# Physics-informed Machine Learning for Calibrating Macroscopic Traffic Flow Models

arXiv: https://arxiv.org/abs/2307.06267 · HTML: https://mlsanity.com/paper/2307.06267/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 49 references that are in the map.
- First posted on arXiv 12 Jul 2023.

## Builds on (most cited first, 6 of 6)

- [A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation](https://mlsanity.com/paper/2106.03142/) (2021)
- [Deep State Space Models for Nonlinear System Identification](https://mlsanity.com/paper/2003.14162/) (2020)
- [Nonlinear state-space identification using deep encoder networks](https://mlsanity.com/paper/2012.07697/) (2020)
- [Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: A New Insight into Machine Learning Applications](https://mlsanity.com/paper/2002.02374/) (2020)
- [Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook](https://mlsanity.com/paper/2303.02063/) (2023)
- [How Does Momentum Benefit Deep Neural Networks Architecture Design? A Few Case Studies](https://mlsanity.com/paper/2110.07034/) (2021)

## Built on by (most cited first, 3 of 3)

- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)
- [Reconstructing Physics-Informed Machine Learning for Traffic Flow Modeling: a Multi-Gradient Descent and Pareto Learning Approach](https://mlsanity.com/paper/2505.13241/) (2025)
- [Machine Unlearning of Traffic State Estimation and Prediction](https://mlsanity.com/paper/2507.17984/) (2025)

## Abstract (arXiv)

Well-calibrated traffic flow models are fundamental to understanding traffic phenomena and designing control strategies. Traditional calibration has been developed base on optimization methods. In this paper, we propose a novel physics-informed, learning-based calibration approach that achieves performances comparable to and even better than those of optimization-based methods. To this end, we combine the classical deep autoencoder, an unsupervised machine learning model consisting of one encoder and one decoder, with traffic flow models. Our approach informs the decoder of the physical traffic flow models and thus induces the encoder to yield reasonable traffic parameters given flow and speed measurements. We also introduce the denoising autoencoder into our method so that it can handles not only with normal data but also with corrupted data with missing values. We verified our approach with a case study of I-210 E in California.