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.

翻译：许多材料性质依赖于势能面的高阶导数，然而通过标准能量、力和应力误差损失函数训练的机器学习原子间势（MLIPs）可能在曲率预测上存在误差，从而降低振动性质的预测精度。本文提出声子微调（PFT）方法，通过将MLIP的能量Hessian矩阵与基于有限位移声子计算获得的DFT力常数相匹配，直接对材料的二阶力常数进行监督。为扩展至大超胞体系，PFT随机采样Hessian矩阵列向量，并通过单次Hessian-向量乘积计算损失函数。同时采用简单的协同训练策略融合上游数据以缓解灾难性遗忘问题。在MDR声子基准测试中，PFT将Nequix MP模型在声子热力学性质上的平均预测精度提升55%，并在基于Materials Project轨迹训练的模型中达到最优精度。PFT还展现出超越二阶导数的泛化能力，显著改善了依赖势能三阶导数的热导率预测性能。