  We design generative neural networks that generate Monte Carlo configurations
with complete absence of autocorrelation from which only short Markov chains
are needed before making measurements for physical observables, irrespective of
the system locating at the classical critical point, fermionic Mott insulator,
Dirac semimetal, or quantum critical point. We further propose a
network-initialized Monte Carlo scheme based on such neural networks, which
provides independent samplings and can accelerate the Monte Carlo simulations
by significantly reducing the thermalization process. We demonstrate the
performance of our approach on the two-dimensional Ising and fermion Hubbard
models, and expect it can systematically speed up the Monte Carlo simulations
especially for the very challenging many-electron problems.
