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

arXiv: https://arxiv.org/abs/2408.12171 · HTML: https://mlsanity.com/paper/2408.12171/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 85 of its 223 references that are in the map.
- First posted on arXiv 22 Aug 2024.

## Builds on (most cited first, 30 of 85)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Conditional Image Generation with Score-Based Diffusion Models](https://mlsanity.com/paper/2111.13606/) (2021)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behavior](https://mlsanity.com/paper/2306.00258/) (2023)
- [Scalable Transformer for PDE Surrogate Modeling](https://mlsanity.com/paper/2305.17560/) (2023)
- [Incorporating Symmetry into Deep Dynamics Models for Improved Generalization](https://mlsanity.com/paper/2002.03061/) (2020)
- [Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems](https://mlsanity.com/paper/2307.08423/) (2023)

## Built on by (most cited first, 28 of 28)

- [AB-UPT: Scaling Neural CFD Surrogates for High-Fidelity Automotive Aerodynamics Simulations via Anchored-Branched Universal Physics Transformers](https://mlsanity.com/paper/2502.09692/) (2025)
- [VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Prediction](https://mlsanity.com/paper/2411.16063/) (2024)
- [RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Data](https://mlsanity.com/paper/2601.01829/) (2026)
- [A Multimodal PDE Foundation Model for Prediction and Scientific Text Descriptions](https://mlsanity.com/paper/2502.06026/) (2025)
- [Physics-Informed Regularization for Domain-Agnostic Dynamical System Modeling](https://mlsanity.com/paper/2410.06366/) (2024)
- [ChatCFD: An LLM-Driven Agent for End-to-End CFD Automation with Structured Knowledge and Reasoning](https://mlsanity.com/paper/2506.02019/) (2025)
- [FourierFlow: Frequency-aware Flow Matching for Generative Turbulence Modeling](https://mlsanity.com/paper/2506.00862/) (2025)
- [Light-Weight Diffusion Multiplier and Uncertainty Quantification for Fourier Neural Operators](https://mlsanity.com/paper/2508.00643/) (2025)
- [FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulation](https://mlsanity.com/paper/2505.20349/) (2025)
- [Incomplete Data, Complete Dynamics: A Diffusion Approach](https://mlsanity.com/paper/2509.20098/) (2025)
- [A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks](https://mlsanity.com/paper/2412.09752/) (2024)
- [Hybrid Two-Stage Reconstruction of Multiscale Subsurface Flow with Physics-informed Residual Connected Neural Operator](https://mlsanity.com/paper/2501.13271/) (2025)
- [Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems](https://mlsanity.com/paper/2505.18857/) (2025)
- [A Mixture of Experts Gating Network for Enhanced Surrogate Modeling in External Aerodynamics](https://mlsanity.com/paper/2508.21249/) (2025)
- [M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations](https://mlsanity.com/paper/2509.10659/) (2025)
- [PIRF: Physics-Informed Reward Fine-Tuning for Diffusion Models](https://mlsanity.com/paper/2509.20570/) (2025)
- [A Physics-Informed Fourier-Wavelet Transformer for Multiscale Computational Fluid Dynamics Surrogate Modeling](https://mlsanity.com/paper/2606.24696/) (2026)
- [Multi-Stage Graph Neural Networks for Data-Driven Prediction of Natural Convection in Enclosed Cavities](https://mlsanity.com/paper/2509.06041/) (2025)
- [A Flow-rate-conserving CNN-based Domain Decomposition Method for Blood Flow Simulations](https://mlsanity.com/paper/2509.15900/) (2025)
- [PhyNiKCE: A Neurosymbolic Agentic Framework for Autonomous Computational Fluid Dynamics](https://mlsanity.com/paper/2602.11666/) (2026)
- [Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects](https://mlsanity.com/paper/2605.16966/) (2026)
- [Is Zero-Shot Super-Resolution Possible in Operator Learning?](https://mlsanity.com/paper/2606.00296/) (2026)
- [Trading Devil RL: Backdoor attack via Stock market, Bayesian Optimization and Reinforcement Learning](https://mlsanity.com/paper/2412.17908/) (2024)
- [FoilDiff: A Hybrid Transformer Backbone for Diffusion-based Modelling of 2D Airfoil Flow Fields](https://mlsanity.com/paper/2510.04325/) (2025)
- [Deep Wave Network for Modeling Multi-Scale Physical Dynamics](https://mlsanity.com/paper/2605.04198/) (2026)
- [APPSolver: Adaptive Patch Partitioning for Point-Wise Ship Flow Prediction on Unstructured Meshes](https://mlsanity.com/paper/2608.29355/) (2026)
- [Reconstruction of 4D Mitral Regurgitation Hemodynamics from Sparse Planar Data using Deep Operator Networks with Test-Time Adaptation](https://mlsanity.com/paper/2609.20857/) (2026)
- [PDE-JEPA: Predictive Representation Learning of Latent Dynamics Modeling for Parametric PDEs](https://mlsanity.com/paper/2609.34715/) (2026)

## 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.