Hierarchical machine learning of potential energy surfaces

We present hierarchical machine learning (hML) of highly accurate potential energy surfaces (PESs). Our scheme is based on adding predictions of multiple Δ-machine learning models trained on energies and energy corrections calculated with a hierarchy of quantum chemical methods. Our (semi-)automatic procedure determines the optimal training set size and composition of each constituent machine learning model, simultaneously minimizing the computational effort necessary to achieve the required accuracy of the hML PES. Machine learning models are built using kernel ridge regression, and training points are selected with structure-based sampling. As an illustrative example, hML is applied to a high-level ab initio CH₃Cl PES and is shown to significantly reduce the computational cost of generating the PES by a factor of 100 while retaining similar levels of accuracy (errors of ∼1 cm^-1).