# STDEN: Towards Physics-Guided Neural Networks for Traffic Flow Prediction

arXiv: https://arxiv.org/abs/2209.00225 · HTML: https://mlsanity.com/paper/2209.00225/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 1 Sep 2022.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Spatial-Temporal Fusion Graph Neural Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2012.09641/) (2020)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Deep Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/1804.04272/) (2018)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Learning Long-Term Dependencies in Irregularly-Sampled Time Series](https://mlsanity.com/paper/2006.04418/) (2020)
- [A Physics-Informed Deep Learning Paradigm for Car-Following Models](https://mlsanity.com/paper/2012.13376/) (2020)
- [Joint Modeling of Local and Global Temporal Dynamics for Multivariate Time Series Forecasting with Missing Values](https://mlsanity.com/paper/1911.10273/) (2019)

## Built on by (most cited first, 30 of 45)

- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [PDFormer: Propagation Delay-Aware Dynamic Long-Range Transformer for Traffic Flow Prediction](https://mlsanity.com/paper/2301.07945/) (2023)
- [DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models](https://mlsanity.com/paper/2301.13629/) (2023)
- [Spatio-Temporal Self-Supervised Learning for Traffic Flow Prediction](https://mlsanity.com/paper/2212.04475/) (2022)
- [Self-supervised Trajectory Representation Learning with Temporal Regularities and Travel Semantics](https://mlsanity.com/paper/2211.09510/) (2022)
- [Deciphering Spatio-Temporal Graph Forecasting: A Causal Lens and Treatment](https://mlsanity.com/paper/2309.13378/) (2023)
- [A Unified Replay-based Continuous Learning Framework for Spatio-Temporal Prediction on Streaming Data](https://mlsanity.com/paper/2404.14999/) (2024)
- [Continuous Trajectory Generation Based on Two-Stage GAN](https://mlsanity.com/paper/2301.07103/) (2023)
- [AirPhyNet: Harnessing Physics-Guided Neural Networks for Air Quality Prediction](https://mlsanity.com/paper/2402.03784/) (2024)
- [Air Quality Prediction with Physics-Guided Dual Neural ODEs in Open Systems](https://mlsanity.com/paper/2410.19892/) (2024)
- [Cross-city Few-Shot Traffic Forecasting via Traffic Pattern Bank](https://mlsanity.com/paper/2308.09727/) (2023)
- [TodyNet: Temporal Dynamic Graph Neural Network for Multivariate Time Series Classification](https://mlsanity.com/paper/2304.05078/) (2023)
- [BIGCity: A Universal Spatiotemporal Model for Unified Trajectory and Traffic State Data Analysis](https://mlsanity.com/paper/2412.00953/) (2024)
- [Dynamic Hypergraph Structure Learning for Traffic Flow Forecasting](https://mlsanity.com/paper/2309.12028/) (2023)
- [Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook](https://mlsanity.com/paper/2303.02063/) (2023)
- [Multi-scale Traffic Pattern Bank for Cross-city Few-shot Traffic Forecasting](https://mlsanity.com/paper/2402.00397/) (2024)
- [FDTI: Fine-grained Deep Traffic Inference with Roadnet-enriched Graph](https://mlsanity.com/paper/2306.10945/) (2023)
- [A Physics Enhanced Residual Learning (PERL) Framework for Vehicle Trajectory Prediction](https://mlsanity.com/paper/2309.15284/) (2023)
- [Multi-Factor Spatio-Temporal Prediction based on Graph Decomposition Learning](https://mlsanity.com/paper/2310.10374/) (2023)
- [Frequency Enhanced Pre-training for Cross-city Few-shot Traffic Forecasting](https://mlsanity.com/paper/2406.02614/) (2024)
- [UniTE: A Survey and Unified Pipeline for Pre-training Spatiotemporal Trajectory Embeddings](https://mlsanity.com/paper/2407.12550/) (2024)
- [Learning Universal Multi-level Market Irrationality Factors to Improve Stock Return Forecasting](https://mlsanity.com/paper/2502.04737/) (2025)
- [Physics-guided Active Sample Reweighting for Urban Flow Prediction](https://mlsanity.com/paper/2407.13605/) (2024)
- [Unified Data Management and Comprehensive Performance Evaluation for Urban Spatial-Temporal Prediction [Experiment, Analysis & Benchmark]](https://mlsanity.com/paper/2308.12899/) (2023)
- [COOL: A Conjoint Perspective on Spatio-Temporal Graph Neural Network for Traffic Forecasting](https://mlsanity.com/paper/2403.01091/) (2024)
- [RePST: Language Model Empowered Spatio-Temporal Forecasting via Semantic-Oriented Reprogramming](https://mlsanity.com/paper/2408.14505/) (2024)
- [A Gravity-informed Spatiotemporal Transformer for Human Activity Intensity Prediction](https://mlsanity.com/paper/2506.13678/) (2025)
- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)
- [Urban Traffic Forecasting with Integrated Travel Time and Data Availability in a Conformal Graph Neural Network Framework](https://mlsanity.com/paper/2407.12238/) (2024)
- [Multi-View Neural Differential Equations for Continuous-Time Stream Data in Long-Term Traffic Forecasting](https://mlsanity.com/paper/2408.06445/) (2024)

## Abstract (arXiv)

High-performance traffic flow prediction model designing, a core technology of Intelligent Transportation System, is a long-standing but still challenging task for industrial and academic communities. The lack of integration between physical principles and data-driven models is an important reason for limiting the development of this field. In the literature, physics-based methods can usually provide a clear interpretation of the dynamic process of traffic flow systems but are with limited accuracy, while data-driven methods, especially deep learning with black-box structures, can achieve improved performance but can not be fully trusted due to lack of a reasonable physical basis. To bridge the gap between purely data-driven and physics-driven approaches, we propose a physics-guided deep learning model named Spatio-Temporal Differential Equation Network (STDEN), which casts the physical mechanism of traffic flow dynamics into a deep neural network framework. Specifically, we assume the traffic flow on road networks is driven by a latent potential energy field (like water flows are driven by the gravity field), and model the spatio-temporal dynamic process of the potential energy field as a differential equation network. STDEN absorbs both the performance advantage of data-driven models and the interpretability of physics-based models, so is named a physics-guided prediction model. Experiments on three real-world traffic datasets in Beijing show that our model outperforms state-of-the-art baselines by a significant margin. A case study further verifies that STDEN can capture the mechanism of urban traffic and generate accurate predictions with physical meaning. The proposed framework of differential equation network modeling may also cast light on other similar applications.