In order to reduce the cost of constructing the correction PES as much as possible, it is crucial to select points from the DFT dataset. Namely, the selecting should be efficient and the final number of the selected points for high-level calculations need be as few as possible. Note that NN has limited extrapolation ability. That is, for regions lacking sampled points, different NN PESs may give very different predictions. For any DFT point, if several NN correction PESs yield significantly different corrections, then this DFT point should be included to improve the correction PES. This idea, which was used to automatically construct NN PESs without running trajectories, was employed to actively and effectively sample points from the DFT data points. For the HO2 + HO2 PES, only 14% points were selected and calculated at the high-level (UCCSD(T)-F12a/AVTZ) to bring the DFT PES to the target UCCSD(T)-F12a level. In this work, we employ this promising PIP-NN based ∆-ML approach to tackle the construction of the full-dimensional accurate PES for the title reaction OH + CH3OH. Briefly, for VLL, 140 192 points are calculated at the level of UM05-2X/6-311+G(3df, 2p), and fitted by the PIP-NN approach. Only 7586 points are calculated at the UCCSD(T)-F12a/AVTZ level, and required to represent the correction PES ∆VHL-LL. Over 92% calculation cost is saved! The fitting error of the final PES is 0.467 kcal/mol.