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A Review of Physics-Informed Machine Learning in Fluid Mechanics

Author

Listed:
  • Pushan Sharma

    (Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA)

  • Wai Tong Chung

    (Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA)

  • Bassem Akoush

    (Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA)

  • Matthias Ihme

    (Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
    Department of Photon Science, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA)

Abstract

Physics-informed machine-learning (PIML) enables the integration of domain knowledge with machine learning (ML) algorithms, which results in higher data efficiency and more stable predictions. This provides opportunities for augmenting—and even replacing—high-fidelity numerical simulations of complex turbulent flows, which are often expensive due to the requirement of high temporal and spatial resolution. In this review, we (i) provide an introduction and historical perspective of ML methods, in particular neural networks (NN), (ii) examine existing PIML applications to fluid mechanics problems, especially in complex high Reynolds number flows, (iii) demonstrate the utility of PIML techniques through a case study, and (iv) discuss the challenges and opportunities of developing PIML for fluid mechanics.

Suggested Citation

  • Pushan Sharma & Wai Tong Chung & Bassem Akoush & Matthias Ihme, 2023. "A Review of Physics-Informed Machine Learning in Fluid Mechanics," Energies, MDPI, vol. 16(5), pages 1-21, February.
    • Handle: RePEc:gam:jeners:v:16:y:2023:i:5:p:2343-:d:1083835
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    References listed on IDEAS

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    1. Volodymyr Mnih & Koray Kavukcuoglu & David Silver & Andrei A. Rusu & Joel Veness & Marc G. Bellemare & Alex Graves & Martin Riedmiller & Andreas K. Fidjeland & Georg Ostrovski & Stig Petersen & Charle, 2015. "Human-level control through deep reinforcement learning," Nature, Nature, vol. 518(7540), pages 529-533, February.
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    Cited by:

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    2. Ivan S. Maksymov, 2023. "Analogue and Physical Reservoir Computing Using Water Waves: Applications in Power Engineering and Beyond," Energies, MDPI, vol. 16(14), pages 1-26, July.
    3. Zhixiang Liu & Yuanji Chen & Ge Song & Wei Song & Jingxiang Xu, 2023. "Combination of Physics-Informed Neural Networks and Single-Relaxation-Time Lattice Boltzmann Method for Solving Inverse Problems in Fluid Mechanics," Mathematics, MDPI, vol. 11(19), pages 1-29, October.
    4. Raphael Hartner & Martin Kozek & Stefan Jakubek, 2026. "Multi-task learning with state propagation for quality forecasts in polymer extrusion lines," Journal of Intelligent Manufacturing, Springer, vol. 37(4), pages 1701-1715, April.
    5. Vo Thanh, Hung, 2026. "Physics informed machine learning for prediction hydrogen solubility in aqueous solution to implication for underground hydrogen storage formations," Renewable Energy, Elsevier, vol. 256(PG).
    6. Zhang, Dongkuan & Anjum, Tanzila & Chu, Zhiqiang & Cross, Jeffrey S. & Ji, Guozhao, 2025. "Simulation of multiphase flow with thermochemical reactions: A review of computational fluid dynamics (CFD) theory to AI integration," Renewable and Sustainable Energy Reviews, Elsevier, vol. 221(C).
    7. Zhang, Qingang & Long, Wenjun & Wang, Ruihang & Cao, Zhiwei & Wang, Zhaoyang & Yan, Yuejun & Wen, Yonggang, 2025. "CAPER: Dual-level physics-data fusion with modular metamodels for reliable generalization in predictive digital twins," Applied Energy, Elsevier, vol. 398(C).
    8. Hiyam Farhat & Amani Altarawneh, 2025. "Physics-Informed Machine Learning for Intelligent Gas Turbine Digital Twins: A Review," Energies, MDPI, vol. 18(20), pages 1-27, October.
    9. Sergiy Plankovskyy & Yevgen Tsegelnyk & Nataliia Shyshko & Igor Litvinchev & Tetyana Romanova & José Manuel Velarde Cantú, 2025. "Review of Physics-Informed Neural Networks: Challenges in Loss Function Design and Geometric Integration," Mathematics, MDPI, vol. 13(20), pages 1-51, October.

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