Lattice QCD generates Monte Carlo samples of quantum fields on a 4D space time lattice, typically with billions of degrees of freedom, in order to carry out the Feyman path integral. Even with the state of art HMC algorithm, the cost of generating independent samples becomes exponentially large while approaching the continuum limit. This is due to slow modes of the field resisting changes from the dynamics, and, on the other hand, high potential barriers separating topological modes. We apply a neural network parametrized change of variables to the path integral, respecting the underlying gauge group symmetry, and search for the efficient field transformations that would lower the cost of generating field samples with optimized neural network weights. While we are still working on 4D SU(3) gauge fields, this talk presents our results from 2D U(1) gauge fields, and discuss the challenges in scaling up.