Capsule graph networks for accurate and interpretable crystalline materials property prediction

Area of Science:

• Materials Science
• Artificial Intelligence
• Computational Chemistry

Background:

• Accurate modeling of crystalline materials is crucial for accelerating materials discovery and understanding structure-property relationships.
• Existing graph neural networks (GNNs) lack physical interpretability and fail to model crystal hierarchies and symmetries.
• There is a need for advanced deep learning frameworks that combine predictive accuracy with physical insights.

Purpose of the Study:

• To develop a novel deep learning framework, Capsule Graph Networks with E(3)-Equivariance (CGN-e3), for interpretable modeling of crystalline materials.
• To integrate E(3)-equivariant message passing with capsule networks to capture geometric symmetries and hierarchical structures in crystals.
• To provide physically meaningful interpretations of material properties derived from learned representations.

Main Methods:

• Developed CGN-e3, integrating E(3)-equivariant message passing with capsule networks.
• Employed dynamic routing-by-agreement to aggregate local motifs into higher-order capsules.
• Validated the framework on bandgap and formation energy prediction and material classification tasks using Materials Project and Matbench datasets.

Main Results:

• Achieved competitive performance on formation energy (MAE 0.054 eV/atom) and bandgap prediction (MAE 0.379 eV).
• CGN-e3 outperformed CGCNN and matched MEGNet on benchmark datasets.
• Demonstrated insightful interpretations of learned capsule representations, identifying contributions of specific structural motifs like TiO6 octahedra.

Conclusions:

• CGN-e3 offers a powerful and interpretable approach for modeling crystalline materials, capturing both physical symmetries and hierarchical structures.
• The framework provides an unsupervised pathway for motif discovery and moves beyond "black-box" predictions in materials science.
• This work represents the first integration of E(3)-equivariant GNNs with capsule networks for crystalline material modeling, paving the way for enhanced materials discovery.