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

arXiv: https://arxiv.org/abs/2503.14053 · HTML: https://mlsanity.com/paper/2503.14053/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 33 references that are in the map.
- First posted on arXiv 18 Mar 2025.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [Learning Operators with Coupled Attention](https://mlsanity.com/paper/2201.01032/) (2022)
- [NOMAD: Nonlinear Manifold Decoders for Operator Learning](https://mlsanity.com/paper/2206.03551/) (2022)
- [DeepONet-Grid-UQ: A Trustworthy Deep Operator Framework for Predicting the Power Grid's Post-Fault Trajectories](https://mlsanity.com/paper/2202.07176/) (2022)
- [Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs](https://mlsanity.com/paper/2208.01565/) (2022)
- [Physics-informed Learning for Identification and State Reconstruction of Traffic Density](https://mlsanity.com/paper/2103.13852/) (2021)
- [Learning-based Traffic State Reconstruction using Probe Vehicles](https://mlsanity.com/paper/2011.05031/) (2020)
- [Learning-based State Reconstruction for a Scalar Hyperbolic PDE under noisy Lagrangian Sensing](https://mlsanity.com/paper/2011.09871/) (2020)
- [Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids](https://mlsanity.com/paper/2402.08187/) (2024)
- [An Advanced Physics-Informed Neural Operator for Comprehensive Design Optimization of Highly-Nonlinear Systems: An Aerospace Composites Processing Case Study](https://mlsanity.com/paper/2406.14715/) (2024)
- [Real-Time Prediction of Gas Flow Dynamics in Diesel Engines using a Deep Neural Operator Framework](https://mlsanity.com/paper/2304.00567/) (2023)
- [Numerical Investigation of Traffic State Reconstruction and Control Using Connected Automated Vehicles](https://mlsanity.com/paper/2010.02564/) (2020)

## Built on by (most cited first, 1 of 1)

- [DETNO: A Diffusion-Enhanced Transformer Neural Operator for Long-Term Traffic Forecasting](https://mlsanity.com/paper/2508.19389/) (2025)

## Abstract (arXiv)

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.