Robust Reconstruction of Continuously Time-Varying Topologies of Weighted Networks

Methodological advance in reconstructing the structure of a complex dynamical network have enabled increasingly intricate comprehension of its evolutionary mechanisms and functional behaviors. However, we are often involved in such a situation that only a limited number of observations can be collected and the network structures are completely unknown and continuously time-varying and state-dependent. Few studies have been involved in reconstructing the continuously varying topologies of networks in time intervals via limited discrete observations. We develop a new way to reconstruct the structures of continuously time-varying and state-dependent networks by reconstructing the Taylor expansion coefficients of couplings. The alternating direction method of multipliers algorithm is applied to solve the reconstruction problem by integrating each component’s information of a high-dimensional node. The robustness analysis of our method shows that the structure reconstruction under noisy observations and outliers approximates the one under accurate observations as nodal dimension increases. Different from the existing works, the advantage of our method lies in two aspects. First, the ability to reconstruct network structures via one-time dynamical evolution. Second, instead of reconstructing structures at discrete time points, we obtain the continuously varying structures in continuous time intervals. Numerical simulations are provided to illustrate the feasibility, effectiveness, and robustness of the reconstruction scheme.