Science machine learning
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Scientific machine learning (SciML) is a novel interdisciplinary field at the intersection of scientific computing and machine learning. SciML integrates physics-based modeling and numerical simulation to address complex modeling, simulation, and inference tasks in the natural and engineering sciences[1][2]. This field aims to produce methods that are robust, interpretable, scalable, and physically consistent[3][4].
Overview
SciML combines traditional physical modeling and numerical analysis, often expressed as numerical solutions of partial differential equations (PDEs)[5], with modern techniques from machine learning such as neural networks and deep learning. By leveraging both paradigms, SciML methods seek to retain the reliability and theoretical guarantees of scientific computing while exploiting the flexibility and representation capacity of data-driven models.
Key objectives of SciML include improved model accuracy, reduced computational cost for simulation and inference, enhanced generalizability across regimes, and increased interpretability of learned models. SciML is increasingly applied in domains such as computational fluid dynamics[6], materials science[7], automation and control, energy management, and sustainable mobility[8].
Methods
SciML has some major methods:
- Physics-informed models: methods that enforce governing equations, boundary conditions, or conservation laws within learning algorithms, e.g. Physics-informed neural networks (PINNs)[9][10][11].
- Operator learning: methods that learn mappings between function spaces (operators) rather than finite-dimensional parameter mappings, useful for surrogate modeling of PDE solvers[12].
- Hybrid modeling: combinations of first-principles (white-box) models and data-driven (black-box) components to balance interpretability and flexibility[13].
- Uncertainty quantification: methods that represent and propagate uncertainty in predictions, enabling risk-aware decision making[14][15][16].
See also
References
- ↑ Huang, L., Vrinceanu, D., Wang, Y., Kulathunga, N., & Ranasinghe, N. (2021). Discovering Nonlinear Dynamics Through Scientific Machine Learning. Lecture Notes in Networks and Systems, 332, 235–251.
- ↑ 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. USDOE Office of Science (SC), Washington, DC (United States). Page 8
- ↑ Dietrich, F., & Schilders, W. (2025). Scientific machine learning. Mathematische Semesterberichte, 72(2), 89-115.
- ↑ Müller, J., & Zeinhofer, M. (2024). Position: Optimization in SciML should employ the function space geometry. arXiv preprint arXiv:2402.07318.
- ↑ Rackauckas, C., Ma, Y., Martensen, J., Warner, C., Zubov, K., Supekar, R., ... & Edelman, A. (2020). Universal differential equations for scientific machine learning. arXiv preprint arXiv:2001.04385.
- ↑ 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.
- ↑ 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.
- ↑ Dietrich, F., & Schilders, W. (2025). Scientific machine learning. Mathematische Semesterberichte, 1-27.
- ↑ Dietrich, F., & Schilders, W. (2025). Scientific machine learning. Mathematische Semesterberichte, 72(2), 89-115.
- ↑ Iwema, J. (2024). Scientific Machine Learning. Wageningen University & Research (Jan. 2023). url: https://sciml. wur. nl/reviews/sciml/sciml. html.
- ↑ Meng, C., Griesemer, S., Cao, D., Seo, S., & Liu, Y. (2025). When physics meets machine learning: A survey of physics-informed machine learning. Machine Learning for Computational Science and Engineering, 1(1), 20.
- ↑ Dietrich, F., & Schilders, W. (2025). Scientific machine learning. Mathematische Semesterberichte, 72(2), 89-115.
- ↑ Dietrich, F., & Schilders, W. (2025). Scientific machine learning. Mathematische Semesterberichte, 72(2), 89-115.
- ↑ Dietrich, F., & Schilders, W. (2025). Scientific machine learning. Mathematische Semesterberichte, 72(2), 89-115.
- ↑ Zou, Z., Meng, X., Psaros, A. F., & Karniadakis, G. E. (2024). NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators. SIAM Review, 66(1), 161-190.
- ↑ Kong, L., Kamarthi, H., Chen, P., Prakash, B. A., & Zhang, C. (2023, August). Uncertainty quantification in deep learning. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (pp. 5809-5810).
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