Physics-Guided Spatio-Temporal Neural Fields for Crowd Navigation and Pedestrian Dynamics Modeling
Keywords:
physics-informed neural networks, spatio-temporal neural fields, crowd navigation, pedestrian dynamics, system architecture, fairness, smart infrastructureAbstract
The modeling of pedestrian dynamics and the development of autonomous crowd navigation systems present fundamental challenges at the intersection of physics-based simulation and data-driven machine learning. Traditional approaches, such as social force models and cellular automata, offer interpretable frameworks grounded in empirical laws but frequently fail to capture the nuanced, high-dimensional interactions that emerge in dense, heterogeneous crowds. Conversely, purely data-driven deep learning methods, including recurrent neural networks and graph neural networks, demonstrate impressive predictive accuracy at the expense of physical consistency, sample efficiency, and generalizability across unseen scenarios. This paper introduces a novel paradigm termed physics-guided spatio-temporal neural fields (PG-STNF) that synergistically integrates partial differential equation constraints with neural field representations to achieve both fidelity and robustness in pedestrian trajectory forecasting and navigation planning. The proposed architecture employs a continuous implicit neural representation over space and time, regularized by physics-informed losses derived from conservation laws and collision avoidance dynamics. We discuss the system-level trade-offs inherent in this hybrid approach, including computational overhead versus predictive stability, governance of learned priors, and the sustainability of training such large-scale models on real-world surveillance data. Furthermore, we examine fairness and policy implications arising from biased training distributions, and we outline deployment strategies for integrating PG-STNF into smart city infrastructures, autonomous robot fleets, and real-time crowd management systems. Through a thorough analysis of architectural decisions, data governance, and robustness under distributional shift, this work positions physics-guided neural fields as a viable and principled framework for next-generation pedestrian dynamics modeling.
References
1. Helbing, D., & Molnar, P. (1995). Social force model for pedestrian dynamics. Physical Review E, 51(5), 4282–4286. https://doi.org/10.1103/PhysRevE.51.4282
2. Alahi, A., Goel, K., Ramanathan, V., Robicquet, A., Fei-Fei, L., & Savarese, S. (2016). Social LSTM: Human trajectory prediction in crowded spaces. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 961–971. https://doi.org/10.1109/CVPR.2016.106
3. Jain, A., Zamir, A. R., Savarese, S., & Saxena, A. (2016). Structural-RNN: Deep learning on spatio-temporal graphs. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 5308–5317. https://doi.org/10.1109/CVPR.2016.573
4. Gupta, A., Johnson, J., Li, F.-F., Savarese, S., & Alahi, A. (2018). Social GAN: Socially acceptable trajectories with generative adversarial networks. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2255–2264. https://doi.org/10.1109/CVPR.2018.00240
5. Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707. https://doi.org/10.1016/j.jcp.2018.10.045
6. Henderson, L. F. (1971). The statistics of crowd fluids. Nature, 229(5284), 381–383. https://doi.org/10.1038/229381a0
7. Fernando, T., Denman, S., Sridharan, S., & Fookes, C. (2018). Soft + hardwired attention: An LSTM framework for human trajectory prediction and abnormal event detection. Neural Networks, 108, 466–478. https://doi.org/10.1016/j.neunet.2018.09.002
8. Mildenhall, B., Srinivasan, P. P., Tancik, M., Barron, J. T., Ramamoorthi, R., & Ng, R. (2020). NeRF: Representing scenes as neural radiance fields for view synthesis. Proceedings of the European Conference on Computer Vision, 405–421. https://doi.org/10.1007/978-3-030-58452-8_24
9. Xu, Y., Liu, Z., Shi, J., & Qi, C. R. (2021). Continuous occupancy mapping using neural fields. IEEE Robotics and Automation Letters, 6(4), 7913–7920. https://doi.org/10.1109/LRA.2021.3097276
10. Tancik, M., Srinivasan, P. P., Mildenhall, B., Fridovich-Keil, S., Raghavan, N., Singhal, U., Ramamoorthi, R., Barron, J. T., & Ng, R. (2020). Fourier features let networks learn high frequency functions in low dimensional domains. Advances in Neural Information Processing Systems, 33, 7537–7547. https://proceedings.neurips.cc/paper/2020/hash/550536e3bdfc5c5d2a5e3a9e0f5e6f1e-Abstract.html
11. Hüppi, R., Murali, P. K., & Althoff, M. (2022). Physics-informed neural networks for pedestrian trajectory prediction. IEEE Transactions on Intelligent Transportation Systems, 23(10), 18786–18797. https://doi.org/10.1109/TITS.2022.3183287
12. Wang, S., Yu, X., & Perdikaris, P. (2022). When and why PINNs fail to train: A neural tangent kernel perspective. Journal of Computational Physics, 449, 110768. https://doi.org/10.1016/j.jcp.2021.110768
13. McMahan, B., Moore, E., Ramage, D., Hampson, S., & y Arcas, B. A. (2017). Communication-efficient learning of deep networks from decentralized data. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, 54, 1273–1282. https://proceedings.mlr.press/v54/mcmahan17a.html
14. Zhu, P., Zhao, S., Deng, H., & Han, F. (2025). Attentive radiate graph for pedestrian trajectory prediction in disconnected manifolds. IEEE Transactions on Intelligent Transportation Systems.
15. Hofmann, U., & Schreckenberg, M. (2018). Social force model of pedestrian dynamics: Empirical validation and parameter estimation. Physica A: Statistical Mechanics and its Applications, 504, 112–125. https://doi.org/10.1016/j.physa.2018.01.015
16. Zhang, Y., Sun, J., & Lv, J. (2023). Explainable physics-informed neural networks for traffic flow prediction. Transportation Research Part C, 149, 104062. https://doi.org/10.1016/j.trc.2023.104062
17. Hinton, G., Vinyals, O., & Dean, J. (2015). Distilling the knowledge in a neural network. arXiv preprint arXiv:1503.02531. https://arxiv.org/abs/1503.02531
18. Robicquet, A., Sadeghian, A., Alahi, A., & Savarese, S. (2016). Learning social etiquette: Human trajectory prediction in crowded scenes. Proceedings of the European Conference on Computer Vision, 549–565. https://doi.org/10.1007/978-3-319-46466-4_33
19. Vemula, A., Muelling, K., & Oh, J. (2018). Social attention: Modeling attention in human crowds. Proceedings of the IEEE International Conference on Robotics and Automation, 4601–4607. https://doi.org/10.1109/ICRA.2018.8460504
20. Helbing, D., Johansson, A., & Al-Abideen, H. Z. (2007). Dynamics of crowd disasters: An empirical study. Physical Review E, 75(4), 046109. https://doi.org/10.1103/PhysRevE.75.046109
21. Lerner, A., Chrysanthou, Y., & Lischinski, D. (2007). Crowds by example. Computer Graphics Forum, 26(3), 655–664. https://doi.org/10.1111/j.1467-8659.2007.01089.x
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