Phonon predictions with E(3)-equivariant graph neural networks

We present an equivariant neural network for predicting vibrational and phonon modes of molecules and periodic crystals, respectively. These predictions are made by evaluating the second derivative Hessian matrices of the learned energy model that is trained with the energy and force data. Using this method, we are able to efficiently predict phonon dispersion and the density of states for inorganic crystal materials. For molecules, we also derive the symmetry constraints for IR/Raman active modes by analyzing the phonon mode irreducible representations. Additionally, we demonstrate that using Hessian as a new type of higher-order training data improves energy models beyond models that only use lower-order energy and force data. With this second derivative approach, one can directly relate the energy models to the experimental observations for the vibrational properties. This approach further connects to a broader class of physical observables with a generalized energy model that includes external fields.