Title: Accelerating Ensemble Error Bar Prediction with Single Models Fits

Abstract: 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.