Although many deep-learning-based super-resolution approaches have been proposed in recent years, because no ground truth is available in the inference stage, few can quantify the errors and uncertainties of the super-resolved results. For scientific visualization applications, however, conveying uncertainties of the results to scientists is crucial to avoid generating misleading or incorrect information. In this paper, we propose PSRFlow, a novel normalizing flow-based generative model for scientific data super-resolution that incorporates uncertainty quantification into the super-resolution process. PSRFlow learns the conditional distribution of the high-resolution data based on the low-resolution counterpart. By sampling from a Gaussian latent space that captures the missing information in the high-resolution data, one can generate different plausible super-resolution outputs. The efficient sampling in the Gaussian latent space allows our model to perform uncertainty quantification for the super-resolved results. During model training, we augment the training data with samples across various scales to make the model adaptable to data of different scales, achieving flexible super-resolution for a given input. Our results demonstrate superior performance and robust uncertainty quantification compared with existing methods such as interpolation and GAN-based super-resolution networks.

翻译：尽管近年来提出了许多基于深度学习的超分辨率方法，但由于推理阶段缺乏真实数据，这些方法很少能量化超分辨率结果中的误差和不确定性。然而，在科学可视化应用中，将结果的不确定性传达给科学家对于避免生成误导性或错误信息至关重要。本文提出PSRFlow，一种用于科学数据超分辨率的新型归一化流生成模型，该模型将不确定性量化融入超分辨率过程。PSRFlow基于低分辨率数据学习高分辨率数据的条件分布。通过从捕获高分辨率数据缺失信息的高斯潜空间中进行采样，可生成多种合理的超分辨率输出。高斯潜空间中的高效采样使模型能够对超分辨率结果进行不确定性量化。在模型训练过程中，我们使用跨不同尺度的样本增强训练数据，使模型能够适应不同尺度的数据，从而实现对给定输入的灵活超分辨率。与插值方法和基于GAN的超分辨率网络等现有方法相比，我们的结果展示了优越的性能和稳健的不确定性量化能力。