两个自由度哈密顿系统中混沌与有序的深度分类器
A deep classifier of chaos and order in Hamiltonian systems of two degrees of freedom
AI总结：
提出基于卷积架构的深度分类器，通过Poincaré maps对两自由度哈密顿系统中的混沌与有序进行分类，并成功应用于非Kerr致密天体测地线动力学。
摘要：
混沌是一种可以在众多系统中发现的引人入胜的现象。将其从其对立面有序中检测并区分出来是一项有趣的挑战。为了解决这一问题，我们提出了一种深度分类器，能够通过 Poincaré maps 的机制，对两个自由度哈密顿系统离散化动力学中的混沌与有序进行分类。我们的深度网络主要基于卷积架构，得益于深度网络学习到的受扰摆的普遍特征，它在未见过的数据集上以良好的准确率泛化。我们详细讨论了训练集的意义和准备过程，并展示了如何将我们的深度网络应用于偏离 Kerr black hole 范式的轴对称且稳态的致密天体时空中测地线运动的动力学。最后，我们讨论了当前的挑战和一些有前景的未来方向。
英文摘要：
Chaos is an intriguing phenomenon that can be found in an immense variate of systems. Its detection and discrimination from its counterpart order poses an interesting challenge. To address it, we present a deep classifier capable of classifying chaos from order in the discretised dynamics of Hamiltonian systems of two degrees of freedom, through the machinery of Poincaré maps. Our deep network is based predominantly on a convolutional architecture, and generalises with good accuracy on unseen datasets, thanks to the universal features of a perturbed pendulum learned by the deep network. We discuss in detail the significance and the preparation of our training set, and we showcase how our deep network can be applied to the dynamics of geodesic motion in an axi-symmetric and stationary spacetime of a compact object deviating from the Kerr black hole paradigm. Finally, we discuss current challenges and some promising future directions.
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