Persistent homology-based descriptor for machine-learning potential

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.