Abstract
Spatial-temporal forecasting is crucial in various domains, including traffic flow prediction for Intelligent Transportation Systems (ITS). Despite the challenges posed by complex spatial-temporal dependencies in traffic networks, Partial Differential Equations (PDEs) have proven effective for capturing traffic dynamics. However, recent trends favor data-driven approaches like Graph Neural Networks (GNNs) for traffic forecasting, often overlooking the principles described by PDEs. In this paper, we propose a Graph Partial Differential Equation Network (GPDE) that integrates PDE principles with GNNs to enhance traffic flow forecasting. Our approach leverages dynamic graph structures based on PDE flux functions, incorporating residual connections and learnable rates for improved model performance. Extensive experiments on real-world traffic datasets demonstrate the superiority of GPDE over existing methods in both short-term and long-term traffic speed prediction tasks.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
The code for this paper can be found at https://drive.google.com/drive/folders/1FzKPIfORu54vQ2oWDSFjh4tvepIFIEVW?usp=drive_link.
References
Aw, A., Rascle, M.: Resurrection of “second order’’ models of traffic flow. SIAM J. Appl. Math. 60(3), 916–938 (2000)
Bao, T., Chen, S., Johnson, T.T., Givi, P., Sammak, S., Jia, X.: Physics guided neural networks for spatio-temporal super-resolution of turbulent flows. In: Uncertainty in Artificial Intelligence, pp. 118–128. PMLR (2022)
Bao, T., et al.: Partial differential equation driven dynamic graph networks for predicting stream water temperature. In: 2021 IEEE International Conference on Data Mining (ICDM), pp. 11–20. IEEE (2021)
Chen, C., Petty, K., Skabardonis, A., Varaiya, P., Jia, Z.: Freeway performance measurement system: mining loop detector data. Transp. Res. Rec. 1748(1), 96–102 (2001)
Choi, J., Choi, H., Hwang, J., Park, N.: Graph neural controlled differential equations for traffic forecasting. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 36, pp. 6367–6374 (2022)
Claudel, C.G., Bayen, A.M.: Guaranteed bounds for traffic flow parameters estimation using mixed lagrangian-eulerian sensing. In: 2008 46th Annual Allerton Conference on Communication, Control, and Computing, pp. 636–645. IEEE (2008)
Di, X., Shi, R., Mo, Z., Fu, Y.: Physics-informed deep learning for traffic state estimation: a survey and the outlook. Algorithms 16(6), 305 (2023)
Fang, Z., Long, Q., Song, G., Xie, K.: Spatial-temporal graph ode networks for traffic flow forecasting. In: Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, pp. 364–373 (2021)
Gloudemans, D., et al.: I-24 motion: an instrument for freeway traffic science. Transp. Res. Part C: Emerging Technol. 155, 104311 (2023)
Greenshields, B.D., Bibbins, J., Channing, W., Miller, H.: A study of traffic capacity. In: Highway Research Board Proceedings, vol. 14, pp. 448–477. Washington, DC (1935)
Guo, S., Lin, Y., Feng, N., Song, C., Wan, H.: Attention based spatial-temporal graph convolutional networks for traffic flow forecasting. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 33, pp. 922–929 (2019)
He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 770–778 (2016)
Jones, N.: How machine learning could help to improve climate forecasts. Nature 548(7668) (2017)
Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016)
Li, Q., Han, Z., Wu, X.M.: Deeper insights into graph convolutional networks for semi-supervised learning. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32 (2018)
Li, Y., Yu, R., Shahabi, C., Liu, Y.: Diffusion convolutional recurrent neural network: Data-driven traffic forecasting. arXiv preprint arXiv:1707.01926 (2017)
Liu, Q., Wu, S., Wang, L., Tan, T.: Predicting the next location: a recurrent model with spatial and temporal contexts. In: AAAI’16 (2016)
Long, Q., Jin, Y., Wu, Y., Song, G.: Theoretically improving graph neural networks via anonymous walk graph kernels. In: Proceedings of the Web Conference 2021, pp. 1204–1214 (2021)
Ng, M.K., Chan, R.H., Tang, W.C.: A fast algorithm for deblurring models with neumann boundary conditions. SIAM J. Sci. Comput. 21(3), 851–866 (1999)
Pan, Y.A., Guo, J., Chen, Y., Li, S., Li, W., et al.: Incorporating traffic flow model into a deep learning method for traffic state estimation: a hybrid stepwise modeling framework. J. Adv. Transp. 2022 (2022)
Plötz, P., Jakobsson, N., Sprei, F.: On the distribution of individual daily driving distances. Transp. Res. Part B: Methodological 101, 213–227 (2017)
Rascle, M.: An improved macroscopic model of traffic flow: derivation and links with the lighthill-whitham model. Math. Comput. Model. 35(5–6), 581–590 (2002)
Shi, R., Mo, Z., Di, X.: Physics-informed deep learning for traffic state estimation: a hybrid paradigm informed by second-order traffic models. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 35, pp. 540–547 (2021)
Song, C., Lin, Y., Guo, S., Wan, H.: Spatial-temporal synchronous graph convolutional networks: a new framework for spatial-temporal network data forecasting. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 34, pp. 914–921 (2020)
Wang, J., Jiang, J., Jiang, W., Li, C., Zhao, W.X.: Libcity: An open library for traffic prediction. In: Proceedings of the 29th International Conference on Advances in Geographic Information Systems, pp. 145–148 (2021)
Wang, X., Chen, C., Min, Y., He, J., Yang, B., Zhang, Y.: Efficient metropolitan traffic prediction based on graph recurrent neural network. arXiv preprint arXiv:1811.00740 (2018)
Wu, Z., Pan, S., Long, G., et al.: Graph wavenet for deep spatial-temporal graph modeling. arXiv:1906.00121 (2019)
Yao, H., Tang, X., Wei, H., Zheng, G., Li, Z.: Revisiting spatial-temporal similarity: a deep learning framework for traffic prediction. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 33, pp. 5668–5675 (2019)
Yao, H., Wu, F., Ke, J., et al.: Deep multi-view spatial-temporal network for taxi demand prediction. In: AAAI (2018)
Yu, B., Yin, H., Zhu, Z.: Spatio-temporal graph convolutional networks: A deep learning framework for traffic forecasting. arXiv preprint arXiv:1709.04875 (2017)
Yu, R., Li, Y., Shahabi, C., Demiryurek, U., Liu, Y.: Deep learning: A generic approach for extreme condition traffic forecasting. In: SDM’17 (2017)
Zhang, H.M.: A non-equilibrium traffic model devoid of gas-like behavior. Transp. Res. art B: Methodological 36(3), 275–290 (2002)
Zhang, J., Zheng, Y., Qi, D.: Deep spatio-temporal residual networks for citywide crowd flows prediction. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 31 (2017)
Zhang, X., Huang, C., et al.: Spatial-temporal convolutional graph attention networks for citywide traffic flow forecasting. In: CIKM’18 (2020)
Zhang, Y., Quinones-Grueiro, M., Zhang, Z., Wang, Y., Barbour, W., Biswas, G., Work, D.: Marvel: Multi-agent reinforcement-learning for large-scale variable speed limits. arXiv preprint arXiv:2310.12359 (2023)
Acknowledgments
The work was partially supported by NSF awards #2028001 and #2421839. The views and conclusions contained in this paper are those of the authors and should not be interpreted as representing any funding agencies.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Bao, T., Wei, H., Ji, J., Work, D., Johnson, T.T. (2024). Spatial-Temporal PDE Networks for Traffic Flow Forecasting. In: Bifet, A., Krilavičius, T., Miliou, I., Nowaczyk, S. (eds) Machine Learning and Knowledge Discovery in Databases. Applied Data Science Track. ECML PKDD 2024. Lecture Notes in Computer Science(), vol 14950. Springer, Cham. https://doi.org/10.1007/978-3-031-70381-2_11
Download citation
DOI: https://doi.org/10.1007/978-3-031-70381-2_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-70380-5
Online ISBN: 978-3-031-70381-2
eBook Packages: Computer ScienceComputer Science (R0)