关于原子结构表示的完备性
On the Completeness of Atomic Structure Representations
摘要：
多体描述符被广泛用于在机器学习的原子间势的构造中表示原子环境，并且更广泛地用于原子结构上的拟合、分类和嵌入任务。人们普遍认为三体描述符唯一地指定了原子的环境，直到类似原子的旋转和排列。我们产生了几个反例，这种信念，其后果是，任何分类器，回归或嵌入模型的原子为中心的属性，使用3（或4）体功能将不正确地给出相同的结果为不同的配置。将全局属性（如总能量）写为许多以原子为中心的贡献的总和，可以减轻但不能消除这一基本缺陷的影响，这解释了当前“机器学习”力场的成功。我们预测随着所需精度的提高而出现的问题，并提出潜在的解决方案。
英文摘要：
Many-body descriptors are widely used to represent atomic environments in the construction of machine learned interatomic potentials and more broadly for fitting, classification and embedding tasks on atomic structures. It was generally believed that 3-body descriptors uniquely specify the environment of an atom, up to a rotation and permutation of like atoms. We produce several counterexamples to this belief, with the consequence that any classifier, regression or embedding model for atom-centred properties that uses 3 (or 4)-body features will incorrectly give identical results for different configurations. Writing global properties (such as total energies) as a sum of many atom-centred contributions mitigates, but does not eliminate, the impact of this fundamental deficiency -- explaining the success of current "machine-learning" force fields. We anticipate the issues that will arise as the desired accuracy increases, and suggest potential solutions.
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