Tensorial learning. The tensorial learning targets the full EFG tensor V, and correspondingly we can now employ CQ , η and the quaternion q as performance metrics for hyperparameter optimization. The extension to predicting tensors requires to additionally encode the rotational symmetry of tensorial properties, i.e. how the individual tensor elements change under rotations, cf. Fig. . A corresponding equivariant description is achieved by the λ-SOAP kernels, which are built on the definition of the scalar SOAP descriptor. These kernels exploit that by transforming the tensor of interest into its irreducible spherical tensor (IST) representation, the GPR procedure can be simplified from learning on a tensor of order λ into a vector of length k = 2λ + 1. In this representation, all symmetry operations follow the same transformations as the spherical harmonics, shown visually in Fig. , and thus all kernel transformations can be written as Wigner matrices, D λ . The corresponding k-component vector kernel K λ SOAP is then written as