  Recently, deep Convolutional Neural Networks (CNNs) have revolutionized image
super-resolution (SR), dramatically outperforming past methods for enhancing
image resolution. They could be a boon for the many scientific fields that
involve image or gridded datasets: satellite remote sensing, radar meteorology,
medical imaging, numerical modeling etc. Unfortunately, while SR-CNNs produce
visually compelling outputs, they may break physical conservation laws when
applied to scientific datasets. Here, a method for ``Downsampling Enforcement"
in SR-CNNs is proposed. A differentiable operator is derived that, when applied
as the final transfer function of a CNN, ensures the high resolution outputs
exactly reproduce the low resolution inputs under 2D-average downsampling while
improving performance of the SR schemes. The method is demonstrated across
seven modern CNN-based SR schemes on several benchmark image datasets, and
applications to weather radar, satellite imager, and climate model data are
also shown. The approach improves training time and performance while ensuring
physical consistency between the super-resolved and low resolution data.
