  Machine learning methods are being actively considered as a new tool of
describing many body physics. However, so far, their capabilities has been only
demonstrated in previously studied models, such as e.g. Ising model. Here, we
consider a simple problem, demonstrating that neural networks can be
successfully used to give new insights in statistical physics. Specifically, we
consider 3D lattice dimer model, which consists of sites forming a lattice and
bonds connecting the neighboring sites, in such a way that every bond can be
either empty or filled with a dimer, and the total number of dimers ending at
one site is fixed to be one. Dimer configurations can be viewed as equivalent
if they are connected through a series of local flips, i.e. simultaneous
'rotation' of a pair of parallel neighboring dimers. It turns out that the
whole set of dimer configurations on a given 3D lattice can be split into
distinct topological classes, such that dimer configurations belonging to
different classes are not equivalent. In this paper we identify these classes
by using neural networks. More specifically, we train the neural networks to
distinguish dimer configurations from two known topological classes, and after
it, we test them on dimer configurations from unknown topological classes. We
demonstrate that 3D lattice dimer model on a bipartite lattice can be described
by an integer topological invariant ('Hopf number'), whereas lattice dimer
model on a non-bipartite lattice is described by $Z_2$ invariant. Thus, we
demonstrate that neural networks can be successfully used to identify new
topological phases in condensed matter systems, whose existence can be later
verified by other (e.g. analytical) techniques.
