Inferring structure and dynamics of multiplex networks from single-type observations.

Abstract

Multiplex networks provide a fundamental framework for representing systems with multiple types of interactions, which are widely applied across physics, biology, and social sciences. Reconstructing the underlying network topology, represented by the layerwise adjacency matrices, from limited observations is crucial for understanding system functionality and control or prediction of system dynamics. In real-world settings, available data are typically restricted to a single aggregated type of nodal information-far more common than layer-resolved observations-whereas the number of structural variables to be inferred grows rapidly with the number of layers. This creates a fundamental and challenging problem for accurate system reconstruction. To address this issue, we propose a mean-field maximum-likelihood estimation framework that reduces the nonlinear, high-dimensional reconstruction problem to a tractable system of linear equations. Through construction and analysis, we show that the resulting solution intrinsically couples network structure with dynamical parameters, under the assumption of homogeneous dynamics, i.e., all nodes within a given layer share identical parameter values. Building on this framework, we develop an adaptive alternating iteration algorithm to jointly decouple and accurately reconstruct both the multiplex structure and its associated dynamics. Experimental results demonstrate superior reconstruction accuracy across diverse synthetic and real social networks, robust noise tolerance, and broad applicability to canonical dynamical models. Our framework offers a universal, stable, and theoretically grounded solution for multiplex network reconstruction, laying a solid foundation for modeling and analyzing complex systems.