{"volume":33,"external_id":{"arxiv":["2301.07928"]},"publication_status":"published","file_date_updated":"2023-04-26T16:20:56Z","title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","user_id":"85279","author":[{"first_name":"Eva","last_name":"Dierkes","full_name":"Dierkes, Eva"},{"full_name":"Offen, Christian","orcid":"0000-0002-5940-8057","last_name":"Offen","first_name":"Christian","id":"85279"},{"full_name":"Ober-Blöbaum, Sina","id":"16494","last_name":"Ober-Blöbaum","first_name":"Sina"},{"last_name":"Flaßkamp","first_name":"Kathrin","full_name":"Flaßkamp, Kathrin"}],"status":"public","publisher":"AIP Publishing","article_number":"063115","ddc":["510"],"article_type":"original","file":[{"file_size":5200111,"relation":"main_file","file_id":"44205","title":"Hamiltonian Neural Networks with Automatic Symmetry Detection","date_updated":"2023-04-26T16:20:56Z","access_level":"open_access","creator":"coffen","description":"Incorporating physical system knowledge into data-driven\nsystem identification has been shown to be beneficial. The\napproach presented in this article combines learning of an\nenergy-conserving model from data with detecting a Lie\ngroup representation of the unknown system symmetry.\nThe proposed approach can improve the learned model\nand reveal underlying symmetry simultaneously.","date_created":"2023-04-26T16:20:56Z","file_name":"JournalPaper_main.pdf","content_type":"application/pdf"}],"doi":"10.1063/5.0142969","department":[{"_id":"636"}],"issue":"6","has_accepted_license":"1","related_material":{"link":[{"description":"GitHub","relation":"software","url":"https://github.com/eva-dierkes/HNN_withSymmetries"}]},"oa":"1","date_updated":"2023-08-10T08:37:01Z","type":"journal_article","intvolume":"        33","date_created":"2023-01-20T09:10:06Z","publication":"Chaos","year":"2023","_id":"37654","publication_identifier":{"issn":["1054-1500"]},"language":[{"iso":"eng"}],"abstract":[{"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.","lang":"eng"}],"citation":{"short":"E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023).","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>.","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>.","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>","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>","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} }"}}