Efficient ensemble uncertainty estimation in Gaussian Processes Regression

Reliable uncertainty measures are required when using data based machine learning interatomic potentials (MLIPs) for atomistic simulations. In this work, we propose for sparse Gaussian Process Regression type MLIP a stochastic uncertainty measure akin to the query-by-committee approach often used in conjunction with neural network based MLIPs. The uncertainty measure is coined \textit{"label noise"} ensemble uncertainty as it emerges from adding noise to the energy labels in the training data. We find that this method of calculating an ensemble uncertainty is as well calibrated as the one obtained from the closed-form expression for the posterior variance when the sparse GPR is treated as a projected process. Comparing the two methods, our proposed ensemble uncertainty is, however, faster to evaluate than the closed-form expression. Finally, we demonstrate that the proposed uncertainty measure acts better to support a Bayesian search for optimal structure of Au$_{20}$ clusters.