Wuping Xin

Wuping Xin

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.

Wuping Xin

Large Language Models (LLMs) have advanced reasoning through techniques like Chain-of-Thought (CoT). However, their reasoning largely re-mains textual and hypothetical, lacking empirical grounding in complex, dynamic domains like transportation. This paper introduces Simulation-in-the-Reasoning (SiR), a novel conceptual framework that embeds domain-specific simulators directly into the LLM reasoning loop. By treating intermediate reasoning steps as executable simulation experiments, SiR transforms LLM reasoning from narrative plausibility into a falsifiable, hypothesis-simulate-analyze workflow. We discuss applications, where LLM can formulate Intelligent Transport System (ITS) strategy hypotheses, invoke a traffic simulator via the Model Context Protocol (MCP), evaluate results under different demand patterns, and refine strategies through verification and aggregation. While implementing the framework is part of our ongoing work, this paper primarily establishes the conceptual foundation, discusses design considerations like API granularity, and outlines the vision of SiR as a cornerstone for interactive transportation digital twins. We argue that SiR represents a critical step towards trustworthy, empirically-validated AI for autonomous transportation systems.