# Multi-variable Hard Physical Constraints for Climate Model Downscaling

arXiv: https://arxiv.org/abs/2308.01868 · HTML: https://mlsanity.com/paper/2308.01868/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 41 references that are in the map.
- First posted on arXiv 2 Aug 2023.

## Builds on (most cited first, 11 of 11)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [DeepSD: Generating High Resolution Climate Change Projections through Single Image Super-Resolution](https://mlsanity.com/paper/1703.03126/) (2017)
- [MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework](https://mlsanity.com/paper/2005.01463/) (2020)
- [Physically Constrained Generative Adversarial Networks for Improving Precipitation Fields from Earth System Models](https://mlsanity.com/paper/2209.07568/) (2022)
- [Fast and accurate learned multiresolution dynamical downscaling for precipitation](https://mlsanity.com/paper/2101.06813/) (2021)
- [A Survey on AI Assurance](https://mlsanity.com/paper/2111.07505/) (2021)
- [Deep-learning based down-scaling of summer monsoon rainfall data over Indian region](https://mlsanity.com/paper/2011.11313/) (2020)
- [Physics-Informed Learning of Aerosol Microphysics](https://mlsanity.com/paper/2207.11786/) (2022)
- [Using Explainability to Inform Statistical Downscaling Based on Deep Learning Beyond Standard Validation Approaches](https://mlsanity.com/paper/2302.01771/) (2023)
- [Strict Enforcement of Conservation Laws and Invertibility in CNN-Based Super Resolution for Scientific Datasets](https://mlsanity.com/paper/2011.05586/) (2020)

## Built on by (most cited first, 6 of 6)

- [Foundation Models for Weather and Climate Data Understanding: A Comprehensive Survey](https://mlsanity.com/paper/2312.03014/) (2023)
- [On Global Applicability and Location Transferability of Generative Deep Learning Models for Precipitation Downscaling](https://mlsanity.com/paper/2512.01400/) (2025)
- [MetaSD: A Unified Framework for Scalable Downscaling of Meteorological Variables in Diverse Situations](https://mlsanity.com/paper/2404.17611/) (2024)
- [Harnessing AI data-driven global weather models for climate attribution: An analysis of the 2017 Oroville Dam extreme atmospheric river](https://mlsanity.com/paper/2409.11605/) (2024)
- [Downscaling climate projections to 1 km with single-image super resolution](https://mlsanity.com/paper/2509.21399/) (2025)
- [A Probabilistic U-Net Approach to Downscaling Climate Simulations](https://mlsanity.com/paper/2511.03197/) (2025)

## Abstract (arXiv)

Global Climate Models (GCMs) are the primary tool to simulate climate evolution and assess the impacts of climate change. However, they often operate at a coarse spatial resolution that limits their accuracy in reproducing local-scale phenomena. Statistical downscaling methods leveraging deep learning offer a solution to this problem by approximating local-scale climate fields from coarse variables, thus enabling regional GCM projections. Typically, climate fields of different variables of interest are downscaled independently, resulting in violations of fundamental physical properties across interconnected variables. This study investigates the scope of this problem and, through an application on temperature, lays the foundation for a framework introducing multi-variable hard constraints that guarantees physical relationships between groups of downscaled climate variables.