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Fluids
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Machine Learning and Artificial Intelligence in Fluid Mechanics
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Machine Learning and Artificial Intelligence in Fluid Mechanics

A special issue of Fluids (ISSN 2311-5521).

Deadline for manuscript submissions: 31 March 2025 | Viewed by 29422

Special Issue Editor

Dr. Filippos Sofos

E-Mail Website
Guest Editor
Department of Physics, School of Science, University of Thessaly, 35100 Lamia, Greece
Interests: machine learning; symbolic regression; computational hydraulics; molecular dynamics; smoothed-particle hydrodynamics; multiscale modeling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fluid mechanics research has evolved during the past few years, towards the direction of exploiting massive amounts of data generated from knowledge gathered insofar, either from experimental measurements or simulations. The application of novel machine learning (ML) techniques is currently the latest trend in the field, and has almost reached standardization. Computational boosting, advanced turbulence modeling, bridging among scales, hybrid simulation schemes, and flow feature extraction are concepts that scientists and engineers must deal with.

This Special Issue aims to join together data science methods and advanced artificial intelligence and machine learning techniques, in order to apply them to popular fluid mechanics problems, in an alternative though effective and accurate manner, strictly bound to the physical problem.

We encourage authors to submit works addressing topics including, but not limited to, physics-inspired neural networks, intelligent fluid dynamics, scientific machine learning, explainable and trustworthy artificial intelligence, symbolic regression and evolutionary algorithms, unsupervised machine learning and clustering, with a focus on fluid mechanics applications.

Dr. Filippos Sofos
Guest Editor

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. Fluids is an international peer-reviewed open access monthly 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 1800 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

  • machine learning
  • data-driven fluid mechanics
  • turbulence modeling
  • reduced-order CFD
  • neural networks
  • symbolic regression

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Published Papers (10 papers)

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Research

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17 pages, 5213 KiB  
Article
Acceleration of Modeling Capability for GDI Spray by Machine-Learning Algorithms
by Yassine El Marnissi, Kyungwon Lee and Joonsik Hwang
Fluids 2024, 9(11), 267; https://doi.org/10.3390/fluids9110267 - 18 Nov 2024
Viewed by 306
Abstract
Cold start causes a high amount of unburned hydrocarbon and particulate matter emissions in gasoline direct injection (GDI) engines. Therefore, it is necessary to understand the dynamics of spray during a cold start and develop a predictive model to form a better air-fuel [...] Read more.
Cold start causes a high amount of unburned hydrocarbon and particulate matter emissions in gasoline direct injection (GDI) engines. Therefore, it is necessary to understand the dynamics of spray during a cold start and develop a predictive model to form a better air-fuel mixture in the combustion chamber. In this study, an Artificial Neural Network (ANN) was designed to predict quantitative 3D liquid volume fraction, liquid penetration, and liquid width under different operating conditions. The model was trained with data derived from high-speed and Schlieren imaging experiments with a gasoline surrogate fuel, conducted in a constant volume spray vessel. A coolant circulator was used to simulate the low-temperature conditions (−7 °C) typical of cold starts. The results showed good agreement between machine learning predictions and experimental data, with an overall accuracy R2 of 0.99 for predicting liquid penetration and liquid width. In addition, the developed ANN model was able to predict detailed dynamics of spray plumes. This confirms the robustness of the ANN in predicting spray characteristics and offers a promising tool to enhance GDI engine technologies. Full article
(This article belongs to the Special Issue Machine Learning and Artificial Intelligence in Fluid Mechanics)
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17 pages, 6268 KiB  
Article
Engine Mass Flow Estimation through Neural Network Modeling in Semi-Transient Conditions: A New Calibration Approach
by T. Savioli, M. Pampanini, G. Visani, L. Esposito and C. A. Rinaldini
Fluids 2024, 9(10), 239; https://doi.org/10.3390/fluids9100239 - 12 Oct 2024
Viewed by 666
Abstract
Nowadays, engine experimental research represents a very expensive field within the automotive industry, but it remains fundamental for engine and vehicle development. The present work aims to investigate a novel approach for engine control system calibration, by adopting machine learning techniques to model [...] Read more.
Nowadays, engine experimental research represents a very expensive field within the automotive industry, but it remains fundamental for engine and vehicle development. The present work aims to investigate a novel approach for engine control system calibration, by adopting machine learning techniques to model physical parameters of the engine starting from experimental data measured at the test bench. The main goal is to create a methodology which accelerates the calibration process without losing accuracy. A model that estimates air mass flow is created by adopting either a tree ensemble model or an artificial neural network trained on a small dataset, which was previously acquired at the test bench using a random calibration of the volumetric efficiency map. The model’s performance is first validated on a larger, random dataset. Then, the volumetric efficiency calculated from the air mass flow model estimation is used to calibrate the transfer function of the Engine Control Unit. Finally, the sensitivity of the model error correlated with the number of data points acquired is used in order to determine the best practice for a Design Of Experiment, which minimizes data acquisition. The methodology proposed can lead to reduced time and costs of the whole calibration process of the engine, without losing accuracy. The analysis was conducted on the entire vehicle, which is crucial for drivability, especially in motorcycles since they are highly sensitive to air-to-fuel ratio adjustments. This work demonstrates that machine learning models can be adopted for the fine-tuning of the calibration process, which is normally performed manually. Full article
(This article belongs to the Special Issue Machine Learning and Artificial Intelligence in Fluid Mechanics)
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23 pages, 1627 KiB  
Article
Data Assimilation and Parameter Identification for Water Waves Using the Nonlinear Schrödinger Equation and Physics-Informed Neural Networks
by Svenja Ehlers, Niklas A. Wagner, Annamaria Scherzl, Marco Klein, Norbert Hoffmann and Merten Stender
Fluids 2024, 9(10), 231; https://doi.org/10.3390/fluids9100231 - 1 Oct 2024
Cited by 1 | Viewed by 758
Abstract
The measurement of deep water gravity wave elevations using in situ devices, such as wave gauges, typically yields spatially sparse data due to the deployment of a limited number of costly devices. This sparsity complicates the reconstruction of the spatio-temporal extent of surface [...] Read more.
The measurement of deep water gravity wave elevations using in situ devices, such as wave gauges, typically yields spatially sparse data due to the deployment of a limited number of costly devices. This sparsity complicates the reconstruction of the spatio-temporal extent of surface elevation and presents an ill-posed data assimilation problem, which is challenging to solve with conventional numerical techniques. To address this issue, we propose the application of a physics-informed neural network (PINN) to reconstruct physically consistent wave fields between two elevation time series measured at distinct locations within a numerical wave tank. Our method ensures this physical consistency by integrating residuals of the hydrodynamic nonlinear Schrödinger equation (NLSE) into the PINN’s loss function. We first showcase a data assimilation task by employing constant NLSE coefficients predetermined from spectral wave properties. However, due to the relatively short duration of these measurements and their possible deviation from the narrow-band assumptions inherent in the NLSE, using constant coefficients occasionally leads to poor reconstructions. To enhance this reconstruction quality, we introduce the base variables of frequency and wavenumber, from which the NLSE coefficients are determined, as additional neural network parameters that are fine tuned during PINN training. Overall, the results demonstrate the potential for real-world applications of the PINN method and represent a step toward improving the initialization of deterministic wave prediction methods. Full article
(This article belongs to the Special Issue Machine Learning and Artificial Intelligence in Fluid Mechanics)
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15 pages, 3403 KiB  
Article
Machine Learning for Dynamic Pressure Coefficient Prediction in Vertical Water Jets
by Amin Salemnia, Seyedehmaryam Hosseini Boldaji, Vida Atashi and Manoochehr Fathi-Moghadam
Fluids 2024, 9(9), 205; https://doi.org/10.3390/fluids9090205 - 1 Sep 2024
Viewed by 712
Abstract
Vertical water jets present significant challenges for hydraulic structures due to their potential to cause erosion and structural damage. This study aimed to predict the dimensionless pressure coefficient (Cp) of vertical water jets by examining the relationships between experimental parameters, such [...] Read more.
Vertical water jets present significant challenges for hydraulic structures due to their potential to cause erosion and structural damage. This study aimed to predict the dimensionless pressure coefficient (Cp) of vertical water jets by examining the relationships between experimental parameters, such as Froude number, slope, and the ratio of waterfall height over the product of the Froude number and diameter, referred to as α, using machine learning models. Two hundred forty controlled experiments were conducted, with pressure data collected. To address the problem’s non-linearity, six machine learning models were tested: linear regression, K-nearest neighbors, decision tree, support vector regression, random forest, and XGBoost. The XGBoost model outperformed others, achieving an R-squared of 0.953 and a Root Mean Squared Error (RMSE) of 0.191. Residual analysis validated its better performance, demonstrating that it delivered the most accurate predictions with minimal bias. Feature importance analysis revealed the Froude number was the most significant predictor, followed by slope and diameter. This study emphasizes the importance of the Froude number in predicting jet behavior and shows the efficacy of advanced machine learning models in capturing complex fluid dynamics, providing valuable insights for optimizing engineering applications such as water jet cutting and cooling systems. Full article
(This article belongs to the Special Issue Machine Learning and Artificial Intelligence in Fluid Mechanics)
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14 pages, 12236 KiB  
Article
Application of Machine Learning Algorithms in Predicting Rheological Behavior of BN-diamond/Thermal Oil Hybrid Nanofluids
by Abulhassan Ali, Nawal Noshad, Abhishek Kumar, Suhaib Umer Ilyas, Patrick E. Phelan, Mustafa Alsaady, Rizwan Nasir and Yuying Yan
Fluids 2024, 9(1), 20; https://doi.org/10.3390/fluids9010020 - 9 Jan 2024
Cited by 3 | Viewed by 2506
Abstract
The use of nanofluids in heat transfer applications has significantly increased in recent times due to their enhanced thermal properties. It is therefore important to investigate the flow behavior and, thus, the rheology of different nanosuspensions to improve heat transfer performance. In this [...] Read more.
The use of nanofluids in heat transfer applications has significantly increased in recent times due to their enhanced thermal properties. It is therefore important to investigate the flow behavior and, thus, the rheology of different nanosuspensions to improve heat transfer performance. In this study, the viscosity of a BN-diamond/thermal oil hybrid nanofluid is predicted using four machine learning (ML) algorithms, i.e., random forest (RF), gradient boosting regression (GBR), Gaussian regression (GR) and artificial neural network (ANN), as a function of temperature (25–65 °C), particle concentration (0.2–0.6 wt.%), and shear rate (1–2000 s−1). Six different error matrices were employed to evaluate the performance of these models by providing a comparative analysis. The data were randomly divided into training and testing data. The algorithms were optimized for better prediction of 700 experimental data points. While all ML algorithms produced R2 values greater than 0.99, the most accurate predictions, with minimum error, were obtained by GBR. This study indicates that ML algorithms are highly accurate and reliable for the rheological predictions of nanofluids. Full article
(This article belongs to the Special Issue Machine Learning and Artificial Intelligence in Fluid Mechanics)
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20 pages, 3810 KiB  
Article
Physics-Informed Super-Resolution of Turbulent Channel Flows via Three-Dimensional Generative Adversarial Networks
by Nicholas J. Ward
Fluids 2023, 8(7), 195; https://doi.org/10.3390/fluids8070195 - 29 Jun 2023
Cited by 1 | Viewed by 1861
Abstract
For a few decades, machine learning has been extensively utilized for turbulence research. The goal of this work is to investigate the reconstruction of turbulence from minimal or lower-resolution datasets as inputs using reduced-order models. This work seeks to effectively reconstruct high-resolution 3D [...] Read more.
For a few decades, machine learning has been extensively utilized for turbulence research. The goal of this work is to investigate the reconstruction of turbulence from minimal or lower-resolution datasets as inputs using reduced-order models. This work seeks to effectively reconstruct high-resolution 3D turbulent flow fields using unsupervised physics-informed deep learning. The first objective of this study is to reconstruct turbulent channel flow fields and verify these with respect to the statistics. The second objective is to compare the turbulent flow structures generated from a GAN with a DNS. The proposed deep learning algorithm effectively replicated the first- and second-order statistics of turbulent channel flows of Reτ= 180 within a 2% and 5% error, respectively. Additionally, by incorporating physics-based corrections to the loss functions, the proposed algorithm was also able to reconstruct λ2 structures. The results suggest that the proposed algorithm can be useful for reconstructing a range of 3D turbulent flows given computational and experimental efforts. Full article
(This article belongs to the Special Issue Machine Learning and Artificial Intelligence in Fluid Mechanics)
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15 pages, 10777 KiB  
Article
DropletAI: Deep Learning-Based Classification of Fluids with Different Ohnesorge Numbers during Non-Contact Dispensing
by Pranshul Sardana, Mohammadreza Zolfaghari, Guilherme Miotto, Roland Zengerle, Thomas Brox, Peter Koltay and Sabrina Kartmann
Fluids 2023, 8(6), 183; https://doi.org/10.3390/fluids8060183 - 17 Jun 2023
Cited by 2 | Viewed by 1777
Abstract
The reliable non-contact dispensing of droplets in the pico- to microliter range is a challenging task. The dispensed drop volume depends on various factors such as the rheological properties of the liquids, the actuation parameters, the geometry of the dispenser, and the ambient [...] Read more.
The reliable non-contact dispensing of droplets in the pico- to microliter range is a challenging task. The dispensed drop volume depends on various factors such as the rheological properties of the liquids, the actuation parameters, the geometry of the dispenser, and the ambient conditions. Conventionally, the rheological properties are characterized via a rheometer, but this adds a large liquid overhead. Fluids with different Ohnesorge number values produce different spatiotemporal motion patterns during dispensing. Once the Ohnesorge number is known, the ratio of viscosity and surface tension of the liquid can be known. However, there exists no mathematical formulation to extract the Ohnesorge number values from these motion patterns. Convolutional neural networks (CNNs) are great tools for extracting information from spatial and spatiotemporal data. The current study compares seven different CNN architectures to classify five liquids with different Ohnesorge numbers. Next, this work compares the results of various data cleaning conditions, sampling strategies, and the amount of data used for training. The best-performing model was based on the ECOmini-18 architecture. It reached a test accuracy of 94.2% after training on two acquisition batches (a total of 12,000 data points). Full article
(This article belongs to the Special Issue Machine Learning and Artificial Intelligence in Fluid Mechanics)
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17 pages, 7480 KiB  
Article
Turbulence Modeling for Physics-Informed Neural Networks: Comparison of Different RANS Models for the Backward-Facing Step Flow
by Fabian Pioch, Jan Hauke Harmening, Andreas Maximilian Müller, Franz-Josef Peitzmann, Dieter Schramm and Ould el Moctar
Fluids 2023, 8(2), 43; https://doi.org/10.3390/fluids8020043 - 26 Jan 2023
Cited by 18 | Viewed by 6010
Abstract
Physics-informed neural networks (PINN) can be used to predict flow fields with a minimum of simulated or measured training data. As most technical flows are turbulent, PINNs based on the Reynolds-averaged Navier–Stokes (RANS) equations incorporating a turbulence model are needed. Several studies demonstrated [...] Read more.
Physics-informed neural networks (PINN) can be used to predict flow fields with a minimum of simulated or measured training data. As most technical flows are turbulent, PINNs based on the Reynolds-averaged Navier–Stokes (RANS) equations incorporating a turbulence model are needed. Several studies demonstrated the capability of PINNs to solve the Naver–Stokes equations for laminar flows. However, little work has been published concerning the application of PINNs to solve the RANS equations for turbulent flows. This study applied a RANS-based PINN approach to a backward-facing step flow at a Reynolds number of 5100. The standard k-ω model, the mixing length model, an equation-free νt and an equation-free pseudo-Reynolds stress model were applied. The results compared favorably to DNS data when provided with three vertical lines of labeled training data. For five lines of training data, all models predicted the separated shear layer and the associated vortex more accurately. Full article
(This article belongs to the Special Issue Machine Learning and Artificial Intelligence in Fluid Mechanics)
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15 pages, 2162 KiB  
Article
The Electrical Conductivity of Ionic Liquids: Numerical and Analytical Machine Learning Approaches
by Theodoros E. Karakasidis, Filippos Sofos and Christos Tsonos
Fluids 2022, 7(10), 321; https://doi.org/10.3390/fluids7100321 - 5 Oct 2022
Cited by 13 | Viewed by 4749
Abstract
In this paper, we incorporate experimental measurements from high-quality databases to construct a machine learning model that is capable of reproducing and predicting the properties of ionic liquids, such as electrical conductivity. Empirical relations traditionally determine the electrical conductivity with the temperature as [...] Read more.
In this paper, we incorporate experimental measurements from high-quality databases to construct a machine learning model that is capable of reproducing and predicting the properties of ionic liquids, such as electrical conductivity. Empirical relations traditionally determine the electrical conductivity with the temperature as the main component, and investigations only focus on specific ionic liquids every time. In addition to this, our proposed method takes into account environmental conditions, such as temperature and pressure, and supports generalization by further considering the liquid atomic weight in the prediction procedure. The electrical conductivity parameter is extracted through both numerical machine learning methods and symbolic regression, which provides an analytical equation with the aid of genetic programming techniques. The suggested platform is capable of providing either a fast, numerical prediction mechanism or an analytical expression, both purely data-driven, that can be generalized and exploited in similar property prediction projects, overcoming expensive experimental procedures and computationally intensive molecular simulations. Full article
(This article belongs to the Special Issue Machine Learning and Artificial Intelligence in Fluid Mechanics)
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Review

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16 pages, 1167 KiB  
Review
Can Artificial Intelligence Accelerate Fluid Mechanics Research?
by Dimitris Drikakis and Filippos Sofos
Fluids 2023, 8(7), 212; https://doi.org/10.3390/fluids8070212 - 19 Jul 2023
Cited by 18 | Viewed by 7261
Abstract
The significant growth of artificial intelligence (AI) methods in machine learning (ML) and deep learning (DL) has opened opportunities for fluid dynamics and its applications in science, engineering and medicine. Developing AI methods for fluid dynamics encompass different challenges than applications with massive [...] Read more.
The significant growth of artificial intelligence (AI) methods in machine learning (ML) and deep learning (DL) has opened opportunities for fluid dynamics and its applications in science, engineering and medicine. Developing AI methods for fluid dynamics encompass different challenges than applications with massive data, such as the Internet of Things. For many scientific, engineering and biomedical problems, the data are not massive, which poses limitations and algorithmic challenges. This paper reviews ML and DL research for fluid dynamics, presents algorithmic challenges and discusses potential future directions. Full article
(This article belongs to the Special Issue Machine Learning and Artificial Intelligence in Fluid Mechanics)
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