The DOI matches its Crossref record; 43 of the 43 references it cites were found in a registry or an index.
Physics-informed neural networks (PINNs) for fluid mechanics: a review
Open accessAbstract
Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier–Stokes equations (NSE), we still cannot incorporate seamlessly noisy data into existing algorithms, mesh-generation is complex, and we cannot tackle high-dimensional problems governed by parametrized NSE. Moreover, solving inverse flow problems is often prohibitively expensive and requires complex and expensive formulations and new computer codes. Here, we review flow physics-informed learning, integrating seamlessly data and mathematical models, and implement them using physics-informed neural networks (PINNs). We demonstrate the effectiveness of PINNs for inverse problems related to three-dimensional wake flows, supersonic flows, and biomedical flows.
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Cites
Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019) · Journal of Computational Physics · doi:10.1016/j.jcp.2018.10.045 · Cited by 20,384
Self-citationBrooks, A. N., & Hughes, T. J. R. (1982) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(82)90071-8 · Cited by 5,332
Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
Raissi, M., Yazdani, A., & Karniadakis, G. E. (2020) · Science · doi:10.1126/science.aaw4741 · Cited by 2,103
Self-citationSmoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments
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Self-citationPhysics-Informed Neural Networks for Heat Transfer Problems
Cai, S., Wang, Z., Wang, S., Perdikaris, P., & Karniadakis, G. E. (2021) · Journal of Heat Transfer · doi:10.1115/1.4050542 · Cited by 1,312
Self-citationPhysics-informed neural networks for high-speed flows
Mao, Z., Jagtap, A. D., & Karniadakis, G. E. (2020) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2019.112789 · Cited by 1,282
Self-citationJin, X., Cai, S., Li, H., & Karniadakis, G. E. (2021) · Journal of Computational Physics · doi:10.1016/j.jcp.2020.109951 · Cited by 1,210
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Self-citation
Cited by
Physics-informed neural networks for solving Reynolds-averaged Navier–Stokes equations
Eivazi, H., Tahani, M., Schlatter, P., & Vinuesa, R. (2022) · Physics of Fluids · doi:10.1063/5.0095270 · Cited by 490
Understanding Physics-Informed Neural Networks: Techniques, Applications, Trends, and Challenges
Farea, A., Yli-Harja, O., & Emmert-Streib, F. (2024) · AI · doi:10.3390/ai5030074 · Cited by 259
Machine Learning for Smart and Energy-Efficient Buildings
Das, H. P., Lin, Y.-W., Agwan, U., Spangher, L., Devonport, A., Yang, Y., Drgoňa, J., Chong, A., Schiavon, S., & Spanos, C. J. (2024) · Environmental Data Science · doi:10.1017/eds.2023.43 · Cited by 78
Du, Z., & Lu, R. (2025) · Batteries · doi:10.3390/batteries11060204 · Cited by 58
Metadata
- Authors
- Cai, S., Mao, Z., Wang, Z., Yin, M., & Karniadakis, G. E.
- Venue
- Acta Mechanica Sinica
- Published
- 2021-12
- Volume
- 37
- Issue
- 12
- Pages
- 1727-1738
- ISSN
- 0567-7718 (ISSN-L)
- 1614-3116
- OpenAlex
- W4220717841
- Cited by
- 2,084
- References
- 43
- FWCI
- 82.76
- Type
- journal article
- Language
- en
- Open access
- green
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