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Physics Informed Deep Learning for Traffic State Estimation: Illustrations with LWR and CTM Models

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# PISE

*P*hysics *I*nformed deep learning for traffic *S*tate *E*stimation (PISE)

Data in this repo -     
1. Synthetic.mat - case study I - simulated traffic state dataset    
2. NGSIM_US80_4pm_Velocity_Data.txt - case study II - NGSIM Velocity Data

### Corresponding publications

- A. J. Huang and S. Agarwal, ["Physics Informed Deep Learning for Traffic State Estimation: Illustrations with LWR and CTM Models"](https://ieeexplore.ieee.org/document/9795676) in *IEEE Open Journal of Intelligent Transportation Systems*, vol. 3, pp. 503-518, 2022, doi: 10.1109/OJITS.2022.3182925.

- A. J. Huang and S. Agarwal, ["Physics Informed Deep Learning for Traffic State Estimation"](https://ieeexplore.ieee.org/document/9294236) 2020 IEEE 23rd International Conference on Intelligent Transportation Systems (ITSC), Rhodes, Greece, 2020, pp. 1-6

### Citations

@ARTICLE{huang2022physics,
      author={Huang, Archie J. and Agarwal, Shaurya},
      journal={IEEE Open Journal of Intelligent Transportation Systems}, 
      title={Physics-Informed Deep Learning for Traffic State Estimation: Illustrations with LWR and CTM Models}, 
      year={2022},
      volume={3},
      number={},
      pages={503-518},
      doi={10.1109/OJITS.2022.3182925}
    }

@inproceedings{huang2020physics,
      title={Physics informed deep learning for traffic state estimation},
      author={Huang, Archie J. and Agarwal, Shaurya},
      booktitle={2020 IEEE 23rd International Conference on Intelligent Transportation Systems (ITSC)},
      pages={1--6},
      year={2020},
      organization={IEEE}
    }

Code is built upon Dr. Maziar Raissi's PINNs - https://github.com/maziarraissi/PINNs    
Source of processed NGSIM data : Dr. Allan Avila - https://github.com/Allan-Avila/Highway-Traffic-Dynamics-KMD-Code

### Reference

- Raissi, Maziar, Paris Perdikaris, and George E. Karniadakis. "[Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations](https://www.sciencedirect.com/science/article/pii/S0021999118307125)." Journal of Computational Physics 378 (2019): 686-707.

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