# Physics Informed Deep Learning: Applications in Transportation

arXiv: https://arxiv.org/abs/2302.12336 · HTML: https://mlsanity.com/paper/2302.12336/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 21 references that are in the map.
- First posted on arXiv 23 Feb 2023.

## Builds on (most cited first, 3 of 3)

- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Highway Traffic State Estimation with Mixed Connected and Conventional Vehicles](https://mlsanity.com/paper/1504.06879/) (2015)
- [Fog Computing: Focusing on Mobile Users at the Edge](https://mlsanity.com/paper/1502.01815/) (2015)

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

- [Online Traffic Density Estimation using Physics-Informed Neural Networks](https://mlsanity.com/paper/2504.03483/) (2025)

## Abstract (arXiv)

A recent development in machine learning - physics-informed deep learning (PIDL) - presents unique advantages in transportation applications such as traffic state estimation. Consolidating the benefits of deep learning (DL) and the governing physical equations, it shows the potential to complement traditional sensing methods in obtaining traffic states. In this paper, we first explain the conservation law from the traffic flow theory as ``physics'', then present the architecture of a PIDL neural network and demonstrate its effectiveness in learning traffic conditions of unobserved areas. In addition, we also exhibit the data collection scenario using fog computing infrastructure. A case study on estimating the vehicle velocity is presented and the result shows that PIDL surpasses the performance of a regular DL neural network with the same learning architecture, in terms of convergence time and reconstruction accuracy. The encouraging results showcase the broad potential of PIDL for real-time applications in transportation with a low amount of training data.