  Monte Carlo (MC) simulations are essential computational approaches with
widespread use throughout all areas of science. We present a method for
accelerating lattice MC simulations using fully connected and convolutional
artificial neural networks that are trained to perform local and global moves
in configuration space, respectively. Both networks take local spacetime MC
configurations as input features and can, therefore, be trained using samples
generated by conventional MC runs on smaller lattices before being utilized for
simulations on larger systems. This new approach is benchmarked for the case of
determinant quantum Monte Carlo (DQMC) studies of the two-dimensional Holstein
model. We find that both artificial neural networks are capable of learning an
unspecified effective model that accurately reproduces the MC configuration
weights of the original Hamiltonian and achieve an order of magnitude speedup
over the conventional DQMC algorithm. Our approach is broadly applicable to
many classical and quantum lattice MC algorithms.
