发表机构
China University of Mining and Technology; Jilin University（中国矿业大学; 吉林大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用下一代储层计算，仅凭低于逃逸阈值的少量时间序列数据，成功预测了哈密顿系统的逃逸阈值及逃逸通道结构，为数据驱动研究提供了新范式。
AI 中文摘要
哈密顿系统展现出丰富的动力学行为，其中逃逸是一种典型现象。在逃逸阈值以下，从中心势阱内部出发的轨迹保持有界。一旦能量超过该阈值，且初始条件位于逃逸盆地内，系统最终将沿无界轨道演化至无穷远。预测逃逸动力学对于理解这些系统的演化至关重要。在本研究中，我们采用下一代储层计算框架，这是一种广泛用于动力学预测的强大机器学习架构，以应对这一挑战性问题。为捕捉系统的内在特征，我们使用多个能量值的数据训练模型。对两个哈密顿系统的数值实验表明，仅使用三条时间序列作为训练数据（每条对应一个低于逃逸阈值的能量值），模型不仅能预测逃逸阈值本身，还能可靠地预测逃逸通道的结构。作为本研究的主要贡献，这些发现表明，在所研究的两个系统中，仅凭亚临界数据即可推断出逃逸动力学，为哈密顿系统的数据驱动研究提供了一种有前景的范式。
英文摘要
Hamiltonian systems exhibit rich dynamical behaviors, among which escape is a typical phenomenon. Below the escape threshold, trajectories initiated inside the central potential well remain bounded. Once the energy exceeds this threshold, and the initial conditions lie within the escape basin, the system eventually evolves along unbounded orbits toward infinity. Predicting the escape dynamics is important for understanding the evolution of these systems. In this study, we employ the next-generation reservoir computing framework, a powerful machine learning architecture widely used in dynamical prediction, to address this challenging issue. To capture the intrinsic features of the system, we train the model using data from multiple energy values. Numerical experiments on two Hamiltonian systems show that, with only three time series as training data, each corresponding to an energy value below the escape threshold, the model is capable of not only predicting the escape threshold itself, but also reliably predicting the structure of the escape channels. As a primary contribution of this work, these findings demonstrate that escape dynamics can be inferred from subcritical data alone in the two systems studied, offering a promising paradigm for data-driven studies of Hamiltonian systems.
Comments21 pages, 58 figures, 4 tables. Any comments are welcome!
