Efficient non-parametric fitting of potential energy surfaces for polyatomic molecules with Gaussian processes (Englisch)

We explore the performance of a statistical learning technique based on Gaussian Process (GP) regression as an efficient non-parametric method for constructing multi-dimensional potential energy surfaces (PES) for polyatomic molecules. Using an example of the molecule N_4, we show that a realistic GP model of the six-dimensional PES can be constructed with only 240 potential energy points. We construct a series of the GP models and illustrate the convergence of the accuracy of the resulting surfaces as a function of the number of {\it ab \ initio} points. We show that the GP model based on \sim 1500 potential energy points achieves the same level of accuracy as the conventional regression fits based on 16,421 points. The GP model of the PES requires no fitting of {\it ab \ initio} data with analytical functions and can be readily extended to surfaces of higher dimensions.