Understanding the structure–property relationship is crucial for designing materials with desired properties. The past few years have witnessed remarkable progress in machine-learning methods for this connection. However, substantial challenges remain, including the generalizability of models and prediction of properties with materials-dependent output dimensions. Here the virtual node graph neural network is presented to address the challenges.

By developing three virtual node approaches, Γ-phonon spectra and full phonon dispersion prediction from atomic coordinates were achieved. It is shown that, compared with the machine-learning interatomic potentials, this approach achieves orders-of-magnitude-higher efficiency with comparable to better accuracy. This allows the generation of databases for Γ-phonon containing over 146,000 materials and phonon band structures of zeolites.

This work provides an avenue for rapid and high-quality prediction of phonon band structures enabling materials design with desired phonon properties. The virtual node method also provides a generic method for machine-learning design with a high level of flexibility.