Evaluation of uncertainty estimations for Gaussian process regression based machine learning interatomic potentials

Uncertainty estimations for machine learning interatomic potentials (MLIPs) are crucial for quantifying model error and identifying informative training samples in active learning strategies. In this study, we evaluate uncertainty estimations of Gaussian process regression (GPR)-based MLIPs, including the predictive GPR standard deviation and ensemble-based uncertainties. We do this in terms of calibration and in terms of impact on model performance in an active learning scheme. We consider GPR models with Coulomb and Smooth Overlap of Atomic Positions (SOAP) representations as inputs to predict potential energy surfaces and excitation energies of molecules. Regarding calibration, we find that ensemble-based uncertainty estimations show already poor global calibration (e.g., averaged over the whole test set). In contrast, the GPR standard deviation shows good global calibration, but when grouping predictions by their uncertainty, we observe a systematical bias for predictions with high uncertainty. Although an increasing uncertainty correlates with an increasing bias, the bias is not captured quantitatively by the uncertainty. Therefore, the GPR standard deviation can be useful to identify predictions with a high bias and error but, without further knowledge, should not be interpreted as a quantitative measure for a potential error range. Selecting the samples with the highest GPR standard deviation from a fixed configuration space leads to a model that overemphasizes the borders of the configuration space represented in the fixed dataset. This may result in worse performance in more densely sampled areas but better generalization for extrapolation tasks.