正则化原子体序置换不变多项式构造原子间相互作用势
Regularised Atomic Body-Ordered Permutation-Invariant Polynomials for the Construction of Interatomic Potentials
摘要：
我们研究了使用不变多项式在材料系统的数据驱动的原子间相互作用势的建设。“原子体有序置换不变多项式”（aPIP）包括系统基础，并被构造为保持势能函数相对于旋转和置换的对称性。与基于核的模型和人工神经网络模型相比，将总能量显式分解为原子体有序项的总和允许保持拟合的维度相当低，对于5体项仅为10。这种分解有助于势的可解释性，因为低体阶分量可以独立地研究和解释。此外，虽然多项式基函数被认为外推差，我们表明，低维结合仔细正则化实际上导致更好的可转移性比高维，基于内核的高斯近似势。
英文摘要：
We investigate the use of invariant polynomials in the construction of data-driven interatomic potentials for material systems. The "atomic body-ordered permutation-invariant polynomials" (aPIPs) comprise a systematic basis and are constructed to preserve the symmetry of the potential energy function with respect to rotations and permutations. In contrast to kernel based and artificial neural network models, the explicit decomposition of the total energy as a sum of atomic body-ordered terms allows to keep the dimensionality of the fit reasonably low, up to just 10 for the 5-body terms. The explainability of the potential is aided by this decomposition, as the low body-order components can be studied and interpreted independently. Moreover, although polynomial basis functions are thought to extrapolate poorly, we show that the low dimensionality combined with careful regularisation actually leads to better transferability than the high dimensional, kernel based Gaussian Approximation Potential.
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