Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, USA.
J Chem Phys. 2013 Nov 28;139(20):204103. doi: 10.1063/1.4832697.
A rigorous, general, and simple method to fit global and permutation invariant potential energy surfaces (PESs) using neural networks (NNs) is discussed. This so-called permutation invariant polynomial neural network (PIP-NN) method imposes permutation symmetry by using in its input a set of symmetry functions based on PIPs. For systems with more than three atoms, it is shown that the number of symmetry functions in the input vector needs to be larger than the number of internal coordinates in order to include both the primary and secondary invariant polynomials. This PIP-NN method is successfully demonstrated in three atom-triatomic reactive systems, resulting in full-dimensional global PESs with average errors on the order of meV. These PESs are used in full-dimensional quantum dynamical calculations.
讨论了一种使用神经网络（NN）严格、通用且简单的拟合全局和置换不变势能面（PES）的方法。这种所谓的置换不变多项式神经网络（PIP-NN）方法通过在输入中使用一组基于 PIP 的对称函数来施加置换对称性。对于具有三个以上原子的系统，结果表明，输入向量中的对称函数数量需要大于内部坐标数量，以便包含主不变多项式和次不变多项式。该 PIP-NN 方法在三个原子三原子反应系统中得到了成功的验证，得到了平均误差在毫电子伏特量级的全维全局 PES。这些 PES 用于全维量子动力学计算。
