Hamiltonian neural networks with automatic symmetry detection

Recently, Hamiltonian neural networks (HNNs) 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 requi...

Full description

Saved in:
Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2023-06, Vol.33 (6)
Main Authors: Dierkes, Eva, Offen, Christian, Ober-Blöbaum, Sina, Flaßkamp, Kathrin
Format: Article
Language:English
Subjects:
Astrodynamics
Hamiltonian functions
Lie groups
Neural networks
Symmetry detection
Two body problem
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Recently, Hamiltonian neural networks (HNNs) 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 HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach allows us 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.
ISSN:1054-1500
1089-7682
DOI:10.1063/5.0142969