Communication: Fitting potential energy surfaces with fundamental invariant neural network

作者：Kejie Shao, Jun Chen, Zhiqiang Zhao, Dong H. Zhang · 发表于：The Journal of Chemical Physics · 年份：2016 · DOI：10.1063/1.4961454 · 被引用次数：272 · 研究领域：Machine Learning in Materials Science、Advanced Chemical Physics Studies、Computational Drug Discovery Methods

A more flexible neural network (NN) method using the fundamental invariants (FIs) as the input vector is proposed in the construction of potential energy surfaces for molecular systems involving identical atoms. Mathematically, FIs finitely generate the permutation invariant polynomial (PIP) ring. In combination with NN, fundamental invariant neural network (FI-NN) can approximate any function to arbitrary accuracy. Because FI-NN minimizes the size of input permutation invariant polynomials, it can efficiently reduce the evaluation time of potential energy, in particular for polyatomic systems. In this work, we provide the FIs for all possible molecular systems up to five atoms. Potential energy surfaces for OH3 and CH4 were constructed with FI-NN, with the accuracy confirmed by full-dimensional quantum dynamic scattering and bound state calculations.