用油藏计算机学习哈密顿动力学
Learning Hamiltonian dynamics by reservoir computer
摘要：
由有限个参数的时间序列重构哈密顿系统的KAM动力学图是非线性科学中的一个突出问题，特别是当控制系统动力学的哈密顿量未知时。在这里，我们证明了这个问题可以通过称为水库计算机（RC）的机器学习方法来解决。具体来说，我们表明，没有先验知识的汉密尔顿的运动方程，训练RC不仅能够预测系统状态的短期演变，但也复制系统动力学的长期遍历特性。此外，通过参数感知RC的架构，我们还表明，由在少数参数下获得的时间序列训练的RC能够通过外部调整控制参数以高精度重建整个KAM动力学图。在两个经典的非线性哈密顿系统，即双摆振子和标准映射的学习技术的可行性和有效性证明。我们的研究表明，作为一个复杂的动力系统，RC是能够从数据中学习的哈密顿量。
英文摘要：
Reconstructing the KAM dynamics diagram of Hamiltonian system from the time series of a limited number of parameters is an outstanding question in nonlinear science, especially when the Hamiltonian governing the system dynamics are unknown. Here, we demonstrate that this question can be addressed by the machine learning approach knowing as reservoir computer (RC). Specifically, we show that without prior knowledge about the Hamilton's equations of motion, the trained RC is able to not only predict the short-term evolution of the system state, but also replicate the long-term ergodic properties of the system dynamics. Furthermore, by the architecture of parameter-aware RC, we also show that the RC trained by the time series acquired at a handful parameters is able to reconstruct the entire KAM dynamics diagram with a high precision by tuning a control parameter externally. The feasibility and efficiency of the learning techniques are demonstrated in two classical nonlinear Hamiltonian systems, namely the double-pendulum oscillator and the standard map. Our study indicates that, as a complex dynamical system, RC is able to learn from data the Hamiltonian.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
