# Physics-Guided Learning of Meteorological Dynamics for Weather Downscaling and Forecasting

arXiv: https://arxiv.org/abs/2505.14555 · HTML: https://mlsanity.com/paper/2505.14555/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 80 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 30 of 32)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers](https://mlsanity.com/paper/2111.13587/) (2021)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [PredRNN: A Recurrent Neural Network for Spatiotemporal Predictive Learning](https://mlsanity.com/paper/2103.09504/) (2021)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Improving data-driven global weather prediction using deep convolutional neural networks on a cubed sphere](https://mlsanity.com/paper/2003.11927/) (2020)
- [Spatio-Temporal Meta-Graph Learning for Traffic Forecasting](https://mlsanity.com/paper/2211.14701/) (2022)
- [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)
- [Deep Dynamical Modeling and Control of Unsteady Fluid Flows](https://mlsanity.com/paper/1805.07472/) (2018)
- [Learning Compositional Koopman Operators for Model-Based Control](https://mlsanity.com/paper/1910.08264/) (2019)
- [DiffCast: A Unified Framework via Residual Diffusion for Precipitation Nowcasting](https://mlsanity.com/paper/2312.06734/) (2023)
- [ClimateLearn: Benchmarking Machine Learning for Weather and Climate Modeling](https://mlsanity.com/paper/2307.01909/) (2023)
- [Joint Air Quality and Weather Prediction Based on Multi-Adversarial Spatiotemporal Networks](https://mlsanity.com/paper/2012.15037/) (2020)
- [Conditional Local Convolution for Spatio-temporal Meteorological Forecasting](https://mlsanity.com/paper/2101.01000/) (2021)
- [Spatiotemporal CNN for Video Object Segmentation](https://mlsanity.com/paper/1904.02363/) (2019)
- [Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning](https://mlsanity.com/paper/2201.12354/) (2022)
- [Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey](https://mlsanity.com/paper/2503.13502/) (2025)
- [STConvS2S: Spatiotemporal Convolutional Sequence to Sequence Network for Weather Forecasting](https://mlsanity.com/paper/1912.00134/) (2019)
- [Short and Long-term Pattern Discovery Over Large-Scale Geo-Spatiotemporal Data](https://mlsanity.com/paper/1902.06792/) (2019)

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

- [Sparse Local Implicit Image Function for sub-km Weather Downscaling](https://mlsanity.com/paper/2510.20228/) (2025)
- [StationPDE: Station-Oriented Surface PDE Learning for Multi-Station Multivariate Weather Forecasting](https://mlsanity.com/paper/2609.22123/) (2026)
- [Physics-Informed Super-Resolution of Atmospheric Data](https://mlsanity.com/paper/2607.18877/) (2026)

## Abstract (arXiv)

Weather forecasting is essential but remains computationally intensive and physically incomplete in traditional numerical weather prediction (NWP) methods. Deep learning (DL) models offer efficiency and accuracy but often ignore physical laws, limiting interpretability and generalization. We propose PhyDL-NWP, a physics-guided deep learning framework that integrates physical equations with latent force parameterization into data-driven models. It predicts weather variables from arbitrary spatiotemporal coordinates, computes physical terms via automatic differentiation, and uses a physics-informed loss to align predictions with governing dynamics. PhyDL-NWP enables resolution-free downscaling by modeling weather as a continuous function and fine-tunes pre-trained models with minimal overhead, achieving up to 170x faster inference with only 55K parameters. Experiments show that PhyDL-NWP improves both forecasting performance and physical consistency.