Large-step neural network for learning the symplectic evolution from partitioned data
Large-step neural network for learning the symplectic evolution from partitioned data
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DOI：
10.1093/mnras/stad1948
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发表时间：
2022-08
影响因子：
4.8
通讯作者：
Xin Li;Jian Li;Zhihong Xia;N. Georgakarakos
中科院分区：
文献类型：
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作者：
Xin Li;Jian Li;Zhihong Xia;N. Georgakarakos
在这项研究中，我们重点学习哈密顿系统，这涉及到预测由辛映射产生的坐标(符号q$)和动量(符号p$)变量。在Chen&Tao(2021)的基础上，用母函数表示辛映射。为了延长预测时间周期，我们提出了一种新的学习方案，将时间序列(符号q_i$，符号p_i$)分成几个分区。然后，我们训练一个大步长神经网络(LSNN)来逼近第一个分区(即初始条件)和每个剩余分区之间的母函数。这种划分方法使我们的LSNN在预测系统演化时有效地抑制了累积误差。然后对LSNN进行训练，学习2：3共振柯伊伯带天体的运动，时间长达25000年。结果表明，该神经网络在两个方面有显著的改进：(1)雅可比积分的守恒性；(2)对轨道演化的高精度预测。总之，我们认为所设计的LSNN有可能显著改善对更一般的哈密顿系统的长期演化的预测。
In this study, we focus on learning Hamiltonian systems, which involves predicting the coordinate ($\boldsymbol q$) and momentum ($\boldsymbol p$) variables generated by a symplectic mapping. Based on Chen & Tao (2021), the symplectic mapping is represented by a generating function. To extend the prediction time period, we develop a new learning scheme by splitting the time series ($\boldsymbol q_i$, $\boldsymbol p_i$) into several partitions. We then train a large-step neural network (LSNN) to approximate the generating function between the first partition (i.e. the initial condition) and each one of the remaining partitions. This partition approach makes our LSNN effectively suppress the accumulative error when predicting the system evolution. Then we train the LSNN to learn the motions of the 2:3 resonant Kuiper belt objects for a long time period of 25 000 yr. The results show that there are two significant improvements over the neural network constructed in our previous work: (1) the conservation of the Jacobi integral and (2) the highly accurate predictions of the orbital evolution. Overall, we propose that the designed LSNN has the potential to considerably improve predictions of the long-term evolution of more general Hamiltonian systems.