Assessing the quality of aleatoric uncertainty estimates from uncertainty quantification (UQ) deep learning methods is important in scientific contexts, where uncertainty is physically meaningful and important to characterize and interpret exactly. We systematically compare aleatoric uncertainty measured by two UQ techniques, Deep Ensembles (DE) and Deep Evidential Regression (DER). Our method focuses on both zero-dimensional (0D) and two-dimensional (2D) data, to explore how the UQ methods function for different data dimensionalities. We investigate uncertainty injected on the input and output variables and include a method to propagate uncertainty in the case of input uncertainty so that we can compare the predicted aleatoric uncertainty to the known values. We experiment with three levels of noise. The aleatoric uncertainty predicted across all models and experiments scales with the injected noise level. However, the predicted uncertainty is miscalibrated to $\rm{std}(\sigma_{\rm al})$ with the true uncertainty for half of the DE experiments and almost all of the DER experiments. The predicted uncertainty is the least accurate for both UQ methods for the 2D input uncertainty experiment and the high-noise level. While these results do not apply to more complex data, they highlight that further research on post-facto calibration for these methods would be beneficial, particularly for high-noise and high-dimensional settings.

本研究针对不确定性量化（UQ）深度学习方法中随机不确定性评估的质量进行了系统比较，填补了当前科学研究中该领域的空白。通过比较深度集成（DE）和深度证据回归（DER）两种技术，我们发现随机不确定性与注入噪声水平相符，但在高噪声及高维度设置中，预测的不确定性存在显著误校准。这一发现表明针对这些方法的后期校准研究极具价值，尤其是在处理高噪声和高维数据时。 

DeepUQ：评估两种深度学习方法中的随机不确定性