where k is a kernel function, p A is a representation vector that encodes the chemical environment of atom A, w B is a regression coefficient and N train is the number of atoms in the training set. We use the SOAP kernel and representation vector, which are widely used in the construction of interatomic potentials and as descriptors of local environments. We refer to the original literature and a recent review for a detailed account of the corresponding theory and implementation. In general, the kernel function measures the similarity of chemical environments and is defined as: