  State-of-the-art simulations of discrete gauge theories are based on Markov
chains with local changes in the field space, which however at very fine
lattice spacings are notoriously difficult due to separated topological sectors
of the gauge field. Hybrid Monte Carlo (HMC) algorithms, which are very
efficient at coarser lattice spacings, suffer from increasing autocorrelation
times. This makes simulation of lattice QCD close to the continuum infeasible
even with exa-scale computing.
  An approach, which can overcome long autocorrelation times, is based on
trivializing maps, where a new gauge proposal is given by mapping a
configuration from a trivial space to the target one, distributed via the
associated Boltzmann factor. Using gauge equivariant coupling layers, the map
can be approximated via machine learning techniques. However the deviations
scale with the volume in case of local theories and extensive distributions,
rendering a global update unfeasible for realistic box sizes.
  In this proceeding, we will discuss the potential of localized updates in
case of the 2D Schwinger Model. Using gauge-equivariant flow maps, a local
update can be fine grained towards finer lattice spacing. Based on this we will
present results on simulating the 2D Schwinger Model with dynamical Nf=2 Wilson
fermions at fine lattice spacings using scalable global correction steps and
compare the performance to the HMC.
