Interpolation and Extrapolation of Global Potential Energy Surfaces for Polyatomic Systems by Gaussian Processes with...

Gaussian process (GP) regression has recently emerged as a powerful, system-agnostic tool for building global potential energy surfaces (PES) of polyatomic molecules. While the accuracy of GP models of PES increases with the number of potential energy points, so does the numerical difficulty of training and evaluating GP models. Here, we demonstrate an approach to improve the accuracy of global PES without increasing the number of energy points. We show that GP models of PES trained by a small number of energy points can be significantly improved by iteratively increasing the complexity of GP kernels. The composite kernels thus obtained maximize the accuracy of GP models for a given distribution of potential energy points. The accuracy can then be further improved by varying the training point distributions. We also show that GP models with composite kernels can be used for physical extrapolation of PES. We illustrate the approach by constructing the six-dimensional PES for H₃O⁺. For the interpolation problem, we show that this algorithm produces a global six-dimensional PES in the energy range between 0 and 21 000 cm^-1 with the root-mean-square error 65.8 cm^-1 using only 500 randomly selected ab initio points as input. To illustrate extrapolation, we produce the PES at high energies using the energy points at low energies. We show that one can obtain an accurate global fit of the PES extending to 21 000 cm^-1 based on 1500 potential energy points at energies below 10 000 cm^-1.