article published Eva Dierkes author Christian Offen author 852790000-0002-5940-8057 Sina Ober-Blöbaum author 16494 Kathrin Flaßkamp author 636 department Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite the data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we enhance the HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach allows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples, a pendulum on a cart and a two-body problem from astrodynamics are considered. https://ris.uni-paderborn.de/download/37654/44205/JournalPaper_main.pdf application/pdfno AIP Publishing2023 eng 1054-1500 2301.0792810.1063/5.0142969 336 https://github.com/eva-dierkes/HNN_withSymmetries 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> 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>. 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>. @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} } E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023). 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>. 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> 376542023-01-20T09:10:06Z2023-08-10T08:37:01Z