  We construct an approximate trivializing map by using a Schwinger-Dyson
equation. The advantage of this method is that: (1) The basis for the flow
kernel can be chosen arbitrarily by hand. (2) It can be applied to the general
action of interest. (3) The coefficients in the kernel are determined by
lattice estimates of the observables, which does not require analytic
calculations beforehand. We perform the HMC with the effective action obtained
by the Schwinger-Dyson method, and show that we can have better control of the
effective action than the known $t$-expansion construction. However, the
algorithmic overhead is still large and overwhelming the gain though faster
decorrelation is observed for long-range observables in some cases. This
contribution reports the preliminary results of this attempt.
