The grid approach used in the interpolation for sampling is very expensive for systems with more than 3 atoms. In previous ∆-ML method, the accuracy of the PES fitted by the PIP method cannot be as high as that of the PES fitted by the NN-based method, like PIP-NN or FI-NN. Furthermore, representing VHL of a system as the sum of two PESs, VLL and ∆VHL-LL, would reduce the efficiency of the PES evaluation, particularly in the dynamical calculations.