Deng Wenfeng, Yang Chunhua, Huang Keke, Wu Wenhan
School of Automation, Central South University, Changsha 410083, China.
Department of Automation, Tsinghua University, Beijing 100084, China.
Chaos. 2022 May;32(5):053105. doi: 10.1063/5.0087740.
Reconstructing the interacting topology from measurable data is fundamental to understanding, controlling, and predicting the collective dynamics of complex networked systems. Many methods have been proposed to address the basic inverse problem and have achieved satisfactory performance. However, a significant challenge arises when we attempt to decode the underlying structure in the presence of inaccessible nodes due to the partial loss of information. For the purpose of improving the accuracy of network reconstruction with hidden nodes, we developed a robust two-stage network reconstruction method for complex networks with hidden nodes from a small amount of observed time series data. Specifically, the proposed method takes full advantage of the natural sparsity of complex networks and the potential symmetry constraints in dynamic interactions. With robust reconstruction, we can not only locate the position of hidden nodes but also precisely recover the overall network structure on the basis of compensated nodal information. Extensive experiments are conducted to validate the effectiveness of the proposed method and superiority compared with ordinary methods. To some extent, this work sheds light on addressing the inverse problem, of which the system lacks complete exploration in the network science community.
从可测量数据重建交互拓扑对于理解、控制和预测复杂网络系统的集体动力学至关重要。已经提出了许多方法来解决基本的逆问题，并取得了令人满意的性能。然而，当我们试图在存在由于部分信息丢失而无法访问的节点的情况下解码潜在结构时，就会出现重大挑战。为了提高具有隐藏节点的网络重建的准确性，我们从少量观测时间序列数据中开发了一种针对具有隐藏节点的复杂网络的鲁棒两阶段网络重建方法。具体而言，所提出的方法充分利用了复杂网络的自然稀疏性和动态交互中的潜在对称约束。通过鲁棒重建，我们不仅可以定位隐藏节点的位置，还可以在补偿节点信息的基础上精确恢复整体网络结构。进行了大量实验以验证所提出方法的有效性以及与普通方法相比的优越性。在某种程度上，这项工作为解决逆问题提供了思路，而该逆问题在网络科学界缺乏全面的探索。
