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Artificial Intelligence for Fluid Mechanics
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Artificial Intelligence for Fluid Mechanics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 31 May 2025 | Viewed by 12829

Special Issue Editors

Dr. Andreas Lintermann

E-Mail Website
Guest Editor
Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH, Wilhelm-Johnen-Straße, 52425 Jülich, Germany
Interests: computational fluid dynamics; multi-physics simulations; code coupling; high-performance computing; modular supercomputing architectures; artificial intelligence; deep learning; hyperparameter optimization; quantum computing
Dr. Guillaume Houzeaux

E-Mail Website
Guest Editor
CASE, Barcelona Supercomputing Center, Barcelona, Spain
Interests: computational mechanics; numerical methods; multi-physics simulations; multi-scale simulations; code coupling; high-performance computing; heterogeneous computing; artificial intelligence

Special Issue Information

Dear Colleagues,

AI methods continuously penetrate into various fields of research and industry. Huge amounts of data in fluid mechanics research are nowadays produced by simulations or experiments. They provide the opportunity to train novel AI technologies resulting in predictive models competing with conventional physical and numerical models. In a rapidly evolving supercomputing context, the AI training process relies more and more on HPC to produce and process data and thus poses implementation and performance challenges.

This Special Issue will present cutting-edge work on novel AI technologies that advance our understanding of fluid mechanics problems. Manuscripts developing AI models, dealing with training on computational or experimental fluid mechanics data, making use of HPC systems in this context, and employing the final models, e.g., in inferencing at simulation runtime to model unresolved small-scale phenomena or in experiments in processing and mining data, are welcome. This includes coupling methods employing state-of-the-art computing hardware to bring traditional fluid mechanics workflows and AI workflows together.

Topics of interest for this Special Issues include, but are not limited to, the following: CFD, multi-physics simulations, experimental fluid mechanics, machine learning, physics-informed neural networks, deep learning, and AI-based subgrid-scale or surrogate modeling. Manuscripts describing original theoretical and applied research are welcome for submission.

Dr. Andreas Lintermann
Dr. Guillaume Houzeaux
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • artificial intelligence
  • machine learning
  • deep learning
  • physics-informed neural networks
  • unsupervised learning
  • fluid mechanics
  • computational fluid dynamics
  • simulation
  • experimental fluid mechanics
  • high-performance computing

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Published Papers (6 papers)

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Research

44 pages, 9048 KiB  
Article
Artificial Neural Network and Response Surface Methodology-Driven Optimization of Cu–Al2O3/Water Hybrid Nanofluid Flow in a Wavy Enclosure with Inclined Periodic Magnetohydrodynamic Effects
by Tarikul Islam, Sílvio Gama and Marco Martins Afonso
Mathematics 2025, 13(1), 78; https://doi.org/10.3390/math13010078 - 28 Dec 2024
Cited by 1 | Viewed by 1834
Abstract
This study explores the optimization of a Cu–Al2O3/water hybrid nanofluid within an irregular wavy enclosure under inclined periodic MHD effects. Hybrid nanofluids, with different mixture ratios of copper (Cu) and alumina (Al2O3) nanoparticles in water, [...] Read more.
This study explores the optimization of a Cu–Al2O3/water hybrid nanofluid within an irregular wavy enclosure under inclined periodic MHD effects. Hybrid nanofluids, with different mixture ratios of copper (Cu) and alumina (Al2O3) nanoparticles in water, are used in this study. Numerical simulations using the Galerkin residual-based finite-element method (FEM) are conducted to solve the governing PDEs. At the same time, artificial neural networks (ANNs) and response surface methodology (RSM) are employed to optimize thermal performance by maximizing the average Nusselt number (Nuav), the key indicator of thermal transport efficiency. Thermophysical properties such as viscosity and thermal conductivity are evaluated for validation against experimental data. The results include visual representations of heatlines, streamlines, and isotherms for various physical parameters. Additionally, Nuav, friction factors, and thermal efficiency index are analyzed using different nanoparticle ratios. The findings show that buoyancy and MHD parameters significantly influence heat transfer, friction, and thermal efficiency. The addition of Cu nanoparticles improves heat transport compared to Al2O3 nanofluid, demonstrating the superior thermal conductivity of the Cu–Al2O3/water hybrid nanofluid. The results also indicate that adding Al2O3 nanoparticles to the Cu/water nanofluid diminishes the heat transport rate. The waviness of the geometry shows a significant impact on thermal management as well. Moreover, the statistical RSM analysis indicates a high R2 value of 98.88% for the response function, which suggests that the model is well suited for predicting Nuav. Furthermore, the ANN model demonstrates high accuracy with a mean squared error (MSE) of 0.00018, making it a strong alternative to RSM analysis. Finally, this study focuses on the interaction between the hybrid nanofluid, a wavy geometry, and MHD effects, which can optimize heat transfer and contribute to energy-efficient cooling or heating technologies. Full article
(This article belongs to the Special Issue Artificial Intelligence for Fluid Mechanics)
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13 pages, 775 KiB  
Article
Prediction of Turbulent Boundary Layer Flow Dynamics with Transformers
by Rakesh Sarma, Fabian Hübenthal, Eray Inanc and Andreas Lintermann
Mathematics 2024, 12(19), 2998; https://doi.org/10.3390/math12192998 - 26 Sep 2024
Cited by 1 | Viewed by 1349
Abstract
Time-marching of turbulent flow fields is computationally expensive using traditional Computational Fluid Dynamics (CFD) solvers. Machine Learning (ML) techniques can be used as an acceleration strategy to offload a few time-marching steps of a CFD solver. In this study, the Transformer (TR) architecture, [...] Read more.
Time-marching of turbulent flow fields is computationally expensive using traditional Computational Fluid Dynamics (CFD) solvers. Machine Learning (ML) techniques can be used as an acceleration strategy to offload a few time-marching steps of a CFD solver. In this study, the Transformer (TR) architecture, which has been widely used in the Natural Language Processing (NLP) community for prediction and generative tasks, is utilized to predict future velocity flow fields in an actuated Turbulent Boundary Layer (TBL) flow. A unique data pre-processing step is proposed to reduce the dimensionality of the velocity fields, allowing the processing of full velocity fields of the actuated TBL flow while taking advantage of distributed training in a High Performance Computing (HPC) environment. The trained model is tested at various prediction times using the Dynamic Mode Decomposition (DMD) method. It is found that under five future prediction time steps with the TR, the model is able to achieve a relative Frobenius norm error of less than 5%, compared to fields predicted with a Large Eddy Simulation (LES). Finally, a computational study shows that the TR achieves a significant speed-up, offering computational savings approximately 53 times greater than those of the baseline LES solver. This study demonstrates one of the first applications of TRs on actuated TBL flow intended towards reducing the computational effort of time-marching. The application of this model is envisioned in a coupled manner with the LES solver to provide few time-marching steps, which will accelerate the overall computational process. Full article
(This article belongs to the Special Issue Artificial Intelligence for Fluid Mechanics)
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19 pages, 4790 KiB  
Article
Graph Neural Networks for Mesh Generation and Adaptation in Structural and Fluid Mechanics
by Ugo Pelissier, Augustin Parret-Fréaud, Felipe Bordeu and Youssef Mesri
Mathematics 2024, 12(18), 2933; https://doi.org/10.3390/math12182933 - 20 Sep 2024
Cited by 1 | Viewed by 3574
Abstract
The finite element discretization of computational physics problems frequently involves the manual generation of an initial mesh and the application of adaptive mesh refinement (AMR). This approach is employed to selectively enhance the accuracy of resolution in regions that encompass significant features throughout [...] Read more.
The finite element discretization of computational physics problems frequently involves the manual generation of an initial mesh and the application of adaptive mesh refinement (AMR). This approach is employed to selectively enhance the accuracy of resolution in regions that encompass significant features throughout the simulation process. In this paper, we introduce Adaptnet, a Graph Neural Networks (GNNs) framework for learning mesh generation and adaptation. The model is composed of two GNNs: the first one, Meshnet, learns mesh parameters commonly used in open-source mesh generators, to generate an initial mesh from a Computer Aided Design (CAD) file; while the second one, Graphnet, learns mesh-based simulations to predict the components of an Hessian-based metric to perform anisotropic mesh adaptation. Our approach is tested on structural (Deforming plate–Linear elasticity) and fluid mechanics (Flow around cylinders–steady-state Stokes) problems. Our findings demonstrate the model’s ability to precisely predict the dynamics of the system and adapt the mesh as needed. The adaptability of the model enables learning resolution-independent mesh-based simulations during training, allowing it to scale effectively to more intricate state spaces during inference. Full article
(This article belongs to the Special Issue Artificial Intelligence for Fluid Mechanics)
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17 pages, 1126 KiB  
Article
Streamlining Ocean Dynamics Modeling with Fourier Neural Operators: A Multiobjective Hyperparameter and Architecture Optimization Approach
by Yixuan Sun, Ololade Sowunmi, Romain Egele, Sri Hari Krishna Narayanan, Luke Van Roekel and Prasanna Balaprakash
Mathematics 2024, 12(10), 1483; https://doi.org/10.3390/math12101483 - 10 May 2024
Cited by 1 | Viewed by 1542
Abstract
Training an effective deep learning model to learn ocean processes involves careful choices of various hyperparameters. We leverage DeepHyper’s advanced search algorithms for multiobjective optimization, streamlining the development of neural networks tailored for ocean modeling. The focus is on optimizing Fourier neural operators [...] Read more.
Training an effective deep learning model to learn ocean processes involves careful choices of various hyperparameters. We leverage DeepHyper’s advanced search algorithms for multiobjective optimization, streamlining the development of neural networks tailored for ocean modeling. The focus is on optimizing Fourier neural operators (FNOs), a data-driven model capable of simulating complex ocean behaviors. Selecting the correct model and tuning the hyperparameters are challenging tasks, requiring much effort to ensure model accuracy. DeepHyper allows efficient exploration of hyperparameters associated with data preprocessing, FNO architecture-related hyperparameters, and various model training strategies. We aim to obtain an optimal set of hyperparameters leading to the most performant model. Moreover, on top of the commonly used mean squared error for model training, we propose adopting the negative anomaly correlation coefficient as the additional loss term to improve model performance and investigate the potential trade-off between the two terms. The numerical experiments show that the optimal set of hyperparameters enhanced model performance in single timestepping forecasting and greatly exceeded the baseline configuration in the autoregressive rollout for long-horizon forecasting up to 30 days. Utilizing DeepHyper, we demonstrate an approach to enhance the use of FNO in ocean dynamics forecasting, offering a scalable solution with improved precision. Full article
(This article belongs to the Special Issue Artificial Intelligence for Fluid Mechanics)
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21 pages, 1014 KiB  
Article
Hybrid AI-Analytical Modeling of Droplet Dynamics on Inclined Heterogeneous Surfaces
by Andreas D. Demou and Nikos Savva
Mathematics 2024, 12(8), 1188; https://doi.org/10.3390/math12081188 - 15 Apr 2024
Viewed by 1491
Abstract
This work presents a novel approach for the study of the movement of droplets on inclined surfaces under the influence of gravity and chemical heterogeneities. The developed numerical methodology uses data-driven modeling to extend the applicability limits of an analytically derived reduced-order model [...] Read more.
This work presents a novel approach for the study of the movement of droplets on inclined surfaces under the influence of gravity and chemical heterogeneities. The developed numerical methodology uses data-driven modeling to extend the applicability limits of an analytically derived reduced-order model for the contact line velocity. More specifically, while the reduced-order model is able to capture the effects of the chemical heterogeneities to a satisfactory degree, it does not account for gravity. To alleviate this shortcoming, datasets generated from direct numerical simulations are used to train a data-driven model for the contact line velocity, which is based on the Fourier neural operator and corrects the reduced-order model predictions to match the reference solutions. This hybrid surrogate model, which comprises of both analytical and data-driven components, is then integrated in time to simulate the droplet movement, offering a speedup of five orders of magnitude compared to direct numerical simulations. The performance of this hybrid model is quantified and assessed in different wetting scenarios, by considering various inclination angles and values for the Bond number, demonstrating the accuracy of the predictions as long as the adopted parameters lie within the ranges considered in the training dataset. Full article
(This article belongs to the Special Issue Artificial Intelligence for Fluid Mechanics)
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23 pages, 15847 KiB  
Article
Toward the Usage of Deep Learning Surrogate Models in Ground Vehicle Aerodynamics
by Benet Eiximeno, Arnau Miró, Ivette Rodríguez and Oriol Lehmkuhl
Mathematics 2024, 12(7), 998; https://doi.org/10.3390/math12070998 - 27 Mar 2024
Cited by 3 | Viewed by 1917
Abstract
This study introduces a deep learning surrogate model designed to predict the evolution of the mean pressure coefficient on the back face of a Windsor body across a range of yaw angles from 2.5∘ to 10∘. Utilizing a [...] Read more.
This study introduces a deep learning surrogate model designed to predict the evolution of the mean pressure coefficient on the back face of a Windsor body across a range of yaw angles from 2.5∘ to 10∘. Utilizing a variational autoencoder (VAE), the model effectively compresses snapshots of back pressure taken at yaw angles of 2.5∘, 5∘, and 10∘ into two latent vectors. These snapshots are derived from wall-modeled large eddy simulations (WMLESs) conducted at a Reynolds number of ReL=2.9×106. The frequencies that dominate the latent vectors correspond closely with those observed in both the drag’s temporal evolution and the dynamic mode decomposition. The projection of the mean pressure coefficient to the latent space yields an increasing linear evolution of the two latent variables with the yaw angle. The mean pressure coefficient distribution at a yaw angle of 7.5∘ is predicted with a mean error of e¯=3.13% when compared to the WMLESs results after obtaining the values of the latent space with linear interpolation. Full article
(This article belongs to the Special Issue Artificial Intelligence for Fluid Mechanics)
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