# Short-term traffic prediction using physics-aware neural networks

arXiv: https://arxiv.org/abs/2109.10253 · HTML: https://mlsanity.com/paper/2109.10253/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 47 references that are in the map.
- First posted on arXiv 21 Sep 2021.

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

- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network](https://mlsanity.com/paper/1812.04426/) (2018)
- [Deep Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/1804.04272/) (2018)
- [Visualizing and Understanding Recurrent Networks](https://mlsanity.com/paper/1506.02078/) (2015)
- [A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation](https://mlsanity.com/paper/2106.03142/) (2021)
- [Solving inverse-PDE problems with physics-aware neural networks](https://mlsanity.com/paper/2001.03608/) (2020)
- [Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: A New Insight into Machine Learning Applications](https://mlsanity.com/paper/2002.02374/) (2020)
- [Data driven approximation of parametrized PDEs by Reduced Basis and Neural Networks](https://mlsanity.com/paper/1904.01514/) (2019)
- [Neural network augmented inverse problems for PDEs](https://mlsanity.com/paper/1712.09685/) (2017)
- [Learning-based Traffic State Reconstruction using Probe Vehicles](https://mlsanity.com/paper/2011.05031/) (2020)
- [Deep Learning on Traffic Prediction: Methods, Analysis and Future Directions](https://mlsanity.com/paper/2004.08555/) (2020)
- [Short-term Traffic Prediction with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2009.00712/) (2020)
- [Parameter and density estimation from real-world traffic data: A kinetic compartmental approach](https://mlsanity.com/paper/2101.11485/) (2021)
- [The Traffic Reaction Model: A kinetic compartmental approach to road traffic modeling](https://mlsanity.com/paper/2101.10190/) (2021)

## Built on by (most cited first, 8 of 8)

- [Fourier neural operator for learning solutions to macroscopic traffic flow models: Application to the forward and inverse problems](https://mlsanity.com/paper/2308.07051/) (2023)
- [A Physics Enhanced Residual Learning (PERL) Framework for Vehicle Trajectory Prediction](https://mlsanity.com/paper/2309.15284/) (2023)
- [Potential failures of physics-informed machine learning in traffic flow modeling: theoretical and experimental analysis](https://mlsanity.com/paper/2505.11491/) (2025)
- [Personalized Dynamic Pricing Policy for Electric Vehicles: Reinforcement learning approach](https://mlsanity.com/paper/2401.00661/) (2024)
- [Controlled Descent Training](https://mlsanity.com/paper/2303.09216/) (2023)
- [Reconstructing Physics-Informed Machine Learning for Traffic Flow Modeling: a Multi-Gradient Descent and Pareto Learning Approach](https://mlsanity.com/paper/2505.13241/) (2025)
- [Proxy Reconstruction Pre-training for Ramp Flow Prediction at Highway Interchanges](https://mlsanity.com/paper/2510.03381/) (2025)
- [Real-Time Traffic Density Estimation: A Hybrid Computer Vision and Predictive Machine Learning Pipeline](https://mlsanity.com/paper/2610.14326/) (2026)

## Abstract (arXiv)

In this work, we propose an algorithm performing short-term predictions of the flux of vehicles on a stretch of road, using past measurements of the flux. This algorithm is based on a physics-aware recurrent neural network. A discretization of a macroscopic traffic flow model (using the so-called Traffic Reaction Model) is embedded in the architecture of the network and yields flux predictions based on estimated and predicted space-time dependent traffic parameters. These parameters are themselves obtained using a succession of LSTM ans simple recurrent neural networks. Besides, on top of the predictions, the algorithm yields a smoothing of its inputs which is also physically-constrained by the macroscopic traffic flow model. The algorithm is tested on raw flux measurements obtained from loop detectors.