{"language":[{"iso":"eng"}],"urn":"urn:nbn:de:hbz:bi10-63592","publisher":"Linköping University Electronic Press","oa":"1","user_id":"240430","publication_status":"published","type":"conference","date_created":"2025-12-02T13:49:45Z","department":[{"_id":"103"}],"editor":[{"first_name":"Dirk","last_name":"Zimmer","full_name":"Zimmer, Dirk"},{"full_name":"Müller, Ulf Christian","last_name":"Müller","first_name":"Ulf Christian"}],"citation":{"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>","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>","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} }","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.","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.","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","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>."},"publication":"Proceedings of the 16th International Modelica&FMI Conference","main_file_link":[{"open_access":"1"}],"conference":{"end_date":"2025-09-10","name":"The 16th International Modelica&FMI Conference","start_date":"2025-09-08","location":"Luzern"},"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"access_level":"open_access","file_name":"paper.pdf","file_size":11486460,"creator":"llangenkamp","file_id":"6360","content_type":"application/pdf","date_created":"2025-12-02T13:48:28Z","success":1,"relation":"main_file","date_updated":"2025-12-02T13:48:28Z"}],"file_date_updated":"2025-12-02T13:48:28Z","date_updated":"2025-12-02T18:05:03Z","title":"Efficient Training of Physics-enhanced Neural ODEs via Direct Collocation and Nonlinear Programming","volume":218,"author":[{"id":"240430","first_name":"Linus","orcid_put_code_url":"https://api.orcid.org/v2.0/0009-0009-7517-4842/work/198540284","last_name":"Langenkamp","full_name":"Langenkamp, Linus","orcid":"0009-0009-7517-4842"},{"orcid_put_code_url":"https://api.orcid.org/v2.0/0009-0003-8902-9079/work/198540286","last_name":"Hannebohm","first_name":"Philip","id":"221456","full_name":"Hannebohm, Philip","orcid":"0009-0003-8902-9079"},{"orcid":"0000-0002-4339-0438","full_name":"Bachmann, Bernhard","id":"33931","first_name":"Bernhard","last_name":"Bachmann","orcid_put_code_url":"https://api.orcid.org/v2.0/0000-0002-4339-0438/work/198540287"}],"intvolume":"       218","page":"445 - 457","abstract":[{"text":"We propose a novel approach for training Physics-enhanced Neural ODEs (PeN-ODEs) by expressing the training process as a dynamic optimization problem. The full model, including neural components, is discretized using a high-order implicit Runge-Kutta method with flipped Legendre-Gauss-Radau points, resulting in a large-scale nonlinear program (NLP) efficiently solved by state-of-the-art NLP solvers such as Ipopt. This formulation enables simultaneous optimization of network parameters and state trajectories, addressing key limitations of ODE solver-based training in terms of stability, runtime, and accuracy. Extending on a recent direct collocation-based method for Neural ODEs, we generalize to PeN-ODEs, incorporate physical constraints, and present a custom, parallelized, open-source implementation. Benchmarks on a Quarter Vehicle Model and a Van-der-Pol oscillator demonstrate superior accuracy, speed, generalization with smaller networks compared to other training techniques. We also outline a planned integration into OpenModelica to enable accessible training of Neural DAEs.","lang":"eng"}],"doi":"10.3384/ecp218445","status":"public","has_accepted_license":"1","_id":"6359","year":"2025","keyword":["Physics-enhanced Neural ODEs","Dynamic Optimization","Nonlinear Programming","Modelica","NeuralODEs","Universal Differential Equations"]}