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The phonon density-of-states (DOS) summarizes the lattice vibrational modes supported by a structure, and gives access to rich information about the material's stability, thermodynamic constants, and thermal transport coefficients. Here, we present an atomistic line graph neural network (ALIGNN) model for the prediction of the phonon density of states and the derived thermal and thermodynamic properties. The model is trained on a database of over 14,000 phonon spectra included in the JARVIS-DFT (Joint Automated Repository for Various Integrated Simulations: Density Functional Theory) database. The model predictions are shown to capture the spectral features of the phonon density-of-states, effectively categorize dynamical stability, and lead to accurate predictions of DOS-derived thermal and thermodynamic properties, including heat capacity $C_{\mathrm{V}}$, vibrational entropy $S_{\mathrm{vib}}$, and the isotopic phonon scattering rate $τ^{-1}_{\mathrm{i}}$. The DOS-mediated ALIGNN model provides superior predictions when compared to a direct deep-learning prediction of these material properties as well as predictions based on analytic simplifications of the phonon DOS, including the Debye or Born-von Karman models. Finally, the ALIGNN model is used to predict the phonon spectra and properties for about 40,000 additional materials listed in the JARVIS-DFT database, which are validated as far as possible against other open-sourced high-throughput DFT phonon databases.