  Ensemble models can be used to estimate prediction uncertainties in machine
learning models. However, an ensemble of N models is approximately N times more
computationally demanding compared to a single model when it is used for
inference. In this work, we explore fitting a single model to predicted
ensemble error bar data, which allows us to estimate uncertainties without the
need for a full ensemble. Our approach is based on three models: Model A for
predictive accuracy, Model $A_{E}$ for traditional ensemble-based error bar
prediction, and Model B, fit to data from Model $A_{E}$, to be used for
predicting the values of $A_{E}$ but with only one model evaluation. Model B
leverages synthetic data augmentation to estimate error bars efficiently. This
approach offers a highly flexible method of uncertainty quantification that can
approximate that of ensemble methods but only requires a single extra model
evaluation over Model A during inference. We assess this approach on a set of
problems in materials science.
