Differentiable Stochastic Traffic Dynamics: Physics-Informed Generative Modelling in Transportation
This work addresses the need for stochastic modeling in transportation systems, offering a novel approach for distributional traffic analysis, though it appears incremental by extending existing physics-informed methods to stochastic settings.
The authors tackled the problem of modeling stochastic macroscopic traffic flow by developing a physics-informed generative framework that incorporates distributional constraints derived from stochastic traffic dynamics, resulting in a model capable of producing data-conditioned density distributions for traffic-state estimation and congestion-risk measures.
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays no role in the learned representation. This work develops a framework in which the physics constraint itself is distributional and directly derived from stochastic traffic-flow dynamics. Starting from an Ito-type Lighthill-Whitham-Richards model with Brownian forcing, we derive a one-point forward equation for the marginal traffic density at each spatial location. The spatial coupling induced by the conservation law appears as an explicit conditional drift term, which makes the closure requirement transparent. Based on this formulation, we derive an equivalent deterministic Probability Flow ODE that is pointwise evaluable and differentiable once a closure is specified. Incorporating this as a physics constraint, we then propose a score network with an advection-closure module, trainable by denoising score matching together with a Fokker-Planck residual loss. The resulting model targets a data-conditioned density distribution, from which point estimates, credible intervals, and congestion-risk measures can be computed. The framework provides a basis for distributional traffic-state estimation and for stochastic fundamental-diagram analysis in a physics-informed generative setting.