  Inexpensive machine learning potentials are increasingly being used to speed
up structural optimization and molecular dynamics simulations of materials by
iteratively predicting and applying interatomic forces. In these settings, it
is crucial to detect when predictions are unreliable to avoid wrong or
misleading results. Here, we present a complete framework for training and
recalibrating graph neural network ensemble models to produce accurate
predictions of energy and forces with calibrated uncertainty estimates. The
proposed method considers both epistemic and aleatoric uncertainty and the
total uncertainties are recalibrated post hoc using a nonlinear scaling
function to achieve good calibration on previously unseen data, without loss of
predictive accuracy. The method is demonstrated and evaluated on two
challenging, publicly available datasets, ANI-1x (Smith et al.) and
Transition1x (Schreiner et al.), both containing diverse conformations far from
equilibrium. A detailed analysis of the predictive performance and uncertainty
calibration is provided. In all experiments, the proposed method achieved low
prediction error and good uncertainty calibration, with predicted uncertainty
correlating with expected error, on energy and forces. To the best of our
knowledge, the method presented in this paper is the first to consider a
complete framework for obtaining calibrated epistemic and aleatoric uncertainty
predictions on both energy and forces in ML potentials.
