  We propose a generic construction of Lie group agnostic and gauge covariant
neural networks, and introduce constraints to make the neural networks
continuous differentiable and invertible. We combine such neural networks and
build gauge field transformations that is suitable for Hybrid Monte Carlo
(HMC). We use HMC to sample lattice gauge configurations in the transformed
space by the neural network parameterized gauge field transformations. Tested
with 2D U(1) pure gauge systems at a range of couplings and lattice sizes,
compared with direct HMC sampling, the neural network transformed HMC (NTHMC)
generates Markov chains of gauge configurations with improved tunneling of
topological charges, while allowing less force calculations as the lattice
coupling increases.
