Permutation invariant polynomial neural network approach to fitting potential energy surfaces

A simple, general, and rigorous scheme for adapting permutation symmetry in molecular systems is proposed and tested for fitting global potential energy surfaces using neural networks (NNs). The symmetry adaptation is realized by using low-order permutation invariant polynomials (PIPs) as inputs for the NNs. This so-called PIP-NN approach is applied to the H + H2 and Cl + H2 systems and the analytical potential energy surfaces for these two systems were accurately reproduced by PIP-NN. The accuracy of the NN potential energy surfaces was confirmed by quantum scattering calculations.