It is important to assess the large body of ML methods to fit electronic energies (and forces) and this has been done numerous times in the literature. Organizing these assessments would be a major task, and perhaps something for AI to do in the future. It is worth noting that the vast majority reactive potentials (some of which were discussed above) use global PIP approaches and not atom-centered ones. By contrast non-reactive potentials for small biomolecules and materials applications have been dominated by atom-centered approaches. We have assessed PIPs against PIP-GPR for small molecules H 3 O + , NNH + NN, formic acid dimer, PIP compared to sGDML for H 3 O - 2 and extensive assessment for The precision and speed of PIPs is clearly seen. In addition, the lower panel plots compare the PIP PES4 with direct, out-of-sample, DFT calculations for an OH stretch and a torsional motion. As seen the PIP PES4 extrapolates well for both.