Accurate Prediction of Tensorial Spectra Using Equivariant Graph Neural Network

Optical spectroscopies offer a powerful means to probe and manipulate light–matter interactions in solids, providing direct access to their electronic structure, excitations, and anisotropic optical responses. Here we introduce the Tensorial Spectra Equivariant Neural Network (TSENN)—an E(3)-equivariant graph neural network that directly maps crystal structures to their full frequency-dependent dielectric tensors. TSENN rigorously enforces crystalline-symmetry constraints while capturing direction-dependent phenomena such as birefringence and polarization anisotropy. Trained on a first-principles dataset of 1,432 non-magnetic semiconductors computed using the OpenMX package, TSENN achieves a mean absolute error (MAE) of 0.127 for the imaginary part of the frequency-dependent dielectric tensor. The real part is subsequently reconstructed via the Kramers–Kronig relations, yielding a physically complete description of the optical response. Beyond dielectric tensors, this framework can be readily extended to predict related tensorial properties such as shift current and higher order nonlinear optical responses, providing a scalable, data-driven approach for exploring light–matter interactions in crystalline materials.