Persistent homology-based descriptor for machine-learning potential

Constructing efficient descriptors for representing atomic configurations is crucial for developing superior machine-learning potentials. The widely used conventional descriptors are local and constructed based on the two- and three-body correlations of atomic distribution around a specific atom. This atom-centered approach is convenient for constructing a machine-learning potential with scalability and invariance under symmetry operations. However, these descriptors show several limitations with respect to the classification of different configurations, which have a detrimental effect on the predictions of physical properties. Here, we show that the persistent diagram, that is, the two-dimensional representation of persistent homology, can be used as a descriptor. First, using the clustering of cyclo-octane conformations as an example, we show that the persistent diagram captures both the local geometrical and global topological characteristics of the atomic configuration. Next, we demonstrate that convolutional neural network models based on the persistent diagram can accurately predict the mean energies per atom of amorphous graphene and amorphous carbon. Moreover, the models can predict the energies for systems larger than those used in the training process, meaning that they are scalable with respect to the system size. Our results provide an effective strategy for improving the machine-learning potential using descriptors that depict both geometrical and topological information.