Hamiltonian Neural Networks with Automatic Symmetry Detection
E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, (n.d.).
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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.
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Dierkes E, Offen C, Ober-Blöbaum S, Flaßkamp K. Hamiltonian Neural Networks with Automatic Symmetry Detection.
Dierkes, E., Offen, C., Ober-Blöbaum, S., & Flaßkamp, K. (n.d.). Hamiltonian Neural Networks with Automatic Symmetry Detection.
@article{Dierkes_Offen_Ober-Blöbaum_Flaßkamp, title={Hamiltonian Neural Networks with Automatic Symmetry Detection}, author={Dierkes, Eva and Offen, Christian and Ober-Blöbaum, Sina and Flaßkamp, Kathrin} }
Dierkes, Eva, Christian Offen, Sina Ober-Blöbaum, and Kathrin Flaßkamp. “Hamiltonian Neural Networks with Automatic Symmetry Detection,” n.d.
E. Dierkes, C. Offen, S. Ober-Blöbaum, and K. Flaßkamp, “Hamiltonian Neural Networks with Automatic Symmetry Detection.” .
Dierkes, Eva, et al. Hamiltonian Neural Networks with Automatic Symmetry Detection.
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Hamiltonian Neural Networks with Automatic Symmetry Detection
Description
Incorporating physical system knowledge into data-based
system identification approaches has 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 thus improve the learned model and reveal underlying symmetry simultaneously.
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2023-01-20T09:19:39Z
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