# Physics-Informed Super-Resolution of Atmospheric Data

arXiv: https://arxiv.org/abs/2607.18877 · HTML: https://mlsanity.com/paper/2607.18877/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 38 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Builds on (most cited first, 22 of 22)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Accelerating the Super-Resolution Convolutional Neural Network](https://mlsanity.com/paper/1608.00367/) (2016)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [DeepSD: Generating High Resolution Climate Change Projections through Single Image Super-Resolution](https://mlsanity.com/paper/1703.03126/) (2017)
- [ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs](https://mlsanity.com/paper/2404.10024/) (2024)
- [ClimateLearn: Benchmarking Machine Learning for Weather and Climate Modeling](https://mlsanity.com/paper/2307.01909/) (2023)
- [Hard-Constrained Deep Learning for Climate Downscaling](https://mlsanity.com/paper/2208.05424/) (2022)
- [Fourier Neural Operators for Arbitrary Resolution Climate Data Downscaling](https://mlsanity.com/paper/2305.14452/) (2023)
- [Air Quality Prediction with Physics-Guided Dual Neural ODEs in Open Systems](https://mlsanity.com/paper/2410.19892/) (2024)
- [Generative Diffusion-based Downscaling for Climate](https://mlsanity.com/paper/2404.17752/) (2024)
- [Generalizing Weather Forecast to Fine-grained Temporal Scales via Physics-AI Hybrid Modeling](https://mlsanity.com/paper/2405.13796/) (2024)
- [Precipitation Downscaling with Spatiotemporal Video Diffusion](https://mlsanity.com/paper/2312.06071/) (2023)
- [Earth System Foundation Model (ESFM): A unified framework for heterogeneous data integration and forecasting](https://mlsanity.com/paper/2605.00850/) (2026)
- [ExEBench: Benchmarking Foundation Models on Extreme Earth Events](https://mlsanity.com/paper/2505.08529/) (2025)
- [DiffScale: Continuous Downscaling and Bias Correction of Subseasonal Wind Speed Forecasts using Diffusion Models](https://mlsanity.com/paper/2503.23893/) (2025)
- [Physics-Guided Learning of Meteorological Dynamics for Weather Downscaling and Forecasting](https://mlsanity.com/paper/2505.14555/) (2025)
- [Assessing the Geographic Generalization and Physical Consistency of Generative Models for Climate Downscaling](https://mlsanity.com/paper/2510.13722/) (2025)

## Abstract (arXiv)

In the context of global warming, extreme events have become more frequent and intense, making their trustworthy detection and forecasting more important than ever. Yet, atmospheric observations lack sufficient spatial resolution, motivating atmospheric data downscaling as a way to reconstruct high-resolution data from coarse observations. This task is now being formulated as a super-resolution (SR) problem with machine learning methods featuring high efficiency. Nevertheless, it remains unclear whether the super-resolved atmospheric data still satisfies fundamental physics governing the Earth system, raising concerns about their trustworthiness in climate-related applications. In this work, we address this challenge by constraining SR models to respect hydrostatic primitive equations that represent multivariate atmospheric physics. First, we propose a Physics-Informed Super-Resolution (PISR) method involving multi-scale physics-informed objectives based on primitive equations. PISR favors the SR outputs to respect these equations and therefore naturally encodes inter-variable relationships. In addition, we propose a metric called Normalized Physical Consistency (NPC) derived from said primitive equations to measure the physical consistency of super-resolved data. Experiments on ERA5, CERRA, and COSMO demonstrate that PISR enhances the reconstruction fidelity by improving physical consistency, SR accuracy, and downstream detection of extreme events, as demonstrated by case studies in heatwaves and extreme winds.