  To accelerate the HMC with field transformation, we consider a variant of the
trivializing map, the decimation map, which can be regarded as a
coarse-graining transformation. Using the 2D $U(1)$ pure gauge model, combined
with the guided Monte Carlo algorithm, we show that the integrated
autocorrelation time of the topological charge can be exponentially improved in
the wall clock time. Our study indicates that incorporating renormalization
group picture is a powerful and essential ingredient to accelerate the HMC at
large $\beta$.
