“…Because the number of the FIs increases mildly with the degree, as in the NRPIP mentioned above, the architecture of the FI-NN is more flexible resulting in a faster evaluation of the energy, in particular, for complicated systems, than for PIP-NNs. 46 All methods, PIP-NN, NRPIP-NN and FI-NN, employ invariant polynomials as the input layer of the NN. As systems become more and more complicated, it is harder and harder, and even impractical for high-dimensional systems beyond approximately 10 like atoms, to employ these NN approaches due to the vast increase in the number of the polynomials, and it is difficult to determine the least order of the PIPs.…”