Physics-informed Learning for Identification and State Reconstruction of Traffic Density

Barreau, Matthieu; Aguiar, Miguel; Liu, John; Johansson, Karl Henrik

doi:10.1109/cdc45484.2021.9683295

Cited by 17 publications

(4 citation statements)

References 15 publications

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“…However, it can be seen that till now, PINN has very few applications in the field of transportation. In the current stage, there is only some progress in identifying traffic density [64], vehicle following models [65], estimating traffic states [66][67][68], and solving incompressible traffic flow fluid equations [69].…”

Section: Solving Pdes Based On Pinnmentioning

confidence: 99%

Compressible Non-Newtonian Fluid Based Road Traffic Flow Equation Solved by Physical-Informed Rational Neural Network

Yang,

Li,

Nai

et al. 2024

IEEE Access

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The study of road traffic flow theory utilizes physics and applied mathematics to analyze relevant parameters and their relationships quanlitatively and quantitatively, in order to explore their dynamic changes. The fluid dynamics model used for traffic flow analysis is highly favored by scholars due to its solid mathematical foundation and good simulation results. However, existing models have two main shortcomings: firstly, existing research is mostly limited to non-viscoelastic fluid equation or incompressible non-Newtonian fluid equation, making it difficult to accurately describe the viscosity state and micro cluster properties of the actual traffic flow; secondly, the existing non-Newtonian fluid partial differential equations (PDEs) rely heavily on the finite element method (FEM) for solving, requiring higher computational cost, larger storage space, and more constraint conditions. Thus, in this paper, a traffic flow equation based on compressible non-Newtonian fluid has been constructed, and it has been solved by using physical-informed rational neural network (PIRNN) and noise heavy-ball acceleration gradient descent (NHAGD) to ensure learning and training speed and accuracy. Numerical results indicate that the proposed method can truly reflect the gradual change process in the viscosity of traffic flow, and has better solving performance than traditional FEM and physical-informed neural network (PINN) with activation functions; under the same conditions, the prediction error of the proposed method is also smaller than that of traditional traffic flow models.

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Section: Solving Pdes Based On Pinnmentioning

confidence: 99%

Compressible Non-Newtonian Fluid Based Road Traffic Flow Equation Solved by Physical-Informed Rational Neural Network

Yang,

Li,

Nai

et al. 2024

IEEE Access

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“…Calibrate FD Fit parameters associated with a pre-selected FD along with parameters of DNNs [26][27][28] Density at u = 0 Density at max q Velocity at maximum…”

Section: Joint Trainingmentioning

confidence: 99%

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

Shi

et al. 2023

Algorithms

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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 (DNNs), 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 the physics is encoded into DNNs and how the physics and data components are represented. In this paper, we offer an overview of 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.

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“…Among the available approaches, deep learning (DL) neural network is a powerful machine learning method increasingly used in many TSE applications [27]- [29]. However, DL neural network also comes with shortcomings, such as the high requirement of training data and computing power, over-fitting, and transferability issues, limiting its appeal for time-critical applications, which calls for the role of physics in aiding the training process of a neural network in TSE [30], [31].…”

Section: Introductionmentioning

confidence: 99%

On the Limitations of Physics-Informed Deep Learning: Illustrations Using First-Order Hyperbolic Conservation Law-Based Traffic Flow Models

Huang

Agarwal

2023

IEEE Open J. Intell. Transp. Syst.

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Since its introduction in 2017, physics-informed deep learning (PIDL) has garnered growing popularity in understanding the systems governed by physical laws in terms of partial differential equations (PDEs). However, empirical evidence points to the limitations of PIDL for learning certain types of PDEs. In this paper, we (a) present the challenges in training PIDL architecture, (b) contrast the performance of PIDL architecture in learning a first order scalar hyperbolic conservation law and its parabolic counterpart, (c) investigate the effect of training data sampling, which corresponds to various sensing scenarios in traffic networks, (d) comment on the implications of PIDL limitations for traffic flow estimation and prediction in practice. Case studies present the contrast in PIDL results between learning the traffic flow model (LWR PDE) and its diffusive variation. The outcome indicates that PIDL experiences significant challenges in learning the hyperbolic LWR equation due to the non-smoothness of its solution. Conversely, the architecture with parabolic PDE, augmented with the diffusion term, leads to the successful reassembly of the density data even with the shockwaves present. The paper concludes by providing a discussion on recent assessments of reasons behind the challenge PIDL encounters with hyperbolic PDEs and the corresponding mitigation strategies.

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Physics-informed Learning for Identification and State Reconstruction of Traffic Density

Cited by 17 publications

References 15 publications

Compressible Non-Newtonian Fluid Based Road Traffic Flow Equation Solved by Physical-Informed Rational Neural Network

Compressible Non-Newtonian Fluid Based Road Traffic Flow Equation Solved by Physical-Informed Rational Neural Network

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

On the Limitations of Physics-Informed Deep Learning: Illustrations Using First-Order Hyperbolic Conservation Law-Based Traffic Flow Models

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