Fig. 4: Validation of uncertainty-aware model distillation for W.

a The uncertainty U shows a strong correlation with force errors (Eq. (5)) across 1139 configurations of W. Dimer and short-range configurations (in red and green, respectively) exhibit both high uncertainty and high errors. b Mixed datasets are constructed using different uncertainty thresholds U_c: configurations with U < U_c use uMLIP predictions, while those with U≥U_c are labeled using DFT. The x-axis indicates the fraction of DFT data. Blue solid and green dashed lines represent the RMSE of the dataset and ACE training error, respectively. Red dash-dot and purple dotted lines denote ACE performance on training and test sets, respectively. c Force and energy RMSE of ACE potentials trained by mixed datasets on the test set reported in³⁰ (Fig. S5). For each dataset, 20 independent models are trained, and the standard deviations of energy and force RMSEs are shown as error bars. d Relative errors (%) for basic physical properties predicted by the ACE model trained on hybrid datasets (ACE_UAMD), compared with the ACE model trained on full DFT data (ACE_DFT). Error bars indicate the standard deviation across five independently trained models. e Comparison of phonon dispersion curves predicted by ACE_UAMD, ACE_DFT, and DFT. f Stress-strain curves from uniaxial tension simulations of Σ3 tilt (above) and twist (below) grain boundaries. ACE_DFT and ACE_UAMD model with U_c = 1.0 eV/Å produce nearly identical results.