Representing globally accurate reactive potential energy surfaces with complex topography by combining Gaussian process regression and neural networks

Abstract

There has been increasing attention in using machine learning technologies, such as neural networks (NNs) and Gaussian process regression (GPR), to model multi-dimensional potential energy surfaces (PESs). A PES constructed using NNs features high accuracy and generalization capability, but a single NN cannot actively select training points as GPR does, resulting in expensive ab initio calculations as the molecular complexity increases. However, a PES constructed using GPR has a slow speed of evaluation and it is difficult to accurately describe a fast-changing potential. Herein, an efficient scheme for representing globally accurate reactive PESs with complex topography based on as few points as possible by incorporating active data selection of GPR into NN fitting is proposed. The validity of this strategy is tested using the BeH₂⁺ system, and only 1270 points are automatically sampled. The generalization performance and speed of evaluation of the generated PES are much better than those of the GPR PES constructed using the same dataset. Moreover, an accurate NN PES is fitted by 12 122 points as a benchmark for comparison to further test the global accuracy of the PES obtained using this scheme, and the corresponding results present extremely consistent topography characteristics and calculated Be⁺(²S) + H₂ reaction probabilities.