论文标题
通过部分测量重建网络结构
Reconstructing Network Structures from Partial Measurements
论文作者
论文摘要
相互作用剂系统的动力学取决于其耦合网络的结构。因此,对后者的知识非常需要开发有效的控制方案,以准确预测动力学或更好地理解代理间的过程。但是,在许多重要且有趣的情况下,网络结构尚不清楚,并且先前的研究表明,从每个代理商的完整测量时间序列中可以推断出它是如何推断出来的。这些方法隐含地表明,即使网络尚不清楚,其所有节点都是。在这里,我们研究了在观察到的/测量药物中推断网络结构的不同问题。对于接近稳定平衡的对称耦合的动力系统,我们在分析上建立并说明速度信号相关器不仅要编码直接耦合,还要编码在可测量代理子集中耦合网络中的地质距离。当所有代理都可以访问动态数据时,我们的方法在算法上比传统数据更有效,因为它不依赖于矩阵倒置。
The dynamics of systems of interacting agents is determined by the structure of their coupling network. The knowledge of the latter is, therefore, highly desirable, for instance, to develop efficient control schemes, to accurately predict the dynamics, or to better understand inter-agent processes. In many important and interesting situations, the network structure is not known, however, and previous investigations have shown how it may be inferred from complete measurement time series on each and every agent. These methods implicitly presuppose that, even though the network is not known, all its nodes are. Here, we investigate the different problem of inferring network structures within the observed/measured agents. For symmetrically coupled dynamical systems close to a stable equilibrium, we establish analytically and illustrate numerically that velocity signal correlators encode not only direct couplings, but also geodesic distances in the coupling network within the subset of measurable agents. When dynamical data are accessible for all agents, our method is furthermore algorithmically more efficient than the traditional ones because it does not rely on matrix inversion.