Constructing efficient descriptors that represent atomic configurations is crucial for developing a superior machine-learning potential. Widely used conventional descriptors are based on two- or three-body correlations of atomic distribution. Recently, several limitations of these many-body descriptors in classifying different configurations were revealed, which have detrimental effects on the prediction of physical properties. We proposed a new class of descriptors based on persistent homology. We focused on the two-dimensional visualization of persistent homology, that is, a persistence diagram, as a descriptor of atomic configurations in the form of an image. We demonstrated that convolutional neural network models based on this descriptor provide sufficient accuracy in predicting the mean energies per atom of amorphous graphene and amorphous carbon. Our results provide an avenue for improving machine-learning potential using descriptors that depict both topological and geometric information.

翻译：构建代表原子配置的高效描述器对于开发高级机器学习潜力至关重要。 广泛使用的常规描述器基于原子分布的两三体相关关系。 最近,披露了这些多体描述器在对不同配置进行分类方面的几个局限性,这对物理特性的预测产生了有害影响。 我们基于持久性同质性提出了一个新的描述器类别。 我们侧重于持续同质的二维直观化,即持久性图,以图像的形式作为原子配置的描述器。 我们演示了基于此描述器的神经网络模型在预测无形态的正态正态和无形态的碳的每个原子的平均能量方面提供了足够的准确性。 我们的结果为利用描述表层和几何信息的描述器改进机器学习潜力提供了一条途径。