Topology-aware E(3)-equivariant learning for physically consistent piezoelectric tensor prediction

Abstract

Accurate prediction of piezoelectric tensors in crystals remains challenging because valid responses must satisfy both continuous geometric symmetries and discrete crystallographic constraints under periodic boundary conditions. Existing learning-based approaches typically emphasize equivariance or periodic geometry, but often do not explicitly incorporate crystal topology with E(3)-equivariant message passing. Here we present TopoTENet, a topology-aware E(3)-equivariant neural network that enriches geometric learning with discrete crystal topology through SLICES (string-based crystal representation using labeled quotient graphs) and optimizes message passing via topology-conditioned attention mechanisms. A final deterministic projection step guarantees exact point-group compliance by removing residual symmetry-forbidden components. Across 369 test crystals spanning 79 space groups, TopoTENet achieves a mean absolute error (MAE) of 0.132 C/m 2 and a root mean squared error (RMSE) of 0.302 C/m 2 . Ablation and consistency analyses show that discrete topology provides complementary information to geometric equivariance, particularly for periodic tensor prediction. These results establish a route to physically consistent surrogate models for high-throughput screening of piezoelectric materials.