Symmetry-Guaranteed Prediction of High-Order Tensor Properties for Crystalline Materials via Irreducible Decomposition

Predicting high-order tensor properties for crystalline materials is crucial for various scientific and engineering applications. Crystal symmetry is one of the primary factors influencing high-order tensor properties, such as elasticity and piezoelectricity, making strict adherence to symmetry constraints essential. However, exactly guaranteeing symmetry compliance remains challenging. Recent approaches rely on enforcing symmetry but often fail to strictly preserve symmetry. In this work, we propose a novel method that guarantees exact symmetry compliance by predicting symmetry-constrained irreducible components of high-order tensors. Specifically, we first develop a computational procedure to identify the basis tensors corresponding to symmetry-constrained irreducible components under various symmetry conditions. This symmetry-constrained basis guarantees that the assembled full tensor strictly adheres to the required symmetry constraints. To predict the numerical values for these irreducible components, we then propose a spherical-harmonic convolutional neural network designed to effectively capture essential high-order tensor information. Extensive experiments validate that our method achieves exact symmetry compliance without compromising prediction accuracy, thereby outperforming state-of-the-art approaches.