We present several methods for predicting the dynamics of Hamiltonian systems from discrete observations of their vector field. Each method is either informed or uninformed of the Hamiltonian property. We empirically and comparatively evaluate the methods and observe that information that the system is Hamiltonian can be effectively informed, and that different methods strike different trade-offs between efficiency and effectiveness for different dynamical systems.

翻译：我们提出了几种方法，用于从哈密顿系统向量场的离散观测中预测其动力学。每种方法要么具备哈密顿性质的先验信息，要么不具备。我们通过实验对这些方法进行了比较评估，并观察到：系统具有哈密顿性质这一信息可以被有效利用；对于不同的动力系统，不同方法在效率与效果之间呈现出不同的权衡关系。