For the Hamiltonian system, this work considers the learning and prediction of the position (q) and momentum (p) variables generated by a symplectic evolution map. Similar to Chen & Tao (2021), the symplectic map is represented by the generating function. In addition, we develop a new learning scheme by splitting the time series (q_i, p_i) into several partitions, and then train a leap-frog neural network (LFNN) to approximate the generating function between the first (i.e. initial condition) and one of the rest partitions. For predicting the system evolution in a short timescale, the LFNN could effectively avoid the issue of accumulative error. Then the LFNN is applied to learn the behavior of the 2:3 resonant Kuiper belt objects, in a much longer time period, and there are two significant improvements on the neural network constructed in our previous work (Li et al. 2022): (1) conservation of the Jacobi integral ; (2) highly accurate prediction of the orbital evolution. We propose that the LFNN may be useful to make the prediction of the long time evolution of the Hamiltonian system.

通过分区训练跳蛙神经网络，学习并预测哈密顿系统的位置和动量变量，以及应用于共振库伯带天体中，改善了神经网络的构造和扩展了应用范围。

基于跳跃神经网络的分块数据标准演化学习