Spectral neighbor representation for vector fields: Machine learning potentials including spin

We introduce a translational and rotational invariant local representation for vector fields, which can be employed in the construction of machine learning energy models solids molecules. This allows us to describe, on same footing, fluctuations due atomic motion, longitudinal transverse excitations field, their mutual interplay. The formalism then applied physical systems where total is determined by density, as case magnetism. Our constructed over power spectrum combined angular momentum describing positions it used conjunction with different schemes data taken from accurate ab initio electronic structure theories. demonstrate descriptive our range classical spin Hamiltonian algorithms. In particular, we construct based both linear Ridge regression, conventional spectral neighbor analysis potentials, Gaussian approximation. These are built represent Heisenberg-type including term spin-lattice coupling.