  Data-driven methods based on machine learning have the potential to
accelerate computational analysis of atomic structures. In this context,
reliable uncertainty estimates are important for assessing confidence in
predictions and enabling decision making. However, machine learning models can
produce badly calibrated uncertainty estimates and it is therefore crucial to
detect and handle uncertainty carefully. In this work we extend a message
passing neural network designed specifically for predicting properties of
molecules and materials with a calibrated probabilistic predictive
distribution. The method presented in this paper differs from previous work by
considering both aleatoric and epistemic uncertainty in a unified framework,
and by recalibrating the predictive distribution on unseen data. Through
computer experiments, we show that our approach results in accurate models for
predicting molecular formation energies with well calibrated uncertainty in and
out of the training data distribution on two public molecular benchmark
datasets, QM9 and PC9. The proposed method provides a general framework for
training and evaluating neural network ensemble models that are able to produce
accurate predictions of properties of molecules with well calibrated
uncertainty estimates.
