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We construct an approximate trivializing map by using a Schwinger-Dysonequation. The advantage of this method is that: (1) The basis for the flowkernel can be chosen arbitrarily by hand. (2) It can be applied to the generalaction of interest. (3) The coefficients in the kernel are determined bylattice estimates of the observables, which does not require analyticcalculations beforehand. We perform the HMC with the effective action obtainedby the Schwinger-Dyson method, and show that we can have better control of theeffective action than the known $t$-expansion construction. However, thealgorithmic overhead is still large and overwhelming the gain though fasterdecorrelation is observed for long-range observables in some cases. Thiscontribution reports the preliminary results of this attempt.

Use of Schwinger-Dyson equation in constructing an approximate trivializing map