A Gaussian process regression adaptive density guided approach for potential energy surface construction

We present a new iterative scheme for potential energy surface (PES) construction, which relies on both physical information and information obtained through statistical analysis. The adaptive density guided approach (ADGA) is combined with a machine learning technique, namely, the Gaussian process regression (GPR), in order to obtain the iterative GPR-ADGA for PES construction. The ADGA provides an average density of vibrational states as a physically motivated importance-weighting and an algorithm for choosing points for electronic structure computations employing this information. The GPR provides an approximation to the full PES given a set of data points, while the statistical variance associated with the GPR predictions is used to select the most important among the points suggested by the ADGA. The combination of these two methods, resulting in the GPR-ADGA, can thereby iteratively determine the PES. Our implementation, additionally, allows for incorporating derivative information in the GPR. The iterative process commences from an initial Hessian and does not require any presampling of configurations prior to the PES construction. We assess the performance on the basis of a test set of nine small molecules and fundamental frequencies computed at the full vibrational configuration interaction level. The GPR-ADGA, with appropriate settings, is shown to provide fundamental excitation frequencies of an root mean square deviation (RMSD) below 2 cm^-1, when compared to those obtained based on a PES constructed with the standard ADGA. This can be achieved with substantial savings of 65%-90% in the number of single point calculations.