mlsanityData to 7 Oct 2026

A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation

arXiv 2106.03142 ↗First posted 6 Jun 2021cs.LGcited by 37

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Abstract (arXiv)

Traffic state estimation (TSE) bifurcates into two categories, model-driven and data-driven (e.g., machine learning, ML), while each suffers from either deficient physics or small data. To mitigate these limitations, recent studies introduced a hybrid paradigm, physics-informed deep learning (PIDL), which contains both model-driven and data-driven components. This paper contributes an improved version, called physics-informed deep learning with a fundamental diagram learner (PIDL+FDL), which integrates ML terms into the model-driven component to learn a functional form of a fundamental diagram (FD), i.e., a mapping from traffic density to flow or velocity. The proposed PIDL+FDL has the advantages of performing the TSE learning, model parameter identification, and FD estimation simultaneously. We demonstrate the use of PIDL+FDL to solve popular first-order and second-order traffic flow models and reconstruct the FD relation as well as model parameters that are outside the FD terms. We then evaluate the PIDL+FDL-based TSE using the Next Generation SIMulation (NGSIM) dataset. The experimental results show the superiority of the PIDL+FDL in terms of improved estimation accuracy and data efficiency over advanced baseline TSE methods, and additionally, the capacity to properly learn the unknown underlying FD relation.

Key facts. Cited by 37 papers in the map (data through 7 Oct 2026). Builds on 8 of its 26 references that are in the map. First posted on arXiv 6 Jun 2021.

Builds on

8 of 26 references.

References · 8

  1. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  2. 2020A Physics-Informed Deep Learning Paradigm for Car-Following Modelscited by 40
  3. 2020Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: A New Insight into Machine Learning Applicationscited by 25
  4. 2020A Survey on Autonomous Vehicle Control in the Era of Mixed-Autonomy: From Physics-Based to AI-Guided Driving Policy Learningcited by 24
  5. 2021Low-Rank Hankel Tensor Completion for Traffic Speed Estimationcited by 22
  6. 2021Physics-informed Learning for Identification and State Reconstruction of Traffic Densitycited by 13
  7. 2020Learning-based Traffic State Reconstruction using Probe Vehiclescited by 10
  8. 2020Learning-based State Reconstruction for a Scalar Hyperbolic PDE under noisy Lagrangian Sensingcited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 5; 2023: 12; 2024: 6; 2025: 9; 2026: 4.

37 papers.

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  1. 2023On the Limitations of Physics-informed Deep Learning: Illustrations Using First Order Hyperbolic Conservation Law-based Traffic Flow Modelscited by 14
  2. 2023Fourier neural operator for learning solutions to macroscopic traffic flow models: Application to the forward and inverse problemscited by 12
  3. 2024Hierarchical Consensus-Based Multi-Agent Reinforcement Learning for Multi-Robot Cooperation Taskscited by 12
  4. 2022TrafficFlowGAN: Physics-informed Flow based Generative Adversarial Network for Uncertainty Quantificationcited by 11
  5. 2023Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlookcited by 11
  6. 2023ESP: Exploiting Symmetry Prior for Multi-Agent Reinforcement Learningcited by 9
  7. 2024Higher-order Spatio-temporal Physics-incorporated Graph Neural Network for Multivariate Time Series Imputationcited by 8
  8. 2022Quantifying Uncertainty In Traffic State Estimation Using Generative Adversarial Networkscited by 7
  9. 2024Traffic expertise meets residual RL: Knowledge-informed model-based residual reinforcement learning for CAV trajectory controlcited by 7
  10. 2021Short-term traffic prediction using physics-aware neural networkscited by 6
  11. 2023Traffic State Estimation from Vehicle Trajectories with Anisotropic Gaussian Processescited by 6
  12. 2025Network-wide Freeway Traffic Estimation Using Sparse Sensor Data: A Dirichlet Graph Auto-Encoder Approachcited by 4
25 more
  1. 2022IDM-Follower: A Model-Informed Deep Learning Method for Long-Sequence Car-Following Trajectory Predictioncited by 3
  2. 2023Generalized adaptive smoothing based neural network architecture for traffic state estimationcited by 3
  3. 2023Physics-informed Machine Learning for Calibrating Macroscopic Traffic Flow Modelscited by 3
  4. 2022Refining time-space traffic diagrams: A simple multiple linear regression modelcited by 2
  5. 2024Privacy-Preserving Data Fusion for Traffic State Estimation: A Vertical Federated Learning Approachcited by 2
  6. 2024Efficient and Robust Freeway Traffic Speed Estimation under Oblique Grid using Vehicle Trajectory Datacited by 2
  7. 2025MoGERNN: An Inductive Traffic Predictor for Unobserved Locationscited by 2
  8. 2025A Survey of Physics-Informed AI for Complex Urban Systemscited by 2
  9. 2023Inverting the Fundamental Diagram and Forecasting Boundary Conditions: How Machine Learning Can Improve Macroscopic Models for Traffic Flowcited by 1
  10. 2023Training Physics-Informed Neural Networks via Multi-Task Optimization for Traffic Density Predictioncited by 1
  11. 2023Incorporating Nonlocal Traffic Flow Model in Physics-informed Neural Networkscited by 1
  12. 2023Learning "Look-Ahead" Nonlocal Traffic Dynamics in a Ring Roadcited by 1
  13. 2024Graph Neural Network Surrogates to leverage Mechanistic Expert Knowledge towards Reliable and Immediate Pandemic Responsecited by 1
  14. 2025Potential failures of physics-informed machine learning in traffic flow modeling: theoretical and experimental analysiscited by 1
  15. 2025Learning to Learn the Macroscopic Fundamental Diagram using Physics-Informed and meta Machine Learning techniquescited by 1
  16. 2022Physics-informed Machine Learning of Parameterized Fundamental Diagramscited by 0
  17. 2023Newell's theory based feature transformations for spatio-temporal traffic predictioncited by 0
  18. 2025Reconstructing Physics-Informed Machine Learning for Traffic Flow Modeling: a Multi-Gradient Descent and Pareto Learning Approachcited by 0
  19. 2025Physics-informed deep operator network for traffic state estimationcited by 0
  20. 2025Proxy Reconstruction Pre-training for Ramp Flow Prediction at Highway Interchangescited by 0
  21. 2025Non-myopic Matching and Rebalancing in Large-Scale On-Demand Ride-Pooling Systems Using Simulation-Informed Reinforcement Learningcited by 0
  22. 2026Curriculum-Learned Vanishing Stacked Residual PINNs for Hyperbolic PDE State Reconstructioncited by 0
  23. 2026Traffic Flow Reconstruction from Limited Collected Datacited by 0
  24. 2026Physics-Informed Teacher-Student Ensemble Learning for Traffic State Estimation with a Varying Speed Limit Scenariocited by 0
  25. 2026A Semiparametric Framework for Stochastic Fundamental Diagram Modelingcited by 0