  Hamiltonian Monte Carlo is a widely used algorithm for sampling from
posterior distributions of complex Bayesian models. It can efficiently explore
high-dimensional parameter spaces guided by simulated Hamiltonian flows.
However, the algorithm requires repeated gradient calculations, and these
computations become increasingly burdensome as data sets scale. We present a
method to substantially reduce the computation burden by using a neural network
to approximate the gradient. First, we prove that the proposed method still
maintains convergence to the true distribution though the approximated gradient
no longer comes from a Hamiltonian system. Second, we conduct experiments on
synthetic examples and real data sets to validate the proposed method.
