多层动力网络的拓扑识别和重构研究

Multilayer dynamical networks, instead of monoplex complex networks, can better describe the reality by big data and example analysis. Taking the power grid collapse of southern Italy for example, H. E. Stanley emphasizes the importance of topology identification of multilayer networks by citing the duplex network which is composed of the power grid network and the Internet. Topology identification of multiplex networks is more complex than that of monoplex networks because of the inter-couplings. Topology identification and reconstruction of multilayer dynamical networks are investigated in this project, in which the inter-couplings are stressed. The inter-couplings in this project include three facts: the proportion, the strengths, the assortativity and the directions. Considering the inter-couplings and the dynamics in each layer, this project study how to identify the topology of the whole multilayer network, the sublayer networks and the inter-couplings theoretically. Further, strategy selection, combined with ROC curve, compressed sensing, or Granger causality test, is considered to ensure the speed and the efficiency of the identification. Theoretically, the investigation helps the comprehension of the fundamental laws of topology identification of multilayer networks. Practically, the investigation helps the construction of real traffic networks, biological networks, social networks and technological networks.

许多大数据和实证分析发现，多层动力网络，而不是以往单层网络，才能更好的描述现实。美国科学院院士Stanley以意大利南部电网大崩溃为例，用电力网与互联网组成的两层网络说明了识别多层网络拓扑的重要性。层间耦合的存在使多层网络比单层网络复杂得多，其拓扑识别因此极具挑战。本项目进行多层动力网络拓扑结构的识别和重构，重点聚焦在层间耦合。层间大致包括三个方面：层间耦合的比例疏密，层间耦合的强度大小，层间耦合的方式如何(同配性、方向性等)。拟考虑层间耦合和各层动力学对多层网络拓扑识别的影响，从理论上系统研究如何反演整体网络结构、重构部分未知层拓扑、预测层间耦合方式。在此基础上，选取策略以提高识别的成功率，并结合ROC曲线、压缩感知、格兰杰因果判断来保证识别的速度和效率。这些研究在理论上有助于深刻理解多层网络结构识别的基本规律，在实际中有助于交通网络构建、生物网络重组、社会网络预测、技术网络实现等等。

本项目深入而细致地分析了复杂网络的识别和同步，并结合项目开展期间经历的新冠疫情，根据兴趣拓展了一部分疾病传播的研究。项目从单层网络开始，深入到多层网络研究其结构和动力学的特性。通过研究，发现多层网络与单层网络在拓扑结构识别、重要节点挖掘、同步性能保持和传播方式分析等方面有着密切的联系，又有着本质的区别。总的来说，网络的连接方式、时滞和噪音都极大地影响着网络结构和动力学的变化，进而对网络中的扩散起着关键作用。实际中要把握这些影响规律，用相关理论结果更好地指导现实网络。比如疫情传播要接种疫苗时，需根据疾病自身的特点和社交网络连接的方式，将重点人群免疫策略和隔离策略按一定程度结合起来效果会更好。项目得到的很多结果为探索实际中大型电力网络、多层交通网络、多重疾病网络和生物神经元网络等提供了理论支撑。项目在 IEEE Transactions on Automatic Control，SIAM Journal on Control and Optimization，IEEE Transactions on Cybernetics，Chaos， Nonlinear Dynamics，IEEE Transactions on Circuits and Systems—II 等国际知名期刊上发表SCI期刊论文13篇。