topology Optimization,” <i>Journal of Optimization Theory and Applications</i>,
    vol. 114, no. 3, pp. 545–571, 2002.
  mla: Hoppe, R. H. W., et al. “Primal-Dual Newton-Type Interior-Point Method for
    Topology Optimization.” <i>Journal of Optimization Theory and Applications</i>,
    vol. 114, no. 3, Springer Science and Business Media LLC, 2002, pp. 545–71, doi:<a
    href="https://doi.org/10.1023/A:1016070928600">10.1023/A:1016070928600</a>.
  short: R.H.W. Hoppe, S. Petrova, V. Schulz, Journal of Optimization Theory and Applications
    114 (2002) 545–571.
date_created: 2024-04-25T12:53:40Z
date_updated: 2026-03-17T15:29:02Z
doi: 10.1023/A:1016070928600
intvolume: '       114'
issue: '3'
keyword:
- Eddy current equations
- topology optimization
- nonlinear programming
- primal-dual interior-point methods
- watchdog strategy
language:
- iso: eng
page: 545-571
project:
- _id: f432a2ee-bceb-11ed-a251-a83585c5074d
  name: Institute for Data Science Solutions
publication: Journal of Optimization Theory and Applications
publication_identifier:
  eissn:
  - 1573-2878
  issn:
  - 0022-3239
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Primal-Dual Newton-Type Interior-Point Method for Topology Optimization
type: journal_article
user_id: '220548'
volume: 114
year: '2002'
...