On the Limitations of Physics-Informed Deep Learning: Illustrations Using First-Order Hyperbolic Conservation Law-Based Traffic Flow Models
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...
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Open Journal of Intelligent Transportation Systems |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10105558/ |
| _version_ | 1797837377975091200 |
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| author | Archie J. Huang Shaurya Agarwal |
| author_facet | Archie J. Huang Shaurya Agarwal |
| author_sort | Archie J. Huang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T15:24:55Z |
| format | Article |
| id | doaj.art-83f8f571d2e240e0b827af7415738eda |
| institution | Directory Open Access Journal |
| issn | 2687-7813 |
| language | English |
| last_indexed | 2024-04-09T15:24:55Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of Intelligent Transportation Systems |
| spelling | doaj.art-83f8f571d2e240e0b827af7415738eda2023-04-28T23:00:43ZengIEEEIEEE Open Journal of Intelligent Transportation Systems2687-78132023-01-01427929310.1109/OJITS.2023.326802610105558On the Limitations of Physics-Informed Deep Learning: Illustrations Using First-Order Hyperbolic Conservation Law-Based Traffic Flow ModelsArchie J. Huanghttps://orcid.org/0000-0001-6736-5627Shaurya Agarwalhttps://orcid.org/0000-0001-7754-6341Since 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.https://ieeexplore.ieee.org/document/10105558/Physics-informed deep learningneural network trainingpartial differential equationstransportation modelsscalar conservation lawsPIDL |
| spellingShingle | Archie J. Huang Shaurya Agarwal On the Limitations of Physics-Informed Deep Learning: Illustrations Using First-Order Hyperbolic Conservation Law-Based Traffic Flow Models IEEE Open Journal of Intelligent Transportation Systems Physics-informed deep learning neural network training partial differential equations transportation models scalar conservation laws PIDL |
| title | On the Limitations of Physics-Informed Deep Learning: Illustrations Using First-Order Hyperbolic Conservation Law-Based Traffic Flow Models |
| title_full | On the Limitations of Physics-Informed Deep Learning: Illustrations Using First-Order Hyperbolic Conservation Law-Based Traffic Flow Models |
| title_fullStr | On the Limitations of Physics-Informed Deep Learning: Illustrations Using First-Order Hyperbolic Conservation Law-Based Traffic Flow Models |
| title_full_unstemmed | On the Limitations of Physics-Informed Deep Learning: Illustrations Using First-Order Hyperbolic Conservation Law-Based Traffic Flow Models |
| title_short | On the Limitations of Physics-Informed Deep Learning: Illustrations Using First-Order Hyperbolic Conservation Law-Based Traffic Flow Models |
| title_sort | on the limitations of physics informed deep learning illustrations using first order hyperbolic conservation law based traffic flow models |
| topic | Physics-informed deep learning neural network training partial differential equations transportation models scalar conservation laws PIDL |
| url | https://ieeexplore.ieee.org/document/10105558/ |
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