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.

翻译：近期，哈密顿神经网络（HNN）被引入以在哈密顿系统动力学方程学习过程中融入先验物理知识。这种数据驱动建模方法能够保留辛系统结构，但对称性的保持需要额外关注。本研究通过李代数框架增强HNN，实现神经网络中对称性的检测与嵌入。该方法可同步学习对称群作用与系统总能量。以推车摆和天体力学中的两体问题作为实例进行验证。