ON-Traffic: An Operator Learning Framework for Online Traffic Flow Estimation and Uncertainty Quantification from Lagrangian Sensors

TL;DR

The paper addresses online estimation of spatio-temporal traffic state from sparse moving-probe data and downstream boundary inputs by proposing ON-Traffic, an online surrogate operator that predicts density $\rho$ and velocity $v$ with quantified aleatoric uncertainty. It advances a DeepONet-inspired architecture with a temporal encoder and nonlinear decoder, augmented by a fundamental diagram network to link $\hat{\rho}$ to $\hat{v}$ and propagate uncertainty, and trains under a receding-horizon strategy to support online deployment. The approach is evaluated on numerical Godunov and microscopic SUMO datasets, showing robustness to noise and sensor dropout, effective handling of irregular inputs, and well-calibrated uncertainty estimates. The work provides a practical pathway for real-time, adaptive traffic management with operator-learning tools that generalize across scenarios and time shifts.

Abstract

Accurate traffic flow estimation and prediction are critical for the efficient management of transportation systems, particularly under increasing urbanization. Traditional methods relying on static sensors often suffer from limited spatial coverage, while probe vehicles provide richer, albeit sparse and irregular data. This work introduces ON-Traffic, a novel deep operator Network and a receding horizon learning-based framework tailored for online estimation of spatio-temporal traffic state along with quantified uncertainty by using measurements from moving probe vehicles and downstream boundary inputs. Our framework is evaluated in both numerical and simulation datasets, showcasing its ability to handle irregular, sparse input data, adapt to time-shifted scenarios, and provide well-calibrated uncertainty estimates. The results demonstrate that the model captures complex traffic phenomena, including shockwaves and congestion propagation, while maintaining robustness to noise and sensor dropout. These advancements present a significant step toward online, adaptive traffic management systems.

Figures (14)

• Figure 1: Overview of the proposed model architecture of ON-Traffic.
• Figure 2: A more detailed illustration of the branch architecture of ON-Traffic based on VIDON prasthofer2022variableinputdeepoperatornetworks and extend with a temporal encoder. Additionally we employ separate outputs for the mean predictions and their standard deviation following the approach of deeponetUQ.
• Figure 3: Probe and boundary inputs for the receding horizon implementation of our model. The first row shows the model's input at $t_{c,j}:=t_c+j\Delta_{\mathrm{horizon}}$ and the second row shows the inputs at $t_{c,j+1}:=t_c+(j+1)\Delta_{\mathrm{horizon}}$
• Figure 4: Three realizations from the randomly sampled initial and boundary condition based on (\ref{['eq: ic']}) and (\ref{['eq:control eq']}).
• Figure 5: Visualization of one test scenario of the Godunov dataset subject to a receding horizon evaluation. The first column shows ON-Traffic's predictions with the coordinates of the inputs in black, the second column shows the absolute error, and the third column shows the performance of a snapshot in the future. For $t_{c, j+2}$, the predicted uncertainty's average value is $0.0424$ and its peak value $0.2961$. The peak value occurs at a space position of $3.04$ km and a time of $t_c + 4.75$.