School of Information Science and Technology, East China Normal University, Shanghai 200241, China.
School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, China.
Phys Rev E. 2019 Nov;100(5-1):052312. doi: 10.1103/PhysRevE.100.052312.
Recent years have witnessed a growing interest in using machine learning to predict and identify critical dynamical phase transitions in physical systems (e.g., many-body quantum systems). The underlying lattice structures in these applications are generally regular. While machine learning has been adopted to complex networks, most existing works concern about the structural properties. To use machine learning to detect phase transitions and accurately identify the critical transition points associated with dynamical processes on complex networks thus stands out as an open and significant problem. Here we develop a framework combining supervised and unsupervised learning, incorporating proper sampling of training data set. In particular, using epidemic spreading dynamics on complex networks as a paradigmatic setting, we start from supervised learning alone and identify situations that degrade the performance. To overcome the difficulties leads to the idea of exploiting confusion scheme, effectively a combination of supervised and unsupervised learning. We demonstrate that the scheme performs well for identifying phase transitions associated with spreading dynamics on homogeneous networks, but the performance deteriorates for heterogeneous networks. To strive to meet this challenge leads to the realization that sampling the training data set is necessary for heterogeneous networks, and we test two sampling methods: one based on the hub nodes together with their neighbors and another based on k-core of the network. The end result is a general comprehensive machine learning framework for detecting phase transition and accurately identifying the critical transition point, which is robust, computationally efficient, and universally applicable to complex networks of arbitrary size and topology. Extensive tests using synthetic and empirical networks verify the virtues of the articulated framework, opening the door to exploiting machine learning for understanding, detection, prediction, and control of complex dynamical systems in general.
近年来，人们越来越感兴趣地使用机器学习来预测和识别物理系统（例如多体量子系统）中的关键动力学相变。这些应用中的基本晶格结构通常是规则的。虽然机器学习已被应用于复杂网络，但大多数现有工作都涉及结构性质。因此，使用机器学习来检测相变并准确识别与复杂网络上的动力学过程相关的关键转折点是一个开放且具有重要意义的问题。在这里，我们开发了一个结合监督学习和无监督学习的框架，包括训练数据集的适当采样。特别是，我们以复杂网络上的传染病传播动力学为例，从仅监督学习开始，并确定了降低性能的情况。为了克服这些困难，我们想到了利用混淆方案，有效地将监督学习和无监督学习结合起来。我们证明，该方案在识别同质网络上传播动力学相关的相变方面表现良好，但在异质网络上性能会恶化。为了应对这一挑战，我们意识到对异质网络进行训练数据集采样是必要的，我们测试了两种采样方法：一种基于集线器节点及其邻居，另一种基于网络的 k 核。最终的结果是一个用于检测相变和准确识别临界点的通用机器学习框架，该框架具有稳健性、计算效率高，并且普遍适用于任意大小和拓扑结构的复杂网络。使用合成和经验网络的广泛测试验证了该框架的优点，为利用机器学习来理解、检测、预测和控制复杂动力系统打开了大门。
