Hamiltonian Neural Networks with Automatic Symmetry Detection

E. Dierkes, C. Offen, S. Ober-Blöbaum, K. Flaßkamp, (n.d.).

Download
OA Hamiltonian Neural Networks with Automatic Symmetry Detection 5.16 MB
Preprint | Submitted | English
Author
Dierkes, Eva; Offen, ChristianLibreCat ; Ober-Blöbaum, SinaLibreCat; Flaßkamp, Kathrin
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
LibreCat-ID

Cite this

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.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]
Main File(s)
File Title
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.
Access Level
OA Open Access
Last Uploaded
2023-01-20T09:19:39Z


Export

Marked Publications

Open Data LibreCat

Sources

arXiv 2301.07928

Search this title in

Google Scholar