Accurate Prediction of Tensorial Spectra Using Equivariant Graph Neural Network

Abstract

Optical spectroscopies provide a powerful tool for harnessing light-matter interactions for unraveling complex electronic features such as the flat bands and nontrivial topologies of materials. These insights are crucial for the development and optimization of optoelectronic devices, including solar cells, light-emitting diodes, and photodetectors, where device performance is closely connected with the nature of the underlying electronic spectrum. Realistic modeling of tensor optical responses in materials, which are computationally quite demanding, however, remains challenging. Here we introduce the Tensorial Spectra Equivariant Neural Network (TSENN), which is a equivariant graph neural network architecture that maps crystal structures directly to their full photon-frequency-dependent optical tensors. By encoding the isotropic sequential scalar components along with the anisotropic sequential tensor components into l = 0 and l = 2 spherical tensor components, TSENN ensures symmetry-aware predictions that are consistent with the constraints of crystalline symmetries of materials. Trained on a dataset of frequency-dependent permittivity tensors of 1,432 bulk semiconductors computed using first-principles methods, our model achieves a mean absolute error (MAE) of 21.181 millifarads per meter (mF/m), demonstrating its potential for efficient modeling of other related properties such as the optical conductivities. Our framework opens new avenues for rational data-driven design of anisotropic optical responses for accelerating materials discovery for advancing optoelectronic applications.