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Scientific machine learning (SciML or SML[1][2][3]) is an interdisciplinary field that combines scientific computing and machine learning to address complicated tasks in modeling, simulation, and inference in the natural and engineering sciences.[4][5][6] In practice, SciML combines traditional physical modeling and numerical analysis, often represented as numerical solutions of partial differential equations (PDEs),[7] with the participation of machine learning, neural networks and deep learning. The purpose of SciML is to maintain the reliability and flexibility of scientific computing and machine learning models. SciML appears in many fields, such as computational fluid dynamics,[8] materials science,[9] automation and control, energy management, and sustainable mobility.[6]

History

An early work mentioned scientific machine learning as a broader field of machine learning,[10] while another one discussed the challenges of applying it to train models on massive data.[11] In 2018, Nathan Baker and his colleagues introduced the concept of scientific machine learning as SciML, in which they stated it is a key part of artificial intelligence and computational technology that trains models on scientific data for augmenting/automating human reasoning and discovery. They also showed scope, definitions, and motivation, impacts of scientific machine learning.[12]

Challenges

There are several challenges that SciML must deal with despite its certain successes. That are, the missing of theory foundations for generalization with high-dimensional and sparse data, the limitation in deploying to scalability of domain knowledge, and the ability in maintaining physical consistency, interpretability, and robustness with changes.[13]

See also

References

  1. ^ Giampaolo, F.; De Rosa, M.; Qi, P.; Izzo, S.; Cuomo, S. (2022). "Physics-informed neural networks approach for 1D and 2D Gray-Scott systems". Advanced Modeling and Simulation in Engineering Sciences. 9 (1): 5. doi:10.1186/s40323-022-00209-7 (inactive 17 October 2025).{{cite journal}}: CS1 maint: DOI inactive as of October 2025 (link)
  2. ^ Sattari, K.; Eddy, L.; Beckham, J. L.; Wyss, K. M.; Byfield, R.; Qian, L.; Lin, J. (2023). "A scientific machine learning framework to understand flash graphene synthesis". Digital Discovery. 2 (4): 1209–1218. doi:10.1039/D3DD00141D (inactive 17 October 2025).{{cite journal}}: CS1 maint: DOI inactive as of October 2025 (link)
  3. ^ Cyr, E. C.; Beckwith, K.; Siefert, C.; Sentz, P.; Olson, L.; Guenther, S.; Schroder, J. B. (2019). Towards Scalable Scientific Machine Learning: Motivation and an Approach (Report). Albuquerque, NM, United States: Sandia National Laboratories (SNL-NM). OSTI 1501785. SAND2019-1957C.
  4. ^ Huang, L.; Vrinceanu, D.; Wang, Y.; Kulathunga, N.; Ranasinghe, N. (2021). "Discovering Nonlinear Dynamics Through Scientific Machine Learning". Lecture Notes in Networks and Systems. Vol. 332. pp. 235–251.
  5. ^ Baker, N.; Alexander, F.; Bremer, T.; Hagberg, A.; Kevrekidis, Y.; Najm, H.; Lee, S. (2019). Workshop report on basic research needs for scientific machine learning: Core technologies for artificial intelligence (Report). Washington, DC: USDOE Office of Science (SC). p. 8.
  6. ^ a b Dietrich, F.; Schilders, W. (2025). "Scientific machine learning". Mathematische Semesterberichte. 72 (2): 89–115. doi:10.1007/s00591-025-00399-4.
  7. ^ Rackauckas, C.; Ma, Y.; Martensen, J.; Warner, C.; Zubov, K.; Supekar, R.; Edelman, A. (2020). "Universal differential equations for scientific machine learning". arXiv:2001.04385 [cs.LG].
  8. ^ Caron, C.; Lauret, P.; Bastide, A. (2025). "Machine Learning to speed up Computational Fluid Dynamics engineering simulations for built environments: A review". Building and Environment. 267 112229. Bibcode:2025BuEnv.26712229C. doi:10.1016/j.buildenv.2024.112229.
  9. ^ Choudhary, K.; DeCost, B.; Chen, C.; Jain, A.; Tavazza, F.; Cohn, R.; Wolverton, C. (2022). "Recent advances and applications of deep learning methods in materials science". npj Computational Materials. 8 (1): 59. arXiv:2110.14820. Bibcode:2022npjCM...8...59C. doi:10.1038/s41524-022-00734-6.
  10. ^ Duraisamy, Karthik (2015). CDS&E: Formalisms and Tools for Data-enabled Turbulence Modeling (Report). Directorate for Engineering. National Science Foundation (NSF). Retrieved 17 October 2025.
  11. ^ Lunga, Delilah D.; Page, David L.; Hughes, D. (2018). Generalizing Semi-supervised and Unsupervised Learning for Domain Adaptation with Very Large Scientific Data (Report). Oak Ridge, TN, United States: Oak Ridge National Laboratory (ORNL). OSTI 1474564. Retrieved 17 October 2025.
  12. ^ Baker, Nathan; Alexander, Francis; Bremer, Thomas; Hagberg, Aric; Kevrekidis, Yannis; Najm, Habib; Lee, Samuel (2019). Workshop Report on Basic Research Needs for Scientific Machine Learning: Core Technologies for Artificial Intelligence (Report). Washington, DC, United States: U.S. Department of Energy, Office of Science (SC). OSTI 1478744. Retrieved 17 October 2025.
  13. ^ Sattari, K.; Eddy, L.; Beckham, J. L.; Wyss, K. M.; Byfield, R.; Qian, L.; Lin, J. (2023). "A scientific machine learning framework to understand flash graphene synthesis". Digital Discovery. 2 (4): 1209–1218. doi:10.1039/D3DD00141D (inactive 17 October 2025).{{cite journal}}: CS1 maint: DOI inactive as of October 2025 (link)
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