Hamiltonian Neural Networks with Automatic Symmetry Detection
E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, Chaos 33 (2023).
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Abstract
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.
Publishing Year
Journal Title
Chaos
Volume
33
Issue
6
Article Number
063115
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Cite this
Dierkes E, Offen C, Ober-Blöbaum S, Flaßkamp K. Hamiltonian Neural Networks with Automatic Symmetry Detection. Chaos. 2023;33(6). doi:10.1063/5.0142969
Dierkes, E., Offen, C., Ober-Blöbaum, S., & Flaßkamp, K. (2023). Hamiltonian Neural Networks with Automatic Symmetry Detection. Chaos, 33(6), Article 063115. https://doi.org/10.1063/5.0142969
@article{Dierkes_Offen_Ober-Blöbaum_Flaßkamp_2023, title={Hamiltonian Neural Networks with Automatic Symmetry Detection}, volume={33}, DOI={10.1063/5.0142969}, number={6063115}, journal={Chaos}, publisher={AIP Publishing}, author={Dierkes, Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin}, year={2023} }
Dierkes, Eva, Christian Offen, Sina Ober-Blöbaum, and Kathrin Flaßkamp. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” Chaos 33, no. 6 (2023). https://doi.org/10.1063/5.0142969.
E. Dierkes, C. Offen, S. Ober-Blöbaum, and K. Flaßkamp, “Hamiltonian Neural Networks with Automatic Symmetry Detection,” Chaos, vol. 33, no. 6, Art. no. 063115, 2023, doi: 10.1063/5.0142969.
Dierkes, Eva, et al. “Hamiltonian Neural Networks with Automatic Symmetry Detection.” Chaos, vol. 33, no. 6, 063115, AIP Publishing, 2023, doi:10.1063/5.0142969.
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Hamiltonian Neural Networks with Automatic Symmetry Detection
Description
Incorporating physical system knowledge into data-driven
system identification has been shown to be beneficial. The
approach presented in this article combines learning of an
energy-conserving model from data with detecting a Lie
group representation of the unknown system symmetry.
The proposed approach can improve the learned model
and reveal underlying symmetry simultaneously.
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Open Access
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2023-04-26T16:20:56Z
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