Model expressiveness and data sampling effects on phonon uncertainty quantification in machine-learning interatomic potentials

Several recent state-of-the-art machine-learning interatomic potential (MLIP) models have achieved remarkable accuracy in predicting potential energies and interatomic forces in a wide variety of materials. Regarding phonons, however, there is yet no standard way to estimate their accuracies or uncertainties. Wen and Tadmor [1] used ensemble methods to quantify the phonon frequency uncertainty of an MLIP model; however, it is unknown how the quality of uncertainty estimates depend on model expressiveness or dataset sampling method on the uncertainties.

We performed a benchmark study of phonon uncertainty quantification (UQ) using ensemble methods for the phonon of silicon in diamond structure. To systematically examine the effect of model expressiveness on phonon UQ, we constructed five expressiveness classes of ensemble samplings, each consisting of around two dozen MLIP models. These classes of expressiveness vary in the number of trainable parameters while the models within the same class share the same. Interestingly, phonon UQ using ensemble methods significantly underestimates uncertainties for incomplete MLIP models with an insufficient number of trainable parameters. To assess the dependence of the data sampling on phonon UQ, we repeated the identical iteration of the benchmarks process to three different training datasets with different coverages of the potential energy surface: 1) molecular dynamics simulation at 300 K with the smallest energy range; 2) randomized atomic-structure generator (RAG) method [2] with small structural deviations (<13% of nearest-neighbor distance); 3) RAG method with large deviations (<38%). From the ensemble approach, we found that a narrower coverage of the potential energy surface results in a more significant underestimation of phonon uncertainties. Our research implies that phonon UQ based on ensemble methods can only be reliable within sufficient model expressiveness and broad potential-energy-surfaces sampling for a training dataset construction.

[1] npj comput. mater. 6, 124 (2020).

[2] J Phys. Chem. B 124, 8704 (2020).