# Predicting Large-scale Urban Network Dynamics with Energy-informed Graph Neural Diffusion

arXiv: https://arxiv.org/abs/2508.00037 · HTML: https://mlsanity.com/paper/2508.00037/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 47 references that are in the map.
- First posted on arXiv 31 Jul 2025.

## Builds on (most cited first, 29 of 29)

- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [Spatial-Temporal Transformer Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2001.02908/) (2020)
- [Spatial-Temporal Identity: A Simple yet Effective Baseline for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2208.05233/) (2022)
- [PDFormer: Propagation Delay-Aware Dynamic Long-Range Transformer for Traffic Flow Prediction](https://mlsanity.com/paper/2301.07945/) (2023)
- [Decoupled Dynamic Spatial-Temporal Graph Neural Network for Traffic Forecasting](https://mlsanity.com/paper/2206.09112/) (2022)
- [LargeST: A Benchmark Dataset for Large-Scale Traffic Forecasting](https://mlsanity.com/paper/2306.08259/) (2023)
- [A Generalization of ViT/MLP-Mixer to Graphs](https://mlsanity.com/paper/2212.13350/) (2022)
- [DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion](https://mlsanity.com/paper/2301.09474/) (2023)
- [Understanding convolution on graphs via energies](https://mlsanity.com/paper/2206.10991/) (2022)
- [Scalable Spatiotemporal Graph Neural Networks](https://mlsanity.com/paper/2209.06520/) (2022)
- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Taming Local Effects in Graph-based Spatiotemporal Forecasting](https://mlsanity.com/paper/2302.04071/) (2023)
- [COLA: Cross-city Mobility Transformer for Human Trajectory Simulation](https://mlsanity.com/paper/2403.01801/) (2024)
- [Do We Really Need Graph Neural Networks for Traffic Forecasting?](https://mlsanity.com/paper/2301.12603/) (2023)
- [Channel-Aware Low-Rank Adaptation in Time Series Forecasting](https://mlsanity.com/paper/2407.17246/) (2024)
- [A Lightweight and Accurate Spatial-Temporal Transformer for Traffic Forecasting](https://mlsanity.com/paper/2201.00008/) (2021)
- [UniFlow: A Foundation Model for Unified Urban Spatio-Temporal Flow Prediction](https://mlsanity.com/paper/2411.12972/) (2024)
- [STNet: Spatial and Temporal feature fusion network for change detection in remote sensing images](https://mlsanity.com/paper/2304.11422/) (2023)
- [A Novel Scene Coupling Semantic Mask Network for Remote Sensing Image Segmentation](https://mlsanity.com/paper/2501.13130/) (2025)

## Built on by (most cited first, 1 of 1)

- [PIMCST: Physics-Informed Multi-Phase Consensus and Spatio-Temporal Few-Shot Learning for Traffic Flow Forecasting](https://mlsanity.com/paper/2602.01936/) (2026)

## Abstract (arXiv)

Networked urban systems facilitate the flow of people, resources, and services, and are essential for economic and social interactions. These systems often involve complex processes with unknown governing rules, observed by sensor-based time series. To aid decision-making in industrial and engineering contexts, data-driven predictive models are used to forecast spatiotemporal dynamics of urban systems. Current models such as graph neural networks have shown promise but face a trade-off between efficacy and efficiency due to computational demands. Hence, their applications in large-scale networks still require further efforts. This paper addresses this trade-off challenge by drawing inspiration from physical laws to inform essential model designs that align with fundamental principles and avoid architectural redundancy. By understanding both micro- and macro-processes, we present a principled interpretable neural diffusion scheme based on Transformer-like structures whose attention layers are induced by low-dimensional embeddings. The proposed scalable spatiotemporal Transformer (ScaleSTF), with linear complexity, is validated on large-scale urban systems including traffic flow, solar power, and smart meters, showing state-of-the-art performance and remarkable scalability. Our results constitute a fresh perspective on the dynamics prediction in large-scale urban networks.