Borra Francesco, Baldovin Marco
Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 5, I-00185 Rome, Italy.
Chaos. 2021 Feb;31(2):023102. doi: 10.1063/5.0036809.
Machine-learning techniques not only offer efficient tools for modeling 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 to gain 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 multiscale structure of the dynamics.
机器学习技术不仅为从数据中对动力系统进行建模提供了高效工具，还可作为探究潜在物理机制的前沿研究手段。通过谨慎运用这些方法，能够获取有关原始动力学的重要信息，而这些信息若采用其他方法则需要复杂的特殊技术。为说明这一点，我们以全局耦合映射系统产生的宏观运动为例进行研究。我们分别用机器学习方法和对粗粒化过程的转移概率进行直接数值计算的方式，为宏观动力学构建一个粗粒化马尔可夫过程，并比较两种分析的结果。我们的目的有两个：一方面，我们想测试随机机器学习方法描述如我们研究中所考虑的非平凡演化规律的能力。另一方面，我们旨在深入了解宏观动力学的物理机制。通过调整网络可用的信息，我们能够推断出关于吸引子有效维度、记忆效应的持续性以及动力学的多尺度结构的重要信息。
