We propose a machine learning method to model molecular tensorial quantities, namely the magnetic anisotropy tensor, based on the Gaussian-moment neural-network approach. We demonstrate that the proposed methodology can achieve an accuracy of 0.3--0.4 cm$^{-1}$ and has excellent generalization capability for out-of-sample configurations. Moreover, in combination with machine-learned interatomic potential energies based on Gaussian moments, our approach can be applied to study the dynamic behavior of magnetic anisotropy tensors and provide a unique insight into spin-phonon relaxation.

翻译：我们提出了一种基于高斯矩神经网络方法的机器学习方法，用于建模分子张量量，即磁各向异性张量。我们证明，所提出的方法能够达到0.3–0.4 cm$^{-1}$的精度，并且对样本外构型具有出色的泛化能力。此外，结合基于高斯矩的机器学习原子间势能，我们的方法可用于研究磁各向异性张量的动态行为，并为自旋-声子弛豫提供独特的见解。