# Strict Enforcement of Conservation Laws and Invertibility in CNN-Based Super Resolution for Scientific Datasets

arXiv: https://arxiv.org/abs/2011.05586 · HTML: https://mlsanity.com/paper/2011.05586/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2020.

## Built on by (most cited first, 3 of 3)

- [OpenForest: A data catalogue for machine learning in forest monitoring](https://mlsanity.com/paper/2311.00277/) (2023)
- [Multi-variable Hard Physical Constraints for Climate Model Downscaling](https://mlsanity.com/paper/2308.01868/) (2023)
- [On Global Applicability and Location Transferability of Generative Deep Learning Models for Precipitation Downscaling](https://mlsanity.com/paper/2512.01400/) (2025)

## Abstract (arXiv)

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.