Title: Machine learning and deep learning techniques for enhancing computational fluid dynamics: a comprehensive review

Authors: Alireza Omrani; Arman Shateri; Arash Goligerdian; Hamid Majidi; Seyed Behzad Hosseini; Saman Aminian; Mohammad Hafezi

Addresses: Department of Mechanical Engineering, Politecnico di Milano, via Giuseppe La Masa 1, 20156, Milan, Italy ' Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran ' University of Houston, Department of Mathematics, 3551 Cullen, Blvd, Houston, Texas, USA ' Department of Mechanical Engineering, Ilam Branch, Islamic Azad University, Ilam, Iran ' Department of Engineering, University of Florence, Florence, Italy ' Department of Mechanical Engineering, University of Kurdistan, Sanandaj, Iran ' Department of Chemical Engineering, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15875-4413, Iran

Abstract: Over the years, computational fluid dynamics (CFD) has undergone significant evolution, establishing it as an essential tool for simulating complex fluid flow phenomena. The integration of deep learning (DL) and machine learning (ML) methodologies with CFD has recently emerged as a promising approach to enhance the accuracy, efficiency, and automation of simulations. This comprehensive review article explores the potential of ML and DL in advancing CFD, providing valuable insights into their transformative impact on the field. In this study, the large eddy simulation (LES), reduced-order models (ROMs), Reynolds-averaged Navier-Stokes (RANS), and direct numerical simulation (DNS) techniques, along with the role of ML in improving these models within CFD, are thoroughly discussed. It was demonstrated that ML and DL techniques can accelerate high-fidelity simulations, provide turbulence models with varying levels of precision, and generate ROMs that surpass the accuracy achieved through conventional methods. Additionally, this paper presents a broad perspective, highlighting recent advancements, opportunities, and unresolved challenges in the field.

Keywords: machine learning; computational fluid dynamics; CFD; reduced-order models; ROMs; deep learning; artificial neural network; large eddy simulation; LES; direct numerical simulation; DNS.

DOI: 10.1504/PCFD.2026.152122

Progress in Computational Fluid Dynamics, An International Journal, 2026 Vol.26 No.2, pp.71 - 99

Received: 22 Nov 2024
Accepted: 07 Mar 2025
Published online: 09 Mar 2026 *

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