Hamiltonian Neural Networks with Automatic Symmetry Detection

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.

References in corpus (6)

• Symplectic integration of learned Hamiltonian systems
• Symplectic Gaussian Process Regression of Hamiltonian Flow Maps
• Automatic Symmetry Discovery with Lie Algebra Convolutional Network
• Variational Learning of Euler-Lagrange Dynamics from Data
• Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves
• Learning Interpretable Dynamics from Images of a Freely Rotating 3D Rigid Body

Cited by in corpus (5)

• Learning of discrete models of variational PDEs from data
• Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves
• On tensor invariants of the Clebsch system
• Group-Convolutional Extended Dynamic Mode Decomposition
• Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification