  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.
