Abstract
Many practical systems can be described by dynamic networks, for which modern technique can measure their outputs, and accumulate extremely rich data. Nevertheless, the network structures producing these data are often deeply hidden in the data. The problem of inferring network structures by analyzing the available data, turns to be of great significance. On one hand, networks are often driven by various unknown facts, such as noises. On the other hand, network structures of practical systems are commonly nonlinear, and different nonlinearities can provide rich dynamic features and meaningful functions of realistic networks. Although many works have considered each fact in studying network reconstructions, much less papers have been found to systematically treat both difficulties together. Here we propose to use high-order correlation computations (HOCC) to treat nonlinear dynamics; use two-time correlations to decorrelate effects of network dynamics and noise driving; and use suitable basis and correlator vectors to unifiedly infer all dynamic nonlinearities, topological interaction links and noise statistical structures. All the above theoretical frameworks are constructed in a closed form and numerical simulations fully verify the validity of theoretical predictions.
Highlights
Many practical systems can be described by dynamic networks, for which modern technique can measure their outputs, and accumulate extremely rich data
Network dynamics is determined in great extent by network structures, mainly classified by dynamics of local nodes and interactions between network nodes
Where T represents the operation of transposition
Summary
Many practical systems can be described by dynamic networks, for which modern technique can measure their outputs, and accumulate extremely rich data. It turns to be crucial to develop effective methods to infer network structures from the available data of nodes This is the so-called inverse problem of network reconstruction, which has become one of the most important topics in the data analysis of complex networks in wide crossing fields, in biological and social sciences. The algorithm is analytical, but complicated if networks are large and noises at different nodes are coupled and multiplicative In this presentation we consider the problem of reconstruction of noise-driven nonlinear dynamic networks. The key points in dealing with the difficulties are: We compute high-order correlations to treat possible nonlinear structures; We use two-time correlations to separate the reconstructions of dynamical networks and noise statistics to two independent steps, and the computation of inference of noise-driven nonlinear networks has been converted to simple linear and algebraic matrix equations. The problems how to treat measurement noises and colored noises and how reconstruction errors of the HOCC method depend on data length, system size and choice of basis sets are briefly discussed (see Supplementary Information)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
