Efficient ensemble uncertainty estimation in Gaussian Processes Regression

TL;DR

This paper introduces a fast, ensemble-based uncertainty estimation method for sparse Gaussian Process Regression in machine learning interatomic potentials, improving calibration and aiding Bayesian structure optimization.

Contribution

It proposes a stochastic ensemble uncertainty measure for sparse GPR MLIPs that is faster and as well calibrated as traditional methods, enhancing atomistic simulation reliability.

Findings

Ensemble uncertainty is as well calibrated as the posterior variance.

The proposed method is faster to evaluate than the closed-form expression.

The uncertainty measure improves Bayesian optimization of Au20 cluster structures.

Abstract

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.