mlsanityData to 7 Oct 2026

Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook

arXiv 2303.02063 ↗First posted 3 Mar 2023cs.LGcited by 11

Not on the map. Why?

Abstract (arXiv)

For its robust predictive power (compared to pure physics-based models) and sample-efficient training (compared to pure deep learning models), physics-informed deep learning (PIDL), a paradigm hybridizing physics-based models and deep neural networks (DNN), has been booming in science and engineering fields. One key challenge of applying PIDL to various domains and problems lies in the design of a computational graph that integrates physics and DNNs. In other words, how physics are encoded into DNNs and how the physics and data components are represented. In this paper, we provide a variety of architecture designs of PIDL computational graphs and how these structures are customized to traffic state estimation (TSE), a central problem in transportation engineering. When observation data, problem type, and goal vary, we demonstrate potential architectures of PIDL computational graphs and compare these variants using the same real-world dataset.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 44 of its 133 references that are in the map. First posted on arXiv 3 Mar 2023.

Builds on

44 of 133 references.

References · 44

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2013Auto-Encoding Variational Bayescited by 3,980
  3. 2016Density estimation using Real NVPcited by 2,029
  4. 2020A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challengescited by 813
  5. 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
  6. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  7. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  8. 2020Discovering Symbolic Models from Deep Learning with Inductive Biasescited by 335
  9. 2016NIPS 2016 Tutorial: Generative Adversarial Networkscited by 284
  10. 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 233
  11. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  12. 2016Theory-guided Data Science: A New Paradigm for Scientific Discovery from Datacited by 169
32 more
  1. 2018Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problemscited by 144
  2. 2018Survey of multifidelity methods in uncertainty propagation, inference, and optimizationcited by 141
  3. 2018Physics-Informed Generative Adversarial Networks for Stochastic Differential Equationscited by 133
  4. 2018Adversarial Uncertainty Quantification in Physics-Informed Neural Networkscited by 120
  5. 2019An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applicationscited by 118
  6. 2018Deep Learning of Vortex Induced Vibrationscited by 74
  7. 2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 64
  8. 2021Meta-learning PINN loss functionscited by 51
  9. 2022STDEN: Towards Physics-Guided Neural Networks for Traffic Flow Predictioncited by 45
  10. 2020A Physics-Informed Deep Learning Paradigm for Car-Following Modelscited by 40
  11. 2021A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimationcited by 37
  12. 2021Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputationcited by 35
  13. 2021Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow modelscited by 34
  14. 2019Modular Meta-Learning with Shrinkagecited by 31
  15. 2020A Nonconvex Low-Rank Tensor Completion Model for Spatiotemporal Traffic Data Imputationcited by 27
  16. 2021Multifidelity Modeling for Physics-Informed Neural Networks (PINNs)cited by 25
  17. 2020A Survey on Autonomous Vehicle Control in the Era of Mixed-Autonomy: From Physics-Based to AI-Guided Driving Policy Learningcited by 24
  18. 2021PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physicscited by 21
  19. 2019ADMM for Efficient Deep Learning with Global Convergencecited by 20
  20. 2021Physics-informed Learning for Identification and State Reconstruction of Traffic Densitycited by 13
  21. 2018Survey on Multi-Access Edge Computing for Internet of Things Realizationcited by 12
  22. 2021Incorporating Kinematic Wave Theory into a Deep Learning Method for High-Resolution Traffic Speed Estimationcited by 12
  23. 2019Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEscited by 11
  24. 2022TrafficFlowGAN: Physics-informed Flow based Generative Adversarial Network for Uncertainty Quantificationcited by 11
  25. 2020Learning-based Traffic State Reconstruction using Probe Vehiclescited by 10
  26. 2019A cooperative game for automated learning of elasto-plasticity knowledge graphs and models with AI-guided experimentationcited by 9
  27. 2020A non-cooperative meta-modeling game for automated third-party calibrating, validating, and falsifying constitutive laws with parallelized adversarial attackscited by 8
  28. 2020Learning-based State Reconstruction for a Scalar Hyperbolic PDE under noisy Lagrangian Sensingcited by 7
  29. 2022Quantifying Uncertainty In Traffic State Estimation Using Generative Adversarial Networkscited by 7
  30. 2023Learning-based solutions to nonlinear hyperbolic PDEs: Empirical insights on generalization errorscited by 6
  31. 2020Model-Informed Machine Learning for Multi-component T2 Relaxometrycited by 5
  32. 2019Stabilizing Traffic via Autonomous Vehicles: A Continuum Mean Field Game Approachcited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 4; 2025: 3; 2026: 1.

11 papers.

  1. 2023Fourier neural operator for learning solutions to macroscopic traffic flow models: Application to the forward and inverse problemscited by 12
  2. 2024Online Test-Time Adaptation of Spatial-Temporal Traffic Flow Forecastingcited by 11
  3. 2025Position: Biology is the Challenge Physics-Informed ML Needs to Evolvecited by 4
  4. 2023Physics-informed Machine Learning for Calibrating Macroscopic Traffic Flow Modelscited by 3
  5. 2024Privacy-Preserving Data Fusion for Traffic State Estimation: A Vertical Federated Learning Approachcited by 2
  6. 2023Incorporating Nonlocal Traffic Flow Model in Physics-informed Neural Networkscited by 1
  7. 2024AI-Powered CPS-Enabled Vulnerable-User-Aware Urban Transportation Digital Twin: Methods and Applicationscited by 1
  8. 2024Scalable Learning of Segment-Level Traffic Congestion Functionscited by 0
  9. 2025Online Traffic Density Estimation using Physics-Informed Neural Networkscited by 0
  10. 2025Physics-informed deep operator network for traffic state estimationcited by 0
  11. 2026Physics-Informed Teacher-Student Ensemble Learning for Traffic State Estimation with a Varying Speed Limit Scenariocited by 0