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

Area of Science:

• Condensed-matter physics
• Materials science
• Computational physics

Background:

• Predicting amorphous material properties is difficult.
• Machine-learning potentials offer an alternative to computationally intensive ab initio calculations.
• Effective descriptors for atomic configurations are crucial for machine-learning potentials.

Purpose of the Study:

• To propose a novel descriptor for machine-learning potentials based on persistent homology (PH).
• To evaluate the descriptor's ability to predict physical properties of amorphous materials.
• To compare the descriptor's characteristics with existing methods like graph neural networks (GNNs).

Main Methods:

• Utilized persistence diagrams (PD), a 2D representation of PH, to construct descriptors.
• Normalized 2D histograms from PD were used to represent atomic configurations.
• Analyzed dimensional reduction of descriptor spaces to understand their properties.

Main Results:

• The proposed descriptor accurately predicted the average energy per atom of amorphous carbon.
• The descriptor performed well even with a simple predictive model.
• Dimensional reduction analysis showed PH descriptors share characteristics with GNN latent spaces.

Conclusions:

• Persistent homology provides a promising approach for developing symmetry-invariant descriptors for machine-learning potentials.
• This method bypasses the need for hyperparameter tuning and deep-learning architectures.
• PH offers a simpler yet effective alternative for materials property prediction.