  The pair-contact process with diffusion (PCPD), a generalized model of the
ordinary pair-contact process (PCP) without diffusion, exhibits a continuous
absorbing phase transition. Unlike the PCP, whose nature of phase transition is
clearly classified into the directed percolation (DP) universality class, the
model of PCPD has been controversially discussed since its infancy. To our best
knowledge, there is so far no consensus on whether the phase transition of the
PCPD falls into the unknown university classes or else conveys a new kind of
non-equilibrium phase transition. In this paper, both unsupervised and
supervised learning are employed to study the PCPD with scrutiny. Firstly, two
unsupervised learning methods, principal component analysis (PCA) and
autoencoder, are taken. Our results show that both methods can cluster the
original configurations of the model and provide reasonable estimates of
thresholds. Therefore, no matter whether the non-equilibrium lattice model is a
random process of unitary (for instance the DP) or binary (for instance the
PCP), or whether it contains the diffusion motion of particles, unsupervised
leaning can capture the essential, hidden information. Beyond that, supervised
learning is also applied to learning the PCPD at different diffusion rates. We
proposed a more accurate numerical method to determine the spatial correlation
exponent $\nu_{\perp}$, which, to a large degree, avoids the uncertainty of
data collapses through naked eyes. Our extensive calculations reveal that
$\nu_{\perp}$ of PCPD depends continuously on the diffusion rate $D$, which
supports the viewpoint that the PCPD may lead to a new type of absorbing phase
transition.
