A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Prediction

Abstract: We consider the prediction of general tensor properties of crystalline materials, including dielectric, piezoelectric, and elastic tensors. A key challenge here is how to make the predictions satisfy the unique tensor equivariance to O(3) group and invariance to crystal space groups. To this end, we propose a General Materials Tensor Network (GMTNet), which is carefully designed to satisfy the required symmetries. To evaluate our method, we curate a dataset and establish evaluation metrics that are tailored to the intricacies of crystal tensor predictions. Experimental results show that our GMTNet not only achieves promising performance on crystal tensors of various orders but also generates predictions fully consistent with the intrinsic crystal symmetries. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

• The paper introduces GMTNet, a neural network designed to predict dielectric, piezoelectric, and elastic tensor properties of crystals while respecting O(3) and space group symmetries.
• Empirical evaluation shows GMTNet outperforms existing methods, achieving a 100% success rate in identifying symmetry-dictated zero and dependent tensor elements.
• GMTNet offers a scalable and accurate alternative to computationally expensive DFT, enabling efficient discovery of new materials with desired tensor properties.

Overview of a Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Prediction

This paper introduces a General Materials Tensor Network (GMTNet) intended for predicting dielectric, piezoelectric, and elastic tensor properties of crystalline materials. These properties are pivotal for applications across various technological domains. Existing methodologies, including density functional theory (DFT), although accurate, are resource-intensive and thus not ideal for large-scale predictions. Consequently, the authors propose an alternative approach using ML for efficient predictions while maintaining critical symmetry properties inherent to crystalline structures.

GMTNet addresses two principal challenges: ensuring tensor predictions adhere to O(3) rotational equivariance and crystal space group symmetry. These symmetries govern the tensorial properties of materials and are essential for accurate physical predictions. To tackle these intricacies, GMTNet implements several modules: symmetry-informed crystal graph construction, crystal-level equivariant feature extraction, equivariant tensor property prediction, and symmetry enforcement.

Structural and Methodological Contributions

The methodological framework includes constructing a crystal graph that respects atomic symmetries, followed by extracting invariant node features using advanced neural network layers such as Comformer and Tensor Field Network (TFN). By leveraging tensor products and Wigner D matrices, GMTNet ensures that predicted tensors such as dielectric, piezoelectric, and elastic tensors adhere to their intrinsic symmetries across diverse crystal systems.

The network’s architecture consists of a feature extraction module that respects both O(3) rotational transformations and specific crystal symmetries, as dictated by the crystal’s space group. This module ensures that the ML predictions are physically meaningful and consistent with symmetry properties derived from the input crystal structures.

Empirical Evaluation and Robustness

The authors conducted comprehensive experiments on a curated dataset derived from the JARVIS-DFT database. The dataset consists of dielectric, piezoelectric, and elastic tensors. GMTNet was evaluated against other methods, such as MEGNET and ETGNN, using tailored metrics including success rates for capturing zero-value and mutually dependent tensor elements and Frobenius norm (Fnorm) distances.

The results demonstrate GMTNet’s superiority, achieving a 100% success rate in identifying zero and mutually dependent elements for crystal systems. Additionally, it showed significant improvements in prediction accuracy and quality, as reflected by high Fnorm accuracy and consistency across various crystal symmetries. These experimental results underscore the capability of GMTNet to make accurate, symmetry-consistent predictions.

Implications and Future Directions

GMTNet's design offers substantial contributions to the ML prediction of tensor properties, presenting a scalable alternative to computationally expensive traditional methods like DFT. By ensuring that predictions adhere to fundamental symmetry principles, GMTNet holds promise for discovering novel materials with tailor-designed properties more efficiently.

Future research might expand the curated dataset to enhance model robustness. Additionally, exploring the adaptation of GMTNet to predict tensor properties in amorphous materials, which present more symmetric complexity compared to crystalline structures, could broaden its applicability and utility.

In conclusion, this paper presents GMTNet as a proficient tool for predicting crystal tensor properties, emphasizing the necessity of incorporating intrinsic symmetries into ML models for accurate scientific computational predictions.