Persistent homology-based descriptor for machine-learning potential of amorphous structures

TL;DR

This paper introduces a novel descriptor based on persistent homology for machine-learning potentials in amorphous materials, demonstrating its effectiveness in predicting properties and its similarity to GNN latent spaces.

Contribution

The study proposes a persistence diagram-based descriptor for amorphous structures, offering a symmetry-invariant, hyperparameter-free alternative to existing methods like GNNs.

Findings

PD-based descriptor predicts average energy of amorphous carbon.

Descriptor space analysis shows similarity to GNN latent space.

PH can construct effective descriptors without deep learning.

Abstract

High-accuracy prediction of the physical properties of amorphous materials is challenging in condensed-matter physics. A promising method to achieve this is machine-learning potentials, which is an alternative to computationally demanding ab initio calculations. When applying machine-learning potentials, the construction of descriptors to represent atomic configurations is crucial. These descriptors should be invariant to symmetry operations. Handcrafted representations using a smooth overlap of atomic positions and graph neural networks (GNN) are examples of methods used for constructing symmetry-invariant descriptors. In this study, we propose a novel descriptor based on a persistence diagram (PD), a two-dimensional representation of persistent homology (PH). First, we demonstrated that the normalized two-dimensional histogram obtained from PD could predict the average energy per atom of amorphous carbon (aC) at various densities, even when using a simple model. Second, an analysis of the dimensional reduction results of the descriptor spaces revealed that PH can be used to construct descriptors with characteristics similar to those of a latent space in a GNN. These results indicate that PH is a promising method for constructing descriptors suitable for machine-learning potentials without hyperparameter tuning and deep-learning techniques.