论文标题
$ n $ body Equivariant功能的递归评估和迭代收缩
Recursive evaluation and iterative contraction of $N$-body equivariant features
论文作者
论文摘要
将原子配置映射到与原子位置相关的字段（例如，原子密度）相关的$ n $点相关性已成为一种优雅有效的解决方案，以表示结构作为机器学习算法的输入。虽然很明显，低阶密度相关性并未提供原子环境的完整表示，但可能的$ n $ body不变性数量的指数增加使得很难设计简洁有效的表示。我们讨论了如何利用不同阶数的模棱两可特征（$ n $ body不变性的概括，提供不当旋转的对称性的完整表示）之间的递归关系，以有效地计算高阶项。结合每个顺序在每个顺序中最表现力组合的自动选择，此方法提供了一个概念性和实用的框架，以生成可系统性化的，对称性适应的代表，以用于原子机器学习。
Mapping an atomistic configuration to an $N$-point correlation of a field associated with the atomic positions (e.g. an atomic density) has emerged as an elegant and effective solution to represent structures as the input of machine-learning algorithms. While it has become clear that low-order density correlations do not provide a complete representation of an atomic environment, the exponential increase in the number of possible $N$-body invariants makes it difficult to design a concise and effective representation. We discuss how to exploit recursion relations between equivariant features of different orders (generalizations of $N$-body invariants that provide a complete representation of the symmetries of improper rotations) to compute high-order terms efficiently. In combination with the automatic selection of the most expressive combination of features at each order, this approach provides a conceptual and practical framework to generate systematically-improvable, symmetry adapted representations for atomistic machine learning.
