  The use of machine learning techniques in classical and quantum systems has
led to novel techniques to classify ordered and disordered phases, as well as
uncover transition points in critical phenomena. Efforts to extend these
methods to dynamical processes in complex networks is a field of active
research. Network-percolation, a measure of resilience and robustness to
structural failures, as well as a proxy for spreading processes, has numerous
applications in social, technological, and infrastructural systems. A
particular challenge is to identify the existence of a percolation cluster in a
network in the face of noisy data. Here, we consider bond-percolation, and
introduce a sampling approach that leverages the core-periphery structure of
such networks at a microscopic scale, using onion decomposition, a refined
version of the $k-$core. By selecting subsets of nodes in a particular layer of
the onion spectrum that follow similar trajectories in the percolation process,
percolating phases can be distinguished from non-percolating ones through an
unsupervised clustering method. Accuracy in the initial step is essential for
extracting samples with information-rich content, that are subsequently used to
predict the critical transition point through the confusion scheme, a recently
introduced learning method. The method circumvents the difficulty of missing
data or noisy measurements, as it allows for sampling nodes from both the core
and periphery, as well as intermediate layers. We validate the effectiveness of
our sampling strategy on a spectrum of synthetic network topologies, as well as
on two real-word case studies: the integration time of the US domestic airport
network, and the identification of the epidemic cluster of COVID-19 outbreaks
in three major US states. The method proposed here allows for identifying phase
transitions in empirical time-varying networks.
