Learning Ordering in Crystalline Materials with Symmetry-Aware Graph Neural Networks (2409.13851v1)

Abstract: Graph convolutional neural networks (GCNNs) have become a machine learning workhorse for screening the chemical space of crystalline materials in fields such as catalysis and energy storage, by predicting properties from structures. Multicomponent materials, however, present a unique challenge since they can exhibit chemical (dis)order, where a given lattice structure can encompass a variety of elemental arrangements ranging from highly ordered structures to fully disordered solid solutions. Critically, properties like stability, strength, and catalytic performance depend not only on structures but also on orderings. To enable rigorous materials design, it is thus critical to ensure GCNNs are capable of distinguishing among atomic orderings. However, the ordering-aware capability of GCNNs has been poorly understood. Here, we benchmark various neural network architectures for capturing the ordering-dependent energetics of multicomponent materials in a custom-made dataset generated with high-throughput atomistic simulations. Conventional symmetry-invariant GCNNs were found unable to discern the structural difference between the diverse symmetrically inequivalent atomic orderings of the same material, while symmetry-equivariant model architectures could inherently preserve and differentiate the distinct crystallographic symmetries of various orderings.

• The paper demonstrates that symmetry-aware GCNN models outperform symmetry-invariant variants in capturing ordering-dependent energetics of crystalline materials.
• It utilizes a high-throughput DFT dataset of multicomponent perovskite oxides to evaluate prediction accuracy using key metrics like mean absolute error and energy above the convex hull.
• Visual analyses with PCA reveal that symmetry-equivariant models develop distinct latent embeddings, underscoring their potential as universal interatomic potentials for material design.

Learning Ordering in Crystalline Materials with Symmetry-Aware Graph Neural Networks

The paper entitled "Learning Ordering in Crystalline Materials with Symmetry-Aware Graph Neural Networks" investigates the capabilities of graph convolutional neural networks (GCNNs) in learning the dependence of materials properties on atomic orderings in crystalline substances. The paper explores the strengths and limitations of various symmetry-aware and symmetry-invariant GCNN architectures using a custom-built dataset derived from high-throughput density functional theory (DFT) calculations, particularly focusing on multicomponent perovskite oxides.

Detailed Comparison of GCNN Architectures

Graph convolutional neural networks are increasingly being applied to the field of materials science for their ability to predict properties of crystalline materials based on their atomic structures. This paper particularly scrutinizes the capability of GCNNs to discern between different atomic orderings within the same chemical compositions. The research highlights that conventional symmetry-invariant GCNN models, such as SchNet, CGCNN, and MEGNet, fail to effectively differentiate symmetrically inequivalent atomic arrangements. In contrast, symmetry-equivariant models, such as e3nn and PaiNN, inherently preserve crystallographic symmetries and demonstrate superior performance in capturing ordering-dependent energetics.

To quantitatively assess these findings, the research uses various datasets of multicomponent perovskite oxides, exemplifying both high-symmetry and low-symmetry atomic structures. The DFT dataset comprises over 10,000 distinct structures, which is a significant scale compared to previous high-throughput studies.

Predicting Thermodynamic Stability

A primary objective was to predict the energy above the convex hull ($E_\mathrm{hull}$), which serves as an indicator of the thermodynamic stability of the material against decomposition into competing phases. Both the symmetry-invariant and symmetry-equivariant models trained on this dataset showed proficiency in predicting composition-dependent thermodynamic stability. However, when rigorously validated, the symmetry-equivariant GCNN e3nn achieved a lower mean absolute error (MAE) compared to the symmetry-invariant CGCNN.

More critically, the paper found that symmetry-aware models significantly outperformed symmetry-invariant models in learning the energy differences between symmetrically different cation arrangements within the same chemical compositions. This characteristic is essential for understanding properties that depend heavily on atomic orderings, such as catalytic performance and mechanical stability.

Visualizing and Understanding Model Performance

The strong performance of symmetry-equivariant models was attributed to their ability to develop more discriminative latent embeddings for different atomic orderings. Principal Component Analysis (PCA) was employed to visualize the embeddings, and it became evident that symmetry-equivariant models encapsulated a more distinct separation among inequivalent orderings. This indicates a richer and more nuanced understanding of atomic environments relative to their invariant counterparts.

Generalizability Across Models and Materials

The research also emphasizes the versatility and generalizability of symmetry-equivariant models across various materials classes and model architectures. When evaluated on different types of perovskite compositions and using different symmetry-equivariant designs, the models consistently outperformed their invariant counterparts. Additionally, symmetry-equivariant models demonstrated potential as universal interatomic potentials, which is crucial for larger-scale simulations and molecular dynamics.

Implications and Future Directions

The findings of this paper have profound implications for computational materials discovery. By enabling rigorous consideration of atomic orderings, symmetry-aware GCNNs can provide more accurate and reliable predictions of material properties, therefore significantly lowering the experimental validation costs. This capability is particularly valuable in domains where atomic ordering critically influences material behavior, such as in the design of ferromagnetic and piezoelectric materials.

Future research could extend these methodologies to other crystalline systems and further optimize the architectures of symmetry-aware GCNNs. One promising direction is to integrate these models with classical sampling methods and active learning strategies to explore high-dimensional atomic configurations more efficiently. Moreover, the perspectives offered by this work can be adapted to other areas in computational chemistry, like the prediction of molecular reactivity and stereoisomerism in complex molecular systems.

In summary, this paper underscores the vital role symmetry-aware GCNNs play in the accurate and efficient prediction of ordering-dependent properties in crystalline materials. These advancements herald a significant step forward in the computational design and discovery of next-generation materials.