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

摘要: 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) polyatomic molecules. Using example molecule N$_4$, we show that realistic GP model six-dimensional PES can be constructed with only 240 points. construct series models and illustrate convergence accuracy resulting function number ${\it ab \ initio}$ $\sim 1500$ points achieves same level conventional fits 16,421 The requires no fitting data analytical functions readily extended to higher dimensions.