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Enhancing Computational Fluid Dynamics with Machine Learning

arXiv 2110.02085 ↗First posted 5 Oct 2021physics.flu-dyn cs.LG physics.comp-phcited by 137

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Abstract (arXiv)

Machine learning is rapidly becoming a core technology for scientific computing, with numerous opportunities to advance the field of computational fluid dynamics. In this Perspective, we highlight some of the areas of highest potential impact, including to accelerate direct numerical simulations, to improve turbulence closure modeling, and to develop enhanced reduced-order models. We also discuss emerging areas of machine learning that are promising for computational fluid dynamics, as well as some potential limitations that should be taken into account.

Key facts. Cited by 137 papers in the map (data through 7 Oct 2026). Builds on 35 of its 156 references that are in the map. First posted on arXiv 5 Oct 2021.

Builds on

35 of 156 references.

References · 35

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  2. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
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  10. 2018Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networkscited by 155
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  1. 2018A Tour of Reinforcement Learning: The View from Continuous Controlcited by 129
  2. 2017Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systemscited by 125
  3. 2020Incorporating Symmetry into Deep Dynamics Models for Improved Generalizationcited by 123
  4. 2019Machine learning for molecular simulationcited by 109
  5. 2019The role of artificial intelligence in achieving the Sustainable Development Goalscited by 100
  6. 2019Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systemscited by 96
  7. 2020A fast and accurate physics-informed neural network reduced order model with shallow masked autoencodercited by 80
  8. 2021Physics-informed neural networks for solving Reynolds-averaged Navierunicodex2013Stokes equationscited by 68
  9. 2019Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Predictioncited by 67
  10. 2021The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?cited by 61
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 9; 2023: 40; 2024: 37; 2025: 31; 2026: 20.

137 papers.

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  2. 2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equationscited by 87
  3. 2023β-Variational autoencoders and transformers for reduced-order modelling of fluid flowscited by 76
  4. 2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 74
  5. 2023A graph convolutional autoencoder approach to model order reduction for parametrized PDEscited by 44
  6. 2024AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fieldscited by 38
  7. 2024Data-Efficient Operator Learning via Unsupervised Pretraining and In-Context Learningcited by 32
  8. 2023Self-Supervised Learning with Lie Symmetries for Partial Differential Equationscited by 29
  9. 2023Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generationcited by 28
  10. 2023The transformative potential of machine learning for experiments in fluid mechanicscited by 26
  11. 2024Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operatorscited by 25
  12. 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
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  2. 2022Physics-informed deep-learning applications to experimental fluid mechanicscited by 21
  3. 2023Machine Learning for Partial Differential Equationscited by 20
  4. 2022Improving aircraft performance using machine learning: a reviewcited by 19
  5. 2023SuperBench: A Super-Resolution Benchmark Dataset for Scientific Machine Learningcited by 18
  6. 2023Earthfarseer: Versatile Spatio-Temporal Dynamical Systems Modeling in One Modelcited by 16
  7. 2022Residual-based physics-informed transfer learning: A hybrid method for accelerating long-term CFD simulations via deep learningcited by 14
  8. 2024AhmedML: High-Fidelity Computational Fluid Dynamics Dataset for Incompressible, Low-Speed Bluff Body Aerodynamicscited by 13
  9. 2024Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operatorcited by 12
  10. 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11
  11. 2023XLB: A differentiable massively parallel lattice Boltzmann library in Pythoncited by 11
  12. 2024The impact of internal variability on benchmarking deep learning climate emulatorscited by 11
  13. 2024NeuralDEM -- Real-time Simulation of Industrial Particulate Flowscited by 10
  14. 2024Inverse Problems with Diffusion Models: A MAP Estimation Perspectivecited by 9
  15. 2023Stochastic Latent Transformer: Efficient Modelling of Stochastically Forced Zonal Jetscited by 8
  16. 2022Local neural operator for solving transient partial differential equations on varied domainscited by 7
  17. 2022Emerging trends in machine learning for computational fluid dynamicscited by 7
  18. 2023Fluid Dynamics Network: Topology-Agnostic 4D Reconstruction via Fluid Dynamics Priorscited by 7
  19. 2023Invariant preservation in machine learned PDE solvers via error correctioncited by 7
  20. 2024JAX-Fluids 2.0: Towards HPC for Differentiable CFD of Compressible Two-phase Flowscited by 7
  21. 2024A conditional latent autoregressive recurrent model for generation and forecasting of beam dynamics in particle acceleratorscited by 7
  22. 2025Generative emulation of chaotic dynamics with coherent priorcited by 7
  23. 2023A Deep Learning algorithm to accelerate Algebraic Multigrid methods in Finite Element solvers of 3D elliptic PDEscited by 6
  24. 2024Generative prediction of flow fields around an obstacle using the diffusion modelcited by 6
  25. 2024Time-inversion of spatiotemporal beam dynamics using uncertainty-aware latent evolution reversalcited by 6
  26. 2025When is a System Discoverable from Data? Discovery Requires Chaoscited by 6
  27. 2023RANS-PINN based Simulation Surrogates for Predicting Turbulent Flowscited by 5
  28. 2023Gradient-free online learning of subgrid-scale dynamics with neural emulatorscited by 5
  29. 2023DiffHybrid-UQ: Uncertainty Quantification for Differentiable Hybrid Neural Modelingcited by 5
  30. 2024FLUID-LLM: Learning Computational Fluid Dynamics with Spatiotemporal-aware Large Language Modelscited by 5
  31. 2024Navigation in a simplified Urban Flow through Deep Reinforcement Learningcited by 5
  32. 2025Harnessing Equivariance: Modeling Turbulence with Graph Neural Networkscited by 5
  33. 2025CP4SBI: Local Conformal Calibration of Credible Sets in Simulation-Based Inferencecited by 5
  34. 2023Adaptive learning of effective dynamics: Adaptive real-time, online modeling for complex systemscited by 4
  35. 2023A reinforcement learning strategy for p-adaptation in high order solverscited by 4
  36. 2023Physics-informed neural networks modeling for systems with moving immersed boundaries: application to an unsteady flow past a plunging foilcited by 4
  37. 2023Physics-Preserving AI-Accelerated Simulations of Plasma Turbulencecited by 4
  38. 2024Reduced-order modeling of unsteady fluid flow using neural network ensemblescited by 4

50 most cited of 137 All 137 (JSON)