论文标题
使用机器学习建模来了解耦合地图系统中的宏观动力学
Using machine-learning modelling to understand macroscopic dynamics in a system of coupled maps
论文作者
论文摘要
机器学习技术不仅提供了从数据中建模动态系统的有效工具，而且还可以用作基础物理学的一线调查工具。可以通过仔细使用此类方法来获得有关原始动力学的非平凡信息，否则需要复杂的临时技术。为了说明这一点，我们认为是一个案例研究，从全球耦合图系统中出现的宏观运动。我们通过机器学习方法以及对粗粒剂过程的过渡概率进行了直接的数值计算，为宏观动力学构建了一个粗粒的马尔可夫过程，我们比较了两个分析的结果。我们的目的是双重的：一方面，我们希望测试随机机器学习方法描述非平凡进化定律的能力，如我们的研究中所考虑的那样。另一方面，我们旨在通过调节网络可用的信息来了解宏观动态物理学的深入了解，我们能够推断出有关吸引子有效维度的重要信息，记忆效应的持久性和动力学的多尺度结构。
Machine learning techniques not only offer efficient tools for modelling dynamical systems from data, but can also be employed as frontline investigative instruments for the underlying physics. Nontrivial information about the original dynamics, which would otherwise require sophisticated ad-hoc techniques, can be obtained by a careful usage of such methods. To illustrate this point, we consider as a case study the macroscopic motion emerging from a system of globally coupled maps. We build a coarse-grained Markov process for the macroscopic dynamics both with a machine learning approach and with a direct numerical computation of the transition probability of the coarse-grained process, and we compare the outcomes of the two analyses. Our purpose is twofold: on the one hand, we want to test the ability of the stochastic machine learning approach to describe nontrivial evolution laws, as the one considered in our study; on the other hand, we aim at gaining some insight into the physics of the macroscopic dynamics by modulating the information available to the network, we are able to infer important information about the effective dimension of the attractor, the persistence of memory effects and the multi-scale structure of the dynamics.
