# PING: physics informed graph neural network for advection-diffusion processes with applications to solar power forecasting

arXiv: https://arxiv.org/abs/2610.18280 · HTML: https://mlsanity.com/paper/2610.18280/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 16 of 16)

- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems](https://mlsanity.com/paper/2107.12146/) (2021)
- [MultiScale MeshGraphNets](https://mlsanity.com/paper/2210.00612/) (2022)
- [Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge](https://mlsanity.com/paper/1711.07970/) (2017)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Deep Learning for Day Forecasts from Sparse Observations](https://mlsanity.com/paper/2306.06079/) (2023)
- [Physics-Guided Deep Learning for Dynamical Systems: A Survey](https://mlsanity.com/paper/2107.01272/) (2021)
- [Spatio-temporal graph neural networks for multi-site PV power forecasting](https://mlsanity.com/paper/2107.13875/) (2021)
- [Multi-Graph Convolutional-Recurrent Neural Network (MGC-RNN) for Short-Term Forecasting of Transit Passenger Flow](https://mlsanity.com/paper/2107.13226/) (2021)

## Abstract (arXiv)

Advection-diffusion plays an essential role in transport phenomena such as atmospheric and cloud dynamics. Improved forecasting of cloud motion, in turn, enhances solar power production forecasts and facilitates the integration of additional photovoltaic (PV) sources into the power grid. However, both classical numerical models and emerging deep learning approaches face challenges when applied to spatially irregular sensor networks such as those formed by weather stations. In this work, we adopt a graph signal processing perspective and model advection-diffusion particles as signals on a graph to capture the dynamics of these processes. We introduce a Physics-Informed Graph Neural Network (PING) for forecasting future advection-diffusion particle concentrations on irregular grids. The model incorporates a discretized advection-diffusion equation as a soft constraint in the loss function to guide learning toward physically consistent solutions. This model is on par with state of the art models on synthetic and real transport phenomena datasets, including sea surface temperature and cloud index datasets. Furthermore, the PING model is successfully coupled with models for forecasting PV power production. This hybrid approach leverages data fusion from ground-based sensors at PV stations and satellite images with cloud concentration to improve the accuracy of intra-day PV power production.