In the HC work by Fu et al., the cubic spline method was used to construct VLL and ΔVHL-LL for the PES of the tri-atom reaction F + H2. For VLL, 15000 symmetry-unique points were sampled. For ΔVHL-LL, only 1400 points were selected from 15000 points. Recently, Bowman and coworkers proposed a Δ-learning approach based on PIP. Correspondingly, VLL and ΔVHL-LL are both fitted by the PIP fitting. Tests for PESs of CH4, H3O + , N-methylacetamide and acetylacetone have shown that significant computational cost can be saved since only a small number of sampling configurations are required to be calculated at the target high level. Similarly, VLL and ΔVHL-LL can be also learned by the PIP-NN fitting. Note that the evaluation of Eq. ( ) can be slow. We propose to employ the ΔVHL-LL PES, based on a much smaller number of points calculated directly at the target high-level ab initio method, to predict the difference energies of the remaining points that are not calculated at the high level. Then, all data are of high quality, and are fitted by the PIP-NN method. The evaluation of the PIP-NN PES is thus not affected. Indeed, the new method, PIP-NN based Δ-ML approach, is essentially to obtain high quality energies of many data points.