Hamiltonian Neural Networks with Automatic Symmetry Detection

• URL: http://arxiv.org/abs/2301.07928v2
• Date: Mon, 24 Apr 2023 12:59:58 GMT
• Title: Hamiltonian Neural Networks with Automatic Symmetry Detection
• Authors: Eva Dierkes and Christian Offen and Sina Ober-Bl\"obaum and Kathrin Fla{\ss}kamp
• Abstract summary: Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge. We enhance HNN with a Lie algebra framework to detect and embed symmetries in the neural network.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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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