Approximate high mode coupling potentials using Gaussian process regression and adaptive density guided sampling.

We present a new efficient approach for potential energy surface construction. The algorithm employs the n-mode representation and combines an adaptive density guided approach with Gaussian process regression for constructing approximate higher-order mode potentials. In this scheme, the n-mode potential construction is conventionally done, whereas for higher orders the data collected in the preceding steps are used for training in Gaussian process regression to infer the energy for new single point computations and to construct the potential. We explore different delta-learning schemes which combine electronic structure methods on different levels of theory. Our benchmarks show that for approximate 2-mode potentials the errors can be adjusted to be in the order of 8 cm-1, while for approximate 3-mode and 4-mode potentials the errors fall below 1 cm-1. The observed errors are, therefore, smaller than contributions due to missing higher-order electron excitations or relativistic effects. Most importantly, the approximate potentials are always significantly better than those with neglected higher-order couplings.