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

TL;DR

This survey consolidates recent progress in applying machine learning to computational fluid dynamics, introducing a novel taxonomy that separates forward modeling into Data-driven Surrogates, Physics-Informed Surrogates, and ML-assisted Numerical Solutions while also detailing ML approaches for inverse design and control. It systematically covers data sources, architectural paradigms (discretization-dependent surrogates, neural operators, PINNs, and discretized constraint-informed nets), and broad applications across aerodynamics, combustion, geophysical flows, biology, and plasma physics. The work highlights core challenges—multiscale dynamics, explicit physical knowledge encoding, multi-physics coupling, and automatic data generation—and outlines future directions such as scientific foundation models and autonomous discovery pipelines. Overall, ML is positioned to significantly accelerate CFD by improving accuracy, reducing compute time, and enabling complex analyses across engineering and scientific domains.

Abstract

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.

Figures (6)

• Figure 1: The approximate annual number of papers on ML for CFD presented at top-tier ML publication and leading journals in fluid dynamics appeared in Table \ref{['tab:method']} and \ref{['tab:method_physics']}
• Figure 2: Taxonomy of CFD methods based on ML techniques. We first investigate into forward modeling approaches, including data-driven surrogates, physics-driven surrogates, and ML-assisted methods. Besides, we conduct an in-depth analysis of inverse problems. Moreover, we review the practical applications of these methods across various domains.
• Figure 3: Demonstration of various datasets of ML for CFD. Row 1 from left to right: (1) 1D Diffusion, (2)-(3) 1D Advection, (4) 1D compressible Navier-Stokes, (5) 1D Reaction-Diffusion, (6) 2D Darcy flow solution, (7) 2D Darcy flow coefficient, (8) Cavity flow. Row 2 from left to right: (1)-(4) 2D Shallow Water at $t=0.25, 0.5, 0.75, 1$, (5)-(8) 2D Reaction-Diffusion at $t=1.25, 2.5, 3.75, 5$. Row 3 from left to right: (1) Cylinder flow, (2) Airfoil flow, (3)-(6) 2D Compressible Navier-Stokes at $t=0, 0.5, 1, 2$., (7)-(8) 3D compressible Navier-Stokes at $t = 1, 2$.
• Figure 4: Overview of ML for computational fluid dynamics simulation. The left column encompasses various types of input data used in the models, including physical laws. The middle columns consist of three common frameworks used in constructing models with ML. The right column pertains to applications in various scenarios.
• Figure 5: Demonstration of inverse design to optimize the design parameters. We review existing methods with a novel classification including PDE-constrained Methods and Data-driven Methods.