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 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.

Automated summary

Recently, Hamiltonian neural networks (HNNs) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems, while preserving the symplectic system structure. However, preserving symmetries requires additional attention. In this research, HNN is enhanced with a Lie algebra framework to detect and embed symmetries in the neural network, allowing simultaneous learning of the symmetry group action and the total energy of the system. Illustrative examples include a pendulum on a cart and a two-body problem from astrodynamics.