Machine learning has demonstrated great power in materials design, discovery, and property prediction. However, despite the success of machine learning in predicting discrete properties, challenges remain for continuous property prediction. The challenge is aggravated in crystalline solids due to crystallographic symmetry considerations and data scarcity. Here we demonstrate the direct prediction of phonon density of states using only atomic species and positions as input. We apply Euclidean neural networks, which by construction are equivariant to 3D rotations, translations, and inversion and thereby capture full crystal symmetry, and achieve high-quality prediction using a small training set of $sim 10^{3}$ examples with over 64 atom types. Our predictive model reproduces key features of experimental data and even generalizes to materials with unseen elements,and is naturally suited to efficiently predict alloy systems without additional computational cost. We demonstrate the potential of our network by predicting a broad number of high phononic specific heat capacity materials. Our work indicates an efficient approach to explore materials phonon structure, and can further enable rapid screening for high-performance thermal storage materials and phonon-mediated superconductors.
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