PFT: Phonon Fine-tuning for Machine Learned Interatomic Potentials

Many materials properties depend on higher-order derivatives of the potential energy surface, yet machine learned interatomic potentials (MLIPs) trained with a standard loss on energy, force, and stress errors can exhibit error in curvature, degrading the prediction of vibrational properties. We introduce phonon fine-tuning (PFT), which directly supervises second-order force constants of materials by matching MLIP energy Hessians to DFT-computed force constants from finite displacement phonon calculations. To scale to large supercells, PFT stochastically samples Hessian columns and computes the loss with a single Hessian-vector product. We also use a simple co-training scheme to incorporate upstream data to mitigate catastrophic forgetting. On the MDR Phonon benchmark, PFT improves Nequix MP by 55% on average across phonon thermodynamic properties and achieves state-of-the-art accuracy among models trained on Materials Project trajectories. PFT also generalizes to improve properties beyond second-derivatives, improving thermal conductivity predictions that rely on third-order derivatives of the potential energy.

AI is increasingly being used to predict the behavior of materials, which can replace very computationally expensive physics calculations. Models are typically trained to predict the energy of a material, and the forces on its atoms; however models are not directly trained on the vibration of the atoms, which govern important material properties such as how well it stores or conducts heat. The vibrations can be modeled by considering "springs" that connect the atoms. The stiffness of these springs controls how they vibrate. We show that models can be trained directly on the stiffness, using data from physics calculations. To make this practical for large systems, we use a mathematical trick to avoid computing all of the stiffness values at once. This extra training step roughly halves the errors in predicted vibrational properties and significantly improves thermal conductivity predictions at a small fraction of the cost of training the original model.