The PES can then be obtained by learning from sufficiently a large number of configuration points of high-quality electronic energies. PIP-NN takes the PIPs as input layer of NN. Therefore, it combines the advantages of the PIPs and the NNs. Namely, the invariant property with respect to the permutation of like elements is enforced by PIP and high fidelity can be obtained by NN. Please refer to refs. for detailed descriptions and discussions of the PIP-NN method, particularly for the translation/rotational/ permutation symmetry adaptation, the maximum order of the PIPs used in NN.