# PFT: Phonon Fine-tuning for Machine Learned Interatomic Potentials

arXiv: https://arxiv.org/abs/2601.07742 · HTML: https://mlsanity.com/paper/2601.07742/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 45 references that are in the map.
- First posted on arXiv 12 Jan 2026.

## Builds on (most cited first, 11 of 11)

- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [UMA: A Family of Universal Models for Atoms](https://mlsanity.com/paper/2506.23971/) (2025)
- [Learning Smooth and Expressive Interatomic Potentials for Physical Property Prediction](https://mlsanity.com/paper/2502.12147/) (2025)
- [Orb: A Fast, Scalable Neural Network Potential](https://mlsanity.com/paper/2410.22570/) (2024)
- [Open Materials 2024 (OMat24) Inorganic Materials Dataset and Models](https://mlsanity.com/paper/2410.12771/) (2024)
- [An Efficient Sparse Kernel Generator for O(3)-Equivariant Deep Networks](https://mlsanity.com/paper/2501.13986/) (2025)
- [High-performance training and inference for deep equivariant interatomic potentials](https://mlsanity.com/paper/2504.16068/) (2025)
- [Towards Fast, Specialized Machine Learning Force Fields: Distilling Foundation Models via Energy Hessians](https://mlsanity.com/paper/2501.09009/) (2025)
- [HIP: Hessian Interatomic Potentials without derivatives](https://mlsanity.com/paper/2509.21624/) (2025)
- [Training a Foundation Model for Materials on a Budget](https://mlsanity.com/paper/2508.16067/) (2025)
- [A Materials Foundation Model via Hybrid Invariant-Equivariant Architectures](https://mlsanity.com/paper/2503.05771/) (2025)

## Built on by (most cited first, 6 of 6)

- [EquiformerV3: Scaling Efficient, Expressive, and General SE(3)-Equivariant Graph Attention Transformers](https://mlsanity.com/paper/2604.09130/) (2026)
- [Projected Hessian Learning: Fast Curvature Supervision for Accurate Machine-Learning Interatomic Potentials](https://mlsanity.com/paper/2603.04523/) (2026)
- [Hessian-informed machine learning interatomic potential towards bridging theory and experiments](https://mlsanity.com/paper/2603.25373/) (2026)
- [Truncated automatic sparse differentiation for machine learning interatomic potentials](https://mlsanity.com/paper/2609.20510/) (2026)
- [A strategic roadmap for an atomistic machine-learning ecosystem](https://mlsanity.com/paper/2609.39090/) (2026)
- [LunaTP: Enabling Efficient and Scalable Tensor Product for Equivariant MLIPs](https://mlsanity.com/paper/2610.18393/) (2026)

## Abstract (arXiv)

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.