  Network reconstruction is fundamental to understanding the dynamical
behaviors of the networked systems. Many systems, modeled by multiplex networks
with various types of interactions, display an entirely different dynamical
behavior compared to the corresponding aggregated network. In many cases,
unfortunately, only the aggregated topology and partial observations of the
network layers are available, raising an urgent demand for reconstructing
multiplex networks. We fill this gap by developing a mathematical and
computational tool based on the Expectation-Maximization framework to
reconstruct multiplex layer structures. The reconstruction accuracy depends on
the various factors, such as partial observation and network characteristics,
limiting our ability to predict and allocate observations. Surprisingly, by
using a mean-field approximation, we discovered that a discrimination indicator
that integrates all these factors universally determines the accuracy of
reconstruction. This discovery enables us to design the optimal strategies to
allocate the fixed budget for deriving the partial observations, promoting the
optimal reconstruction of multiplex networks. To further evaluate the
performance of our method, we predict beside structure also dynamical behaviors
on the multiplex networks, including percolation, random walk, and spreading
processes. Finally, applying our method on empirical multiplex networks drawn
from biological, transportation, and social domains, corroborate the
theoretical analysis.
