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/m², 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.