Parameter-Efficient Fine-Tuning of Machine-Learning Interatomic Potentials for Phonon and Thermal Properties

Abstract

Machine-learning interatomic potentials are widely used as computationally efficient surrogates for density functional theory in atomistic simulations, enabling large-scale, long-time modeling of materials systems. We investigate how different fine-tuning strategies influence the prediction of harmonic phonon band structures, thermal properties, and the potential energy surface along imaginary phonon modes. We achieve substantial accuracy improvements with minimal additional data, with as few as 10 additional training structures already yielding significant gains. In addition to existing approaches, we introduce Equitrain, a finetuning framework that implements LoRA-based adaptation. Across 53 materials systems, we show that fine-tuned models consistently outperform both the underlying pretrained model and models trained from scratch. Equitrain achieves the best overall performance, and our results demonstrate that fine-tuning enables accurate phonon predictions.

Figures (10)

• Figure 1: Overview of the concepts and fine-tuning strategies considered in this work. Rattled structures were generated for each material and used to obtain relaxation trajectories with the foundation MP-0b3 model, from which the DFT fine-tuning data set was constructed. With this, different fine-tuning strategies were tested and evaluated in terms of phonons, thermal and elastic properties and phase transition behavior. Blue boxes indicate the training data, red boxes highlight the model components updated during fine-tuning, and gray boxes represent components that remain frozen. Transfer learning (left) updates both the pre-trained backbone and task-specific head using only the fine-tuning objective. Multihead (center) jointly optimizes a shared backbone using both pretraining and fine-tuning losses, while maintaining separate task heads. Equitrain (right) parametrizes the backbone and output head weights as $\omega = \omega_0 + \Delta\omega$. A weight decay term is applied exclusively to $\Delta\omega$, regularizing deviations from the pre-trained initialization.
• Figure 2: (a) Distribution of crystal systems and the number of atoms per primitive unit cell in the dataset, which contains a total of 53 materials. (b) Median MAE forces errors across all 53 material models within the IQR, as shown in the shaded area in the background. Note that the y-axis is logarithmic, and lines are drawn between data points for improved readability. The performance of the foundation model, MP-0b3, on the validation data is represented by a dashed horizontal line for comparison.
• Figure 3: Deviation of thermal and elastic properties from the DFT reference results. For better readability, outliers are not shown but are included in the SI \ref{['SI:phys_prop_with_out']}.
• Figure 4: (a) Section of the phonon band structure of K$_3$Sb calculated with the ML models and compared to DFT (black). (b) Comparison of the anharmonic double-well potential along the $K$ mode. (c) Phase transition pathway of the models showing imaginary modes.
• Figure 5: (a) A section of the phonon band structure calculation of Cmcm SnSe with the different ML models compared to the DFT benchmark (black). (b) Comparison of the anharmonic double-well PES of the lowest $Y$-mode. (c) Phase transition pathways along the $\Gamma$ and $Y$ imaginary modes.