mlsanityData to 7 Oct 2026

Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey

arXiv 2408.12171 ↗First posted 22 Aug 2024cs.LGcited by 27

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Abstract (arXiv)

This paper explores the recent advancements in enhancing Computational Fluid Dynamics (CFD) tasks through Machine Learning (ML) techniques. We begin by introducing fundamental concepts, traditional methods, and benchmark datasets, then examine the various roles ML plays in improving CFD. The literature systematically reviews papers in recent five years and introduces a novel classification for forward modeling: Data-driven Surrogates, Physics-Informed Surrogates, and ML-assisted Numerical Solutions. Furthermore, we also review the latest ML methods in inverse design and control, offering a novel classification and providing an in-depth discussion. Then we highlight real-world applications of ML for CFD in critical scientific and engineering disciplines, including aerodynamics, combustion, atmosphere & ocean science, biology fluid, plasma, symbolic regression, and reduced order modeling. Besides, we identify key challenges and advocate for future research directions to address these challenges, such as multi-scale representation, physical knowledge encoding, scientific foundation model and automatic scientific discovery. This review serves as a guide for the rapidly expanding ML for CFD community, aiming to inspire insights for future advancements. We draw the conclusion that ML is poised to significantly transform CFD research by enhancing simulation accuracy, reducing computational time, and enabling more complex analyses of fluid dynamics. The paper resources can be viewed at https://github.com/WillDreamer/Awesome-AI4CFD.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). Builds on 85 of its 223 references that are in the map. First posted on arXiv 22 Aug 2024.

Builds on

85 of 223 references.

References · 85

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2022Emergent Abilities of Large Language Modelscited by 2,483
  4. 2021Decision Transformer: Reinforcement Learning via Sequence Modelingcited by 1,528
  5. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  6. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  7. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 748
  8. 2024MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategiescited by 694
  9. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
  10. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 416
  11. 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 396
  12. 2022Message Passing Neural PDE Solverscited by 368
38 more
  1. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 343
  2. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 321
  3. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 299
  4. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
  5. 2021Physics-informed neural networks with hard constraints for inverse designcited by 277
  6. 2022GraphCast: Learning skillful medium-range global weather forecastingcited by 261
  7. 2018Analyzing Inverse Problems with Invertible Neural Networkscited by 239
  8. 2021Factorized Fourier Neural Operatorscited by 237
  9. 2022U-NO: U-shaped Neural Operatorscited by 219
  10. 2023Convolutional Neural Operators for robust and accurate learning of PDEscited by 207
  11. 2020Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solverscited by 201
  12. 2021Conditional Image Generation with Score-Based Diffusion Modelscited by 195
  13. 2024DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Trainingcited by 137
  14. 2020Learning to Control PDEs with Differentiable Physicscited by 131
  15. 2023Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behaviorcited by 128
  16. 2020Incorporating Symmetry into Deep Dynamics Models for Improved Generalizationcited by 123
  17. 2023Scalable Transformer for PDE Surrogate Modelingcited by 123
  18. 2023Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systemscited by 118
  19. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  20. 2022MultiScale MeshGraphNetscited by 94
  21. 2022Clifford Neural Layers for PDE Modelingcited by 91
  22. 2023Multiple Physics Pretraining for Physical Surrogate Modelscited by 90
  23. 2023PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEscited by 84
  24. 2019Model Inversion Networks for Model-Based Optimizationcited by 83
  25. 2022Predicting Physics in Mesh-reduced Space with Temporal Attentioncited by 82
  26. 2022NOMAD: Nonlinear Manifold Decoders for Operator Learningcited by 81
  27. 2023Operator Learning with Neural Fields: Tackling PDEs on General Geometriescited by 80
  28. 2022Continuous PDE Dynamics Forecasting with Implicit Neural Representationscited by 71
  29. 2023PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networkscited by 62
  30. 2024Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolationcited by 45
  31. 2022Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamicscited by 44
  32. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
  33. 2023Group Equivariant Fourier Neural Operators for Partial Differential Equationscited by 42
  34. 2022Learning to Accelerate Partial Differential Equations via Latent Global Evolutioncited by 38
  35. 2022Learning to Solve PDE-constrained Inverse Problems with Graph Networkscited by 37
  36. 2021Meta-Auto-Decoder for Solving Parametric Partial Differential Equationscited by 36
  37. 2023Domain Agnostic Fourier Neural Operatorscited by 36
  38. 2022Implicit Neural Spatial Representations for Time-dependent PDEscited by 35

50 most cited of 85 All 85 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 15; 2026: 8.

27 papers.

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  1. 2025AB-UPT: Scaling Neural CFD Surrogates for High-Fidelity Automotive Aerodynamics Simulations via Anchored-Branched Universal Physics Transformerscited by 49
  2. 2024VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Predictioncited by 22
  3. 2026RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Datacited by 13
  4. 2024Physics-Informed Regularization for Domain-Agnostic Dynamical System Modelingcited by 9
  5. 2025ChatCFD: An LLM-Driven Agent for End-to-End CFD Automation with Structured Knowledge and Reasoningcited by 9
  6. 2025A Multimodal PDE Foundation Model for Prediction and Scientific Text Descriptionscited by 8
  7. 2025FourierFlow: Frequency-aware Flow Matching for Generative Turbulence Modelingcited by 8
  8. 2025Light-Weight Diffusion Multiplier and Uncertainty Quantification for Fourier Neural Operatorscited by 6
  9. 2025FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulationcited by 4
  10. 2024A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networkscited by 2
  11. 2025Hybrid Two-Stage Reconstruction of Multiscale Subsurface Flow with Physics-informed Residual Connected Neural Operatorcited by 2
  12. 2025Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systemscited by 2
15 more
  1. 2025A Mixture of Experts Gating Network for Enhanced Surrogate Modeling in External Aerodynamicscited by 2
  2. 2025M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulationscited by 2
  3. 2025Incomplete Data, Complete Dynamics: A Diffusion Approachcited by 2
  4. 2026A Physics-Informed Fourier-Wavelet Transformer for Multiscale Computational Fluid Dynamics Surrogate Modelingcited by 2
  5. 2025Multi-Stage Graph Neural Networks for Data-Driven Prediction of Natural Convection in Enclosed Cavitiescited by 1
  6. 2025PIRF: Physics-Informed Reward Fine-Tuning for Diffusion Modelscited by 1
  7. 2026PhyNiKCE: A Neurosymbolic Agentic Framework for Autonomous Computational Fluid Dynamicscited by 1
  8. 2024Trading Devil RL: Backdoor attack via Stock market, Bayesian Optimization and Reinforcement Learningcited by 0
  9. 2025A Flow-rate-conserving CNN-based Domain Decomposition Method for Blood Flow Simulationscited by 0
  10. 2025FoilDiff: A Hybrid Transformer Backbone for Diffusion-based Modelling of 2D Airfoil Flow Fieldscited by 0
  11. 2026Deep Wave Network for Modeling Multi-Scale Physical Dynamicscited by 0
  12. 2026Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospectscited by 0
  13. 2026Is Zero-Shot Super-Resolution Possible in Operator Learning?cited by 0
  14. 2026APPSolver: Adaptive Patch Partitioning for Point-Wise Ship Flow Prediction on Unstructured Meshescited by 0
  15. 2026Reconstruction of 4D Mitral Regurgitation Hemodynamics from Sparse Planar Data using Deep Operator Networks with Test-Time Adaptationcited by 0