Accurate piezoelectric tensor prediction with equivariant attention tensor graph neural network

The piezoelectric materials enable the mutual conversion between mechanical and electrical energy, which drive a multi-billion dollar industry through their applications as sensors, actuators, and energy harvesters. The third-rank piezoelectric tensor is the core matrices for piezoelectric materials and their devices. However, the high costs of obtaining full piezoelectric tensor data through either experimental or computational methods make a significant challenge. Here, we propose an equivariant attention tensor graph neural network (EATGNN) that can identify crystal symmetry and remain independent of the reference frame, ultimately enabling the accurate prediction of the complete third-rank piezoelectric tensor. Especially, we perform an irreducible decomposition of the piezoelectric tensor into four irreducible representations to efficiently reserve the symmetry under group transformation operations. Our results further demonstrate that this model performs well in both bulk and two-dimensional materials. Finally, combining EATGNN with first-principles calculations, we discovered several potential high-performance piezoelectric materials.