Precision Metrics for Fragmented and MB-PIP PES for C14H30 immediately renders the trained fit permutationally invariant. The former was done by Guo and co-workers. This approach is known as PIP-NN. The PIPs used for this approach are obtained from the MSA software. What was not clear, and is still the case, is the number of PIPs to use. Basically, the protocol is to increase the number (for a fixed NN architecture) until a precise fit is obtained. In order to mitigate the numbers of PIPs as inputs, Zhang and Fu and co-workers made a significant advance in using so-called "Fundamental Invariants"