PFT: Phonon Fine-tuning for Machine Learned Interatomic Potentials

2026-01-12

AI Summary

This work addresses the limitations of machine learning interatomic potentials in predicting material properties that depend on higher-order derivatives of the potential energy surface—such as lattice dynamics—where errors in the Hessian matrix often degrade performance. The authors propose Phonon Fine-Tuning (PFT), a novel approach that, for the first time, directly uses second-order force constants as supervision signals. By leveraging Hessian-vector products and stochastic column sampling, PFT efficiently aligns with density functional theory phonon calculations, while co-training mitigates catastrophic forgetting. Evaluated on the MDR Phonon benchmark, PFT reduces the average error in phonon thermodynamic properties by 55% for the NequIP-MP model and substantially improves predictions of third-derivative-dependent quantities like thermal conductivity, achieving state-of-the-art accuracy among models trained on Materials Project trajectories.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

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.

Problem

• machine learned interatomic potentials
• phonon properties
• potential energy surface curvature
• vibrational properties
• thermal conductivity

Innovation

• phonon fine-tuning
• machine learned interatomic potentials
• Hessian matching
• second-order force constants
• thermal conductivity prediction