Reconstructing Network Structures from Partial Measurements

Abstract

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. A major shortcoming of theirs is that they cannot provide any reliable information, not even on partial network structures, as soon as some agents are unobservable. Here, we construct a novel method that determines network structures even when not all agents are measurable. 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.

System Size Identification from Sinusoidal Probing in Diffusive Complex Networks

“…Furthermore, to be able to analyze the output of the system, the observer needs some information about the input that triggered the response. Aside of our approach which is to have a direct control on the input signal, one could monitor and analyze a non-controlable input signal [13], but this would require more computation time. A possible improvement could be to rely on shorter time series, which can be long in our case, due to the low frequency of the probing signal.…”

“…The more efficient such inference method are, the closer to real-time it can be performed, allowing an accuate picture of the system at all time. For instance, recovering the underlying structure of a network of dynamical agents, based on measurements, has been an active topic of research along the last decades [6][7][8][9][10][11][12][13]. However, the majority of those approaches rely on the knowledge of most (if not all) the agents composing the system.…”