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This research introduces a physics-informed neural cellular automaton (PI-NCA) to model traffic flow dynamics while strictly enforcing conservation laws and topological consistency. By extending the framework to stochastic settings, the authors demonstrate that machine learning can effectively capture probabilistic transition rules without violating physical constraints inherent in road networks. The work advances interpretable modeling for complex collective systems by integrating data-driven learning with rigorous physical priors.
Learning Traffic Flow Dynamics with Stochastic Physics-Informed Neural Cellular Automata
arXiv:2610.09946v1 Announce Type: new Abstract: Traffic flow modeling is essential for understanding and predicting the collective dynamics of vehicles on road networks. Cellular automata provide a simple, interpretable yet powerful framework for representing these dynamics via local interaction rules, while retaining the ability to reproduce complex macroscopic traffic phenomena. However, learning local transition rules from data while preserving physically meaningful constraints remains challenging, particularly for stochastic models. In this work, we propose a physics-informed neural cellular automaton (PI-NCA) for data-driven traffic flow modeling. Building on the standard neural cellular automaton (NCA), we design a neural architecture that is physically consistent with the road topology and guarantees conservation of the total number of vehicles, thereby constraining the learned transition rules to physically admissible dynamics. We further extend this framework to stochastic dynamics by parameterizing probabilistic transition rules while preserving the same physics-informed constraints. We evaluate the proposed models on multiple traffic scenarios generated by the well-established Nagel-Schreckenberg and Kerner-Klenov-Wolf cellular automata. The results demonstrate that the PI-NCA successfully learns the dynamics of both traffic models and consistently outperforms a standard NCA, while the stochastic extension captures probabilistic transition rules without compromising the imposed physical constraints.
Abstract:Traffic flow modeling is essential for understanding and predicting the collective dynamics of vehicles on road networks. Cellular automata provide a simple, interpretable yet powerful framework for representing these dynamics via local interaction rules, while retaining the ability to reproduce complex macroscopic traffic phenomena. However, learning local transition rules from data while preserving physically meaningful constraints remains challenging, particularly for stochastic models. In this work, we propose a physics-informed neural cellular automaton (PI-NCA) for data-driven traffic flow modeling. Building on the standard neural cellular automaton (NCA), we design a neural architecture that is physically consistent with the road topology and guarantees conservation of the total number of vehicles, thereby constraining the learned transition rules to physically admissible dynamics. We further extend this framework to stochastic dynamics by parameterizing probabilistic transition rules while preserving the same physics-informed constraints. We evaluate the proposed models on multiple traffic scenarios generated by the well-established Nagel-Schreckenberg and Kerner-Klenov-Wolf cellular automata. The results demonstrate that the PI-NCA successfully learns the dynamics of both traffic models and consistently outperforms a standard NCA, while the stochastic extension captures probabilistic transition rules without compromising the imposed physical constraints.
Machine Learning (cs.LG)
arXiv:2610.09946 [cs.LG]
(or arXiv:2610.09946v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.09946 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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