mlsanityData to 7 Oct 2026

Machine Learning for Fluid Mechanics

arXiv 1905.11075 ↗First posted 27 May 2019physics.flu-dyn cs.LG stat.MLcited by 380

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Abstract (arXiv)

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from field measurements, experiments and large-scale simulations at multiple spatiotemporal scales. Machine learning offers a wealth of techniques to extract information from data that could be translated into knowledge about the underlying fluid mechanics. Moreover, machine learning algorithms can augment domain knowledge and automate tasks related to flow control and optimization. This article presents an overview of past history, current developments, and emerging opportunities of machine learning for fluid mechanics. It outlines fundamental machine learning methodologies and discusses their uses for understanding, modeling, optimizing, and controlling fluid flows. The strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experimentation, and simulation. Machine learning provides a powerful information processing framework that can enrich, and possibly even transform, current lines of fluid mechanics research and industrial applications.

Key facts. Cited by 380 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 May 2019.

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Citing papers per year: 2020: 1; 2021: 60; 2022: 62; 2023: 69; 2024: 48; 2025: 72; 2026: 68.

380 papers.

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  1. 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
  2. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
  3. 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
  4. 2021Modern Koopman Theory for Dynamical Systemscited by 269
  5. 2023Neural Operators for Accelerating Scientific Simulations and Designcited by 218
  6. 2021Enhancing Computational Fluid Dynamics with Machine Learningcited by 137
  7. 2021PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEscited by 97
  8. 2023β-Variational autoencoders and transformers for reduced-order modelling of fluid flowscited by 76
  9. 2022Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoderscited by 58
  10. 2021Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learningcited by 55
  11. 2025AB-UPT: Scaling Neural CFD Surrogates for High-Fidelity Automotive Aerodynamics Simulations via Anchored-Branched Universal Physics Transformerscited by 49
  12. 2021Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flowscited by 44
38 more
  1. 2021Data-driven discovery of Green's functions with human-understandable deep learningcited by 43
  2. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
  3. 2022Machine Learning in Aerodynamic Shape Optimizationcited by 39
  4. 2021Physics and Equality Constrained Artificial Neural Networks: Application to Forward and Inverse Problems with Multi-fidelity Data Fusioncited by 38
  5. 2022Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal datacited by 37
  6. 2022JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flowscited by 36
  7. 2022A posteriori learning for quasi-geostrophic turbulence parametrizationcited by 36
  8. 2021Symplectic Learning for Hamiltonian Neural Networkscited by 35
  9. 2021Simulating progressive intramural damage leading to aortic dissection using an operator-regression neural networkcited by 35
  10. 2022SVD Perspectives for Augmenting DeepONet Flexibility and Interpretabilitycited by 35
  11. 2024Data-Efficient Operator Learning via Unsupervised Pretraining and In-Context Learningcited by 32
  12. 2023Synthetic Lagrangian Turbulence by Generative Diffusion Modelscited by 31
  13. 2023Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flowscited by 30
  14. 2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 29
  15. 2023Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generationcited by 28
  16. 2021Robust Optimization and Validation of Echo State Networks for learning chaotic dynamicscited by 27
  17. 2023The transformative potential of machine learning for experiments in fluid mechanicscited by 26
  18. 2022Adaptive Self-supervision Algorithms for Physics-informed Neural Networkscited by 24
  19. 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
  20. 2024HAMLET: Graph Transformer Neural Operator for Partial Differential Equationscited by 24
  21. 2023Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Modelscited by 22
  22. 2022Physics-informed deep-learning applications to experimental fluid mechanicscited by 21
  23. 2023Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learningcited by 21
  24. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  25. 2022Dimensionally Consistent Learning with Buckingham Picited by 20
  26. 2022Explaining the physics of transfer learning a data-driven subgrid-scale closure to a different turbulent flowcited by 20
  27. 2023Learning Reduced-Order Models for Cardiovascular Simulations with Graph Neural Networkscited by 20
  28. 2023Machine Learning for Partial Differential Equationscited by 20
  29. 2025GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformercited by 20
  30. 2021Deep Learning Enhanced Dynamic Mode Decompositioncited by 19
  31. 2022Improving aircraft performance using machine learning: a reviewcited by 19
  32. 2021Solving time dependent Fokker-Planck equations via temporal normalizing flowcited by 17
  33. 2022Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulationscited by 16
  34. 2024Generative Learning of the Solution of Parametric Partial Differential Equations Using Guided Diffusion Models and Virtual Observationscited by 16
  35. 2021Assessments of epistemic uncertainty using Gaussian stochastic weight averaging for fluid-flow regressioncited by 15
  36. 2023MMGP: a Mesh Morphing Gaussian Process-based machine learning method for regression of physical problems under non-parameterized geometrical variabilitycited by 15
  37. 2023Deep learning probability flows and entropy production rates in active mattercited by 15
  38. 2021Machine Learning-Based Optimal Mesh Generation in Computational Fluid Dynamicscited by 14

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