论文标题
向量场的光谱 - 邻域表示：机器学习电位，包括旋转
A spectral-neighbour representation for vector fields: machine-learning potentials including spin
论文作者
论文摘要
我们引入了用于矢量场的翻译和旋转不变的局部表示，该代表性可用于构建固体和分子的机器学习能量模型。这使我们能够在相同的基础上描述由于原子运动，矢量场的纵向和横向激发及其相互作用而引起的能量波动。然后，形式主义可以应用于总能量由矢量密度确定的物理系统，例如磁性。我们的表示形式是在描述局部原子位置和矢量场的组合动量的功率谱上构建的，并且可以与不同的机器学习方案以及从准确的Ab Inlibe电子结构理论中获取的数据结合使用。我们为一系列古典旋转哈密顿和机器学习算法展示了我们表示的描述能力。特别是，我们像常规光谱邻域分析势和高斯近似一样，基于两种线性脊回归的能量模型。这些都代表了海森堡型的哈密顿素化，包括纵向能量术语和自旋晶格耦合。
We introduce a translational and rotational invariant local representation for vector fields, which can be employed in the construction of machine-learning energy models of solids and molecules. This allows us to describe, on the same footing, the energy fluctuations due to the atomic motion, the longitudinal and transverse excitations of the vector field, and their mutual interplay. The formalism can then be applied to physical systems where the total energy is determined by a vector density, as in the case of magnetism. Our representation is constructed over the power spectrum of the combined angular momentum describing the local atomic positions and the vector field, and can be used in conjunction with different machine-learning schemes and data taken from accurate ab initio electronic structure theories. We demonstrate the descriptive power of our representation for a range of classical spin Hamiltonian and machine-learning algorithms. In particular, we construct energy models based on both linear Ridge regression, as in conventional spectral neighbour analysis potentials, and gaussian approximation. These are both built to represent a Heisenberg-type Hamiltonian including a longitudinal energy term and spin-lattice coupling.
