  Lattice vibration frequencies are related to many important materials
properties such as thermal and electrical conductivity as well as
superconductivity. However, computational calculation of vibration frequencies
using density functional theory (DFT) methods is too computationally demanding
for a large number of samples in materials screening. Here we propose a deep
graph neural network-based algorithm for predicting crystal vibration
frequencies from crystal structures with high accuracy. Our algorithm addresses
the variable dimension of vibration frequency spectrum using the zero padding
scheme. Benchmark studies on two data sets with 15,000 and 35,552 samples show
that the aggregated $R^2$ scores of the prediction reaches 0.554 and 0.724
respectively. Our work demonstrates the capability of deep graph neural
networks to learn to predict phonon spectrum properties of crystal structures
in addition to phonon density of states (DOS) and electronic DOS in which the
output dimension is constant.
