  Neural networks have been applied to tackle many-body electron correlations
for small molecules and physical models in recent years. Here we propose a new
architecture that extends molecular neural networks with the inclusion of
periodic boundary conditions to enable ab initio calculation of real solids.
The accuracy of our approach is demonstrated in four different types of
systems, namely the one-dimensional periodic hydrogen chain, the
two-dimensional graphene, the three-dimensional lithium hydride crystal, and
the homogeneous electron gas, where the obtained results, e.g. total energies,
dissociation curves, and cohesive energies, outperform many traditional ab
initio methods and reach the level of the most accurate approaches. Moreover,
electron densities of typical systems are also calculated to provide physical
intuition of various solids. Our method of extending a molecular neural network
to periodic systems can be easily integrated into other neural network
structures, highlighting a promising future of ab initio solution of more
complex solid systems using neural network ansatz, and more generally endorsing
the application of machine learning in materials simulation and condensed
matter physics.
