Learning Piezoelectric Tensors through Strain-Conditioned Polarization Clusters

Accurate prediction of tensorial properties remains challenging because the target must satisfy coupled symmetry, rotational, and anisotropic constraints beyond conventional scalar regression. Here, we develop a physics-informed cluster graph neural network (PCGNN) for piezoelectric tensor prediction by explicitly encoding the strain–polarization response pathway. Instead of directly regressing tensor entries from the crystal structure, the model applies controlled strain perturbations and reconstructs the macroscopic tensor through symmetry-consistent aggregation of strain-conditioned local polarization clusters. A capsule transformer is introduced to identify symmetry-equivalent local environments, enabling recovery of symmetry-imposed sparsity patterns without explicit constraints. On the Materials Project test set, PCGNN achieves a mean absolute error of 0.135 C/m 2, outperforming EATGNN and CGCNN by 32.5% and 52.6%, respectively. The model also supports large-scale screening of unlabeled materials and identifies candidates with strong piezoelectric response, providing a physically grounded route for tensor learning and materials discovery.