Materials science faces the challenge of efficiently discovering materials with desired properties. Traditional methods rely heavily on experience and are time-consuming. Materials informatics (MI) offers a data-driven approach to accelerate this process using machine learning to analyze structural and property data. MI typically involves three key components: datasets, representation of materials, and machine learning algorithms for knowledge extraction and prediction. While deep learning (DL) methods have shown promise in predicting material properties, their "black box" nature hinders interpretability and understanding of structure-property relationships. This study addresses this limitation by proposing a novel interpretable DL architecture.

Existing DL-based MI approaches often employ convolutional neural networks (CNNs), graph neural networks (GNNs), and more recently, transformer-based networks. CNNs with continuous-filter convolution layers have been used to handle atomistic systems. GNNs, such as CGCNN and MEGNet, represent molecules or crystals as graphs to predict properties. Transformer-based networks utilize attention mechanisms to model interatomic interactions. However, many existing models lack interpretability, making it difficult to understand the relationships between material structure and properties. While some studies incorporate additional information or features to improve interpretability, challenges remain in accurately predicting properties and explaining the underlying physical and chemical phenomena.

This study introduces a novel interpretable deep learning architecture, termed SCANN (Self-Consistent Attention-based Neural Network). SCANN leverages a recursive attention mechanism to learn representations of local atomic structures. The local structure of an atom includes the central atom, its neighbors, and their arrangement. The global representation of the material structure is then derived from these local representations. The attention mechanism allows for the incorporation of geometrical information of neighboring atoms. The architecture quantitatively measures the degree of attention given to each local structure, providing insights into the structure-property relationship. Two versions of SCANN are implemented: SCANN and SCANN+. SCANN+ incorporates Voronoi solid angle embedding and multiple LocalAttention layers to improve the representation of the geometrical structure. The models are trained and validated on five datasets: QM9, Materials Project, Fullerene-MD, Pt/graphene-MD, and SmFe12-CD. These datasets contain information about various properties including molecular orbital energies (HOMO, LUMO, energy gap), polarizability, heat capacity, deformation energy, and formation energy. Predictive performance is evaluated using Mean Absolute Error (MAE), and the interpretability is assessed by comparing the learned attention scores (GA scores) with first-principles calculations.

The SCANN models demonstrate strong predictive capabilities, comparable to state-of-the-art models like ALIGNN, especially for energy-related properties. While ALIGNN generally outperforms SCANN in terms of MAE, SCANN achieves chemical accuracy thresholds for several properties in the QM9 dataset. SCANN+ shows significant improvement over the original SCANN model in prediction accuracy, especially for properties sensitive to geometry. The analysis of GA scores reveals a strong correspondence between the attention given to specific local structures and the results from DFT calculations. In small molecules (QM9), the GA scores of local structures align with the HOMO/LUMO orbitals, providing insights into reactivity and chemical behavior. For fullerene molecules (C70 and C72), the GA scores reflect the molecular orbital symmetry. In the Pt/graphene system, high GA scores correlate with structural deformations like elongated C-C bonds and convexed carbon atoms. For SmFe12-based compounds, the GA scores indicate the influence of substituting Fe with other elements on formation energy, suggesting insights into material stability. The analysis demonstrates that the GA scores provide interpretable insights into the structure-property relationships, enabling the identification of crucial structural features.

The findings demonstrate the successful development of an interpretable DL architecture for material property prediction. SCANN's comparable performance to state-of-the-art models, coupled with its ability to provide insights into structure-property relationships through attention scores, offers a significant advantage. The correspondence between GA scores and DFT calculations validates the model's ability to capture important physical and chemical phenomena. The approach addresses the limitations of "black box" DL models in materials science, enabling a deeper understanding of the underlying principles governing material behavior. This interpretability significantly enhances the usefulness of DL in material design and discovery.

This study presents a novel interpretable deep learning architecture, SCANN, for predicting material properties and explaining structure-property relationships. SCANN achieves competitive predictive accuracy while providing valuable insights through its attention mechanism. Future work could focus on extending SCANN to other materials and properties, exploring different attention mechanisms, and integrating additional prior knowledge to further enhance both prediction accuracy and interpretability. The model provides a powerful tool for accelerating materials discovery and design.

While SCANN shows promise, certain limitations exist. The performance is slightly lower than ALIGNN for some properties, particularly those highly sensitive to complex geometric arrangements. The interpretability relies on the correlation between GA scores and DFT calculations, which might not always be straightforward. Furthermore, the accuracy of the interpretations depends on the quality and completeness of the training data.