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

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 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.

Persistence on Quotient Spaces with G-invariant Covering for Structural Analysis

“…Consequently, in many practical scenarios, it may be appropriate to compare filtration functions that are defined on a topological space with certain groups of transformations [9][10][11]. Previous research has utilized persistent homology to capture higher-order structural features as descriptors for data analysis and potential machine learning [12,13]. These topological invariants, including circles, loops, holes, and cavities, cannot be described by traditional graph and network models.…”