Gaussian process machine learning of potential energy hypersurfaces

Born-Oppenheimer potential energy surfaces (PES) are a central concept in computational chemistry. Extensive research has been geared towards developing novel methods of generating accurate but computationally feasible, global potential energy surfaces. Recent approaches have stepped away from the use of analytical methods and have instead honed in on the application of machine learning techniques. These methods primarily focus on just mapping the input-output space of a training data set as accurately as possible, without delving too deeply into the chemistry of the system studied. One such machine learning technique is Gaussian Processes regression - a non-parametric learning tool that has shown significant promise in being able to predict the intermolecular energies of a variety of systems to an arbitrary level of accuracy. This method is adopted in our research, producing high accuracy global PES for several van der Waals bimolecular complexes at a fraction of the usual computational cost, when using accurate training data. The research also introduces several algorithms for sequential design, where the model selects training data points iteratively. Points are chosen based on information learnt from the previous training step. The sequential design results are pitted against ‘one shot’ space-filling designs (where training data are just chosen in bulk on the basis of the best coverage of space). Two of the sequential design methods significantly outperform the space filling sets in terms of predictive accuracy. Global potential energy surfaces are produced for CO2-H2, CO2 – Ne, CO2 – CO, HF-HF, CH4 – N2 and Ar3 but the algorithm can be easily applied to other molecular interactions with a only few trivial modifications.