从头算分子力场的原子指纹算法
An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Fields
摘要：
分子指纹是描述原子邻域结构的特征向量，是势能面和原子间相互作用力数据驱动建模的重要抽象和关键组成部分。在本文中，我们提出了密度编码的正则对齐指纹（DECAF）指纹算法，这是一个强大的和有效的，用于拟合每个原子的标量和矢量量。指纹本质上是一个连续的密度场，它是由以原子为中心的平滑核叠加而成的。指纹的旋转不变性是通过将每个指纹实例的相邻原子对齐到从核最小和优化过程计算的局部正则坐标系上来实现的。我们表明，这种方法是优于PCA为基础的方法，特别是当原子邻域稀疏和/或包含对称性。我们建议，密度场之间的“距离”可以用它们逐点差分的体积积分来测量。这可以有效地计算使用最佳的正交规则，这只需要在一个小数目的网格点离散采样。我们还实验的权重函数的选择，用于构建密度场，并表征其性能拟合原子间的潜力。通过一组基准问题证明了指纹的适用性。
英文摘要：
Molecular fingerprints, i.e. feature vectors describing atomistic neighborhood configurations, is an important abstraction and a key ingredient for data-driven modeling of potential energy surface and interatomic force. In this paper, we present the Density-Encoded Canonically Aligned Fingerprint (DECAF) fingerprint algorithm, which is robust and efficient, for fitting per-atom scalar and vector quantities. The fingerprint is essentially a continuous density field formed through the superimposition of smoothing kernels centered on the atoms. Rotational invariance of the fingerprint is achieved by aligning, for each fingerprint instance, the neighboring atoms onto a local canonical coordinate frame computed from a kernel minisum optimization procedure. We show that this approach is superior over PCA-based methods especially when the atomistic neighborhood is sparse and/or contains symmetry. We propose that the `distance' between the density fields be measured using a volume integral of their pointwise difference. This can be efficiently computed using optimal quadrature rules, which only require discrete sampling at a small number of grid points. We also experiment on the choice of weight functions for constructing the density fields, and characterize their performance for fitting interatomic potentials. The applicability of the fingerprint is demonstrated through a set of benchmark problems.
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