IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i10p1571-d1652943.html
   My bibliography  Save this article

Physics-Informed Neural Networks for the Structural Analysis and Monitoring of Railway Bridges: A Systematic Review

Author

Listed:
  • Yuniel Martinez

    (Escuela de Ingeniería de Construcción y Transporte, Pontifica Universidad Católica de Valparaíso, Valparaíso 2362804, Chile
    These authors contributed equally to this work.)

  • Luis Rojas

    (Escuela de Ingeniería de Construcción y Transporte, Pontifica Universidad Católica de Valparaíso, Valparaíso 2362804, Chile
    These authors contributed equally to this work.)

  • Alvaro Peña

    (Escuela de Ingeniería de Construcción y Transporte, Pontifica Universidad Católica de Valparaíso, Valparaíso 2362804, Chile)

  • Matías Valenzuela

    (Escuela de Ingeniería de Construcción y Transporte, Pontifica Universidad Católica de Valparaíso, Valparaíso 2362804, Chile)

  • Jose Garcia

    (Escuela de Ingeniería de Construcción y Transporte, Pontifica Universidad Católica de Valparaíso, Valparaíso 2362804, Chile
    These authors contributed equally to this work.)

Abstract

Physics-informed neural networks (PINNs) offer a mesh-free approach to solving partial differential equations (PDEs) with embedded physical constraints. Although PINNs have gained traction in various engineering fields, their adoption for railway bridge analysis remains under-explored. To address this gap, a systematic review was conducted across Scopus and Web of Science (2020–2025), filtering records by relevance, journal impact, and language. From an initial pool, 120 articles were selected and categorised into nine thematic clusters that encompass computational frameworks, hybrid integration with conventional solvers, and domain decomposition strategies. Through natural language processing (NLP) and trend mapping, this review evidences a growing but fragmented research landscape. PINNs demonstrate promising capabilities in load distribution modelling, structural health monitoring, and failure prediction, particularly under dynamic train loads on multi-span bridges. However, methodological gaps persist in large-scale simulations, plasticity modelling, and experimental validation. Future work should focus on scalable PINN architectures, refined modelling of inelastic behaviours, and real-time data assimilation, ensuring robustness and generalisability through interdisciplinary collaboration.

Suggested Citation

  • Yuniel Martinez & Luis Rojas & Alvaro Peña & Matías Valenzuela & Jose Garcia, 2025. "Physics-Informed Neural Networks for the Structural Analysis and Monitoring of Railway Bridges: A Systematic Review," Mathematics, MDPI, vol. 13(10), pages 1-40, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1571-:d:1652943
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/10/1571/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/10/1571/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhang, Zhi-Yong & Zhang, Hui & Liu, Ye & Li, Jie-Ying & Liu, Cheng-Bao, 2023. "Generalized conditional symmetry enhanced physics-informed neural network and application to the forward and inverse problems of nonlinear diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Yubiao Sun & Qiankun Sun & Kan Qin, 2021. "Physics-Based Deep Learning for Flow Problems," Energies, MDPI, vol. 14(22), pages 1-24, November.
    3. Peng Zhi & Yuching Wu & Cheng Qi & Tao Zhu & Xiao Wu & Hongyu Wu, 2023. "Surrogate-Based Physics-Informed Neural Networks for Elliptic Partial Differential Equations," Mathematics, MDPI, vol. 11(12), pages 1-16, June.
    4. Qingyang Zhang & Xiaowei Guo & Xinhai Chen & Chuanfu Xu & Jie Liu, 2022. "PINN-FFHT: A physics-informed neural network for solving fluid flow and heat transfer problems without simulation data," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 33(12), pages 1-21, December.
    5. Valentino, Carmine & Pagano, Giovanni & Conte, Dajana & Paternoster, Beatrice & Colace, Francesco & Casillo, Mario, 2025. "Step-by-step time discrete Physics-Informed Neural Networks with application to a sustainability PDE model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 230(C), pages 541-558.
    6. Guozheng Wu & Fajie Wang & Lin Qiu, 2023. "Physics-Informed Neural Network For Solving Hausdorff Derivative Poisson Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(06), pages 1-15.
    7. Ruslan Abdulkadirov & Pavel Lyakhov & Nikolay Nagornov, 2023. "Survey of Optimization Algorithms in Modern Neural Networks," Mathematics, MDPI, vol. 11(11), pages 1-37, May.
    8. Chunyue Lv & Lei Wang & Chenming Xie, 2023. "A hybrid physics-informed neural network for nonlinear partial differential equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(06), pages 1-10, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yin, Yu-Hang & Lü, Xing, 2024. "Multi-parallelized PINNs for the inverse problem study of NLS typed equations in optical fiber communications: Discovery on diverse high-order terms and variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Wenbin Su & Wei Ren & Hui Sun & Canjie Liu & Xuhao Lu & Yingli Hua & Hongbo Wei & Han Jia, 2022. "Data-Based Flow Rate Prediction Models for Independent Metering Hydraulic Valve," Energies, MDPI, vol. 15(20), pages 1-12, October.
    3. Raoof Altaher & Hakan Koyuncu, 2024. "Novel Hybrid Optimization Techniques for Enhanced Generalization and Faster Convergence in Deep Learning Models: The NestYogi Approach to Facial Biometrics," Mathematics, MDPI, vol. 12(18), pages 1-23, September.
    4. Liu, Ye & Li, Jie-Ying & Zhang, Li-Sheng & Guo, Lei-Lei & Zhang, Zhi-Yong, 2024. "Symmetry group based domain decomposition to enhance physics-informed neural networks for solving partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    5. Tao Liu & Di Ouyang & Lianjun Guo & Ruofeng Qiu & Yunfei Qi & Wu Xie & Qiang Ma & Chao Liu, 2023. "Combination of Multigrid with Constraint Data for Inverse Problem of Nonlinear Diffusion Equation," Mathematics, MDPI, vol. 11(13), pages 1-15, June.
    6. Ruslan Abdulkadirov & Pavel Lyakhov & Denis Butusov & Nikolay Nagornov & Dmitry Reznikov & Anatoly Bobrov & Diana Kalita, 2025. "Enhancing Unmanned Aerial Vehicle Object Detection via Tensor Decompositions and Positive–Negative Momentum Optimizers," Mathematics, MDPI, vol. 13(5), pages 1-22, March.
    7. Zhiming Li & Shuangshuang Wu & Wenbai Chen & Fuchun Sun, 2024. "Extrapolation of Physics-Inspired Deep Networks in Learning Robot Inverse Dynamics," Mathematics, MDPI, vol. 12(16), pages 1-19, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1571-:d:1652943. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.