  We introduce a family of neural quantum states for the simulation of strongly
interacting systems in the presence of spatial periodicity. Our variational
state is parameterized in terms of a permutationally-invariant part described
by the Deep Sets neural-network architecture. The input coordinates to the Deep
Sets are periodically transformed such that they are suitable to directly
describe periodic bosonic systems. We show example applications to both one and
two-dimensional interacting quantum gases with Gaussian interactions, as well
as to $^4$He confined in a one-dimensional geometry. For the one-dimensional
systems we find very precise estimations of the ground-state energies and the
radial distribution functions of the particles. In two dimensions we obtain
good estimations of the ground-state energies, comparable to results obtained
from more conventional methods.
