# TG-PhyNN: An Enhanced Physically-Aware Graph Neural Network framework for forecasting Spatio-Temporal Data

arXiv: https://arxiv.org/abs/2408.16379 · HTML: https://mlsanity.com/paper/2408.16379/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 29 references that are in the map.
- First posted on arXiv 29 Aug 2024.

## Builds on (most cited first, 17 of 17)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [PyTorch Geometric Temporal: Spatiotemporal Signal Processing with Neural Machine Learning Models](https://mlsanity.com/paper/2104.07788/) (2021)
- [Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems](https://mlsanity.com/paper/2107.12146/) (2021)
- [A Review of Graph Neural Networks in Epidemic Modeling](https://mlsanity.com/paper/2403.19852/) (2024)
- [N-BEATS neural network for mid-term electricity load forecasting](https://mlsanity.com/paper/2009.11961/) (2020)
- [W-Transformers : A Wavelet-based Transformer Framework for Univariate Time Series Forecasting](https://mlsanity.com/paper/2209.03945/) (2022)
- [Physics-Informed Graph Neural Network for Spatial-temporal Production Forecasting](https://mlsanity.com/paper/2209.11885/) (2022)
- [RBF-MGN:Solving spatiotemporal PDEs with Physics-informed Graph Neural Network](https://mlsanity.com/paper/2212.02861/) (2022)

## Abstract (arXiv)

Accurately forecasting dynamic processes on graphs, such as traffic flow or disease spread, remains a challenge. While Graph Neural Networks (GNNs) excel at modeling and forecasting spatio-temporal data, they often lack the ability to directly incorporate underlying physical laws. This work presents TG-PhyNN, a novel Temporal Graph Physics-Informed Neural Network framework. TG-PhyNN leverages the power of GNNs for graph-based modeling while simultaneously incorporating physical constraints as a guiding principle during training. This is achieved through a two-step prediction strategy that enables the calculation of physical equation derivatives within the GNN architecture. Our findings demonstrate that TG-PhyNN significantly outperforms traditional forecasting models (e.g., GRU, LSTM, GAT) on real-world spatio-temporal datasets like PedalMe (traffic flow), COVID-19 spread, and Chickenpox outbreaks. These datasets are all governed by well-defined physical principles, which TG-PhyNN effectively exploits to offer more reliable and accurate forecasts in various domains where physical processes govern the dynamics of data. This paves the way for improved forecasting in areas like traffic flow prediction, disease outbreak prediction, and potentially other fields where physics plays a crucial role.