Incompleteness of Atomic Structure Representations

Pozdnyakov Sergey N.; Willatt Michael J.; Bartok Albert P.; Ortner Christoph; Csanyi Gabor; Ceriotti Michele

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Incompleteness of Atomic Structure Representations

机译：原子结构表示的不完整性

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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. There is a widespread belief in the community that three-body correlations are likely to provide an overcomplete description of the environment of an atom. We produce several counterexamples to this belief, with the consequence that any classifier, regression, or embedding model for atom-centered properties that uses three- (or four)-body features will incorrectly give identical results for different configurations. Writing global properties (such as total energies) as a sum of many atom-centered contributions mitigates 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.

机译：许多身体描述符被广泛用于表示机器学习的内部电位的构建中的原子环境，并且更广泛地用于拟合，分类和嵌入原子结构上的任务。在社区中存在广泛的信念，即三体相关性可能会提供对原子环境的过度简洁。我们为此信仰产生了几个反例，结果是，使用三（或四个）特征的原子为中心属性的任何分类器，回归或嵌入模型将不正确地给出不同配置的相同结果。作为许多原子为中心的总和写出全球性质（如总能量）减轻了这一基本缺陷的影响 - 解释了当前“机器学习”力领的成功。我们预计随着所需的准确性增加而产生的问题，并提出了潜在的解决方案。

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《Physical review letters》 |2020年第16期|166001.1-166001.6|共6页
作者
Pozdnyakov Sergey N.; Willatt Michael J.; Bartok Albert P.; Ortner Christoph; Csanyi Gabor; Ceriotti Michele;
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Ecole Polytech Fed Lausanne Lab Computat Sci & Modelling Inst Mat CH-1015 Lausanne Switzerland;

Ecole Polytech Fed Lausanne Lab Computat Sci & Modelling Inst Mat CH-1015 Lausanne Switzerland;

Univ Warwick Sch Engn Dept Phys Coventry CV4 7AL W Midlands England|Univ Warwick Sch Engn Warwick Ctr Predict Modelling Coventry CV4 7AL W Midlands England;

Univ Warwick Math Inst Coventry CV4 7AL W Midlands England;

Univ Cambridge Engn Lab Trumpington St Cambridge CB2 1PZ England;

Ecole Polytech Fed Lausanne Lab Computat Sci & Modelling Inst Mat CH-1015 Lausanne Switzerland;

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Incompleteness of Atomic Structure Representations

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