Traditional Computational Fluid Dynamics Research Articles

A modified CFD-DEM method for accurate prediction of the minimum fluidization velocity

Monodisperse fluidized bed experiments have been carried out on 13 kinds of particles with different particle sizes in a cylindrical fluidized bed. The accuracy of nine commonly used monodisperse drag models, including the Gidsapow, BVK, and Zhou–Fan models is verified. It is found that the Zhou–Fan model is the most accurate at low and moderate values of the particle Reynolds number. It is found that with the traditional computational fluid dynamics–discrete element method (CFD-DEM) method it is difficult to obtain an accurate minimum fluidization velocity owing to difficulty in obtaining an accurate value of the minimum fluidization solid volume fraction. A modified method is proposed to increase the accuracy of prediction of the minimum fluidized solid volume fraction by using a virtual particle size in the calculation of the particle collision process. The effectiveness of the modified method is verified by comparing the CFD-DEM simulation results with experimental results for Geldart-D particles. The relative error of the minimum fluidization velocity is found to be reduced from 24.6% to 2%.

A hybrid numerical framework of potential and viscous flows for simulations of free running surface ship maneuvering in waves

This study presents a hybrid numerical framework for the accurate and efficient simulation of free-running surface ship maneuvering in waves. The proposed hybrid framework combines the MOUM (Modified Osaka University Method) body-force method to model the propeller and a hybrid approach of potential and viscous flows for wave-ship interactions. The MOUM body-force method, based on BEMT (Blade Element Momentum Theory), considers the three-dimensional viscous effects of propellers. The hybrid approach of potential and viscous flows decomposes the total physical field into the incident field and the complementary field, where the incident wave is solved by the potential flow theory to ensure the accuracy of wave propagation with coarse grids, and viscous and nonlinear effects are incorporated through the adapted URANS (Unsteady Reynolds Averaged Navier-Stokes) with refined grids. The 6DOF (Degrees of Freedom) motion equations of the rigid body and the dynamic structured grid with the overset technology are adopted to simulate the 6DOF motions of ship maneuvering in waves. Firstly, the applicability of the computational domain, domain-moving strategy, and ship motion-solving method for effectively simulating ship maneuvering in wave conditions are thoroughly examined. Then the reliability of present hybrid approach is validated using turning benchmark model tests of KCS model in regular waves. Simulations of turning circle and zig-zag maneuvers in regular waves are carried out by the traditional viscous CFD (Computational Fluid Dynamics) based on the boundary wave-generation approach and the proposed hybrid framework. The trajectories, motions and forces of ship maneuvering in waves predicted by both methods, as well as the computational efficiency, are compared. Numerical results indicated that the proposed method offers high accuracy and efficiency for predicting ship maneuvering in waves and could serve as a highly credible alternative to existing methods.

Large-scale graph-machine-learning surrogate models for 3D-flowfield prediction in external aerodynamics

The article presents the application of inductive graph machine learning surrogate models for accurate and efficient prediction of 3D flow for industrial geometries, explicitly focusing here on external aerodynamics for a motorsport case. The final aim is to build a surrogate model that can provide quick predictions, bypassing in this way the unfeasible computational burden of traditional computational fluid dynamics (CFD) simulations. We investigate in this contribution the usage of graph neural networks, given their ability to smoothly deal with unstructured data, which is the typical context for industrial simulations. We integrate an efficient subgraph-sampling approach with our model, specifically tailored for large dataset training. REV-GNN is the chosen graph machine learning model, that stands out for its capacity to extract deeper insights from neighboring graph regions. Additionally, its unique feature lies in its reversible architecture, which allows keeping the memory usage constant while increasing the number of network layers. We tested the methodology by applying it to a parametric Navier–Stokes problem, where the parameters control the surface shape of the industrial artifact at hand, here a motorbike.

An innovative end-to-end PINN-based solution for rapidly simulating homogeneous heat flow problems: An adaptive universal physics-guided auto-solver

In contemporary heat flow computations, the widespread application of deep learning, specifically Physical Informed Neural Networks (PINN), has been noted. However, existing PINN methods often exhibit limited applicability to specific operational conditions and are hindered by prolonged training times, rendering them unsuitable for engineering scenarios requiring frequent changes in operational parameters. This study addresses the imperative of enhancing the computational efficiency of conventional PINN methodologies and introduces an innovative end-to-end PINN-based solution—Adaptive Universal Physics-Guided Auto-Solver (AUPgAS) for swift simulation of homogeneous heat flow problems. AUPgAS introduces the operational condition as a variable within the neural network, thereby enhancing the model's versatility in addressing homogeneous problems. Simultaneously, AUPgAS refines training accuracy through the incorporation of adaptive sampling methods. The efficacy of this method is demonstrated through validations on two application cases of laminar incompressible flow with viscosity, namely the flow around a cylinder and the flow around two cylinders. After training, the model demonstrates the capability to predict pressure and velocity fields of the flow around a single cylinder in different locations in case Ⅰ, as well as simulate the flow field when the distance between two cylinders rapidly changes in case Ⅱ. Comparative analyses with traditional computational fluid dynamics methods show that the AUPgAS greatly reduces the solution time, the average time taken by the trained AUPgAS to solve for each problem is 3.4 s, which is a significant improvement in efficiency compared to the average time taken by the traditional fluid dynamics methods, which is 910 s. Furthermore, the agreement of the results obtained by AUPgAS with the reference solution is commendable, with a minimum average error of 13.55%. This end-to-end approach presents an innovative and efficient solution for the rapid simulation of homogeneous heat flow problems, offering promising advancements in the realm of engineering computational efficiency.

Utilizing Artificial intelligence to identify an Optimal Machine learning model for predicting fuel consumption in Diesel engines

This paper describes the utilization of artificial intelligence (AI) techniques to identify an optimal machine learning (ML) model for predicting dodecane fuel consumption in diesel combustion. The study incorporates sensitivity analysis to assess the impact levels of various parameters on fuel consumption, thereby highlighting the most influential factors. In addition, this study addresses the impact of noise and implements data cleaning techniques to ensure the reliability of the obtained results. To validate the accuracy of the predictions, the study performs several metrics and validation process, including comparisons with computational fluid dynamics (CFD) results and experimental data. Comprehensive comparisons are made among neural networks (NN), random forest regression (RFR), and Gaussian process regression (GPR) models, taking into account the complexity associated with fuel consumption predictions. The findings demonstrate that the GPR model outperforms the others in terms of accuracy, as evidenced by metrics such as mean absolute error (MAE), mean squared error (MSE), Pearson coefficient (PC), and R-squared (R2). The GPR model exhibits superior predictive ability, accurately detecting and predicting even individual data points that deviate from the overall trend. The significantly lower absolute error values also consistently indicate its higher accuracy compared with the NN and RFR models. Furthermore, the GPR model shows a remarkable speedup, approximately 1.7 times faster than traditional CFD solvers, and physically captures the momentum and thermal characteristics in a surface field prediction. Finally, the target optimization is assessed using the Euclidean distance as a fitness function, ensuring the reliability of predicted data.

Two-dimensional temperature field inversion of turbine blade based on physics-informed neural networks

Correct evaluation of the blades' surface temperature field is crucial to the structural design and operational safety of aero-engine turbine blades. Current high-temperature measurement technology can only measure the limited discrete points temperature of the hot-end turbine blades. If the boundary conditions are completely unknown, it is still difficult to solve equations through traditional computational fluid dynamics methods. It is an inverse problem to predict the temperature field of the turbine engine blade with unknown boundary conditions. This paper proposes a two-dimensional temperature field inversion of turbine blades based on physics-informed neural networks (PINN) and finite discrete temperature measurement points. The PINN is used to model the nonlinear mapping of input variables and output variables. Only a small amount of data is used to train the neural network. It can be found that adding the loss term of the physical governing equation during training can make the neural network better predict the temperature field of the turbine blade, which can also avoid anomalies such as large temperature errors in some areas that may occur when training with only a small amount of data. When the boundary conditions are completely unknown, the average relative error of PINN trained with only 62 points of temperature data on the test set is below 2%, and the R2−Score is above 0.95. When the training data reaches 122 points of temperature data, the average relative error of PINN on the test set is less than 1%, and the R2−Score reaches 0.99.

Investigation of Compressor Cascade Flow Using Physics-Informed Neural Networks with Adaptive Learning Strategy

In this study, we utilize the emerging physics-informed neural networks (PINNs) approach for the first time to predict the flowfield of a compressor cascade. Different from conventional training methods, a new adaptive learning strategy that mitigates gradient imbalance through incorporating adaptive weights in conjunction with a dynamically adjusting learning rate is used during the training process to improve the convergence of PINNs. The performance of PINNs is assessed here by solving both the forward and inverse problems. In the forward problem, by encapsulating the physical relations among relevant variables, PINNs demonstrate their effectiveness in accurately forecasting the compressor’s flowfield. PINNs also show obvious advantages over the traditional computational fluid dynamics (CFD) approaches, particularly in scenarios lacking complete boundary conditions, as is often the case in inverse engineering problems. PINNs successfully reconstruct the flowfield of the compressor cascade solely based on partial velocity vectors and near-wall pressure information. Furthermore, PINNs show robust performance in the environment of various levels of aleatory uncertainties stemming from labeled data. This research provides evidence that PINNs can offer turbomachinery designers an additional and promising option alongside the current dominant CFD methods.

Mesoscopic Kinetic Approach of Nonequilibrium Effects for Shock Waves.

A shock wave is a flow phenomenon that needs to be considered in the development of high-speed aircraft and engines. The traditional computational fluid dynamics (CFD) method describes it from the perspective of macroscopic variables, such as the Mach number, pressure, density, and temperature. The thickness of the shock wave is close to the level of the molecular free path, and molecular motion has a strong influence on the shock wave. According to the analysis of the Chapman-Enskog approach, the nonequilibrium effect is the source term that causes the fluid system to deviate from the equilibrium state. The nonequilibrium effect can be used to obtain a description of the physical characteristics of shock waves that are different from the macroscopic variables. The basic idea of the nonequilibrium effect approach is to obtain the nonequilibrium moment of the molecular velocity distribution function by solving the Boltzmann-Bhatnagar-Gross-Krook (Boltzmann BGK) equations or multiple relaxation times Boltzmann (MRT-Boltzmann) equations and to explore the nonequilibrium effect near the shock wave from the molecular motion level. This article introduces the theory and understanding of the nonequilibrium effect approach and reviews the research progress of nonequilibrium behavior in shock-related flow phenomena. The role of nonequilibrium moments played on the macroscopic governing equations of fluids is discussed, the physical meaning of nonequilibrium moments is given from the perspective of molecular motion, and the relationship between nonequilibrium moments and equilibrium moments is analyzed. Studies on the nonequilibrium effects of shock problems, such as the Riemann problem, shock reflection, shock wave/boundary layer interaction, and detonation wave, are introduced. It reveals the nonequilibrium behavior of the shock wave from the mesoscopic level, which is different from the traditional macro perspective and shows the application potential of the mesoscopic kinetic approach of the nonequilibrium effect in the shock problem.

A Novel Hybrid Deep Learning Method for Predicting the Flow Fields of Biomimetic Flapping Wings.

The physics governing the fluid dynamics of bio-inspired flapping wings is effectively characterized by partial differential equations (PDEs). Nevertheless, the process of discretizing these equations at spatiotemporal scales is notably time consuming and resource intensive. Traditional PDE-based computations are constrained in their applicability, which is mainly due to the presence of numerous shape parameters and intricate flow patterns associated with bionic flapping wings. Consequently, there is a significant demand for a rapid and accurate solution to nonlinear PDEs, to facilitate the analysis of bionic flapping structures. Deep learning, especially physics-informed deep learning (PINN), offers an alternative due to its great nonlinear curve-fitting capability. In the present work, a hybrid coarse-data-driven physics-informed neural network model (HCDD-PINN) is proposed to improve the accuracy and reliability of predicting the time evolution of nonlinear PDEs solutions, by using an order-of-magnitude-coarser grid than traditional computational fluid dynamics (CFDs) require as internal training data. The architecture is devised to enforce the initial and boundary conditions, and incorporate the governing equations and the low-resolution spatiotemporal internal data into the loss function of the neural network, to drive the training. Compared to the original PINN with no internal data, the training and predicting dynamics of HCDD-PINN with different resolutions of coarse internal data are analyzed on the problem relevant to the two-dimensional unsteady flapping wing, which involves unsteady flow features and moving boundaries. Additionally, a hyper-parametrical study is conducted to obtain an optimal model for the problem under consideration, which is then utilized for investigating the effects of the snapshot and fraction of the coarse internal data on the HCDD-PINN's performances. The results show that the proposed framework has a sufficient stability and accuracy for solving the considered biomimetic flapping-wing problem, and its great potential means that it can be considered as an alternative to accelerate or replace traditional CFD solvers in the future. The interested variables of the flow field at any instant can be rapidly obtained by the trained HCDD-PINN model, which is superior to the traditional CFD method that usually needs to be re-run. For the three-dimensional and optimization problems of flapping wings, the advantages of the proposed method are supposedly even more apparent.

Physics-informed recurrent super-resolution generative reconstruction in rotating detonation combustor

The high-resolution flow field information is crucial for understanding flow systems. Nevertheless, due to limitations in sensor technology and measurement methods, it is challenging to obtain high-resolution data in engineering applications. This study introduces a novel model called physics-informed recurrent generative adversarial network (PIRGAN) to obtain super-resolution results from low-resolution inputs, which is an inverse problem that is difficult to solve using traditional computational fluid dynamics (CFD) methods. The model integrates recurrent framework and embedding physical constraints into its architecture to perform super-resolution generative reconstruction. During the generation process, this model calculates temporal derivatives based on low-resolution inputs and then updates the previous timestep's results by temporal derivatives to obtain the current timestep's results. The proposed PIRGAN model is demonstrated through its application to the reconstruction of flow fields in Rotating Detonation Combustors (RDC). Notably, PIRGAN successfully reconstructs detailed flow structure inside RDC, which is often indiscernible in low-resolution or interpolated results. Besides, the introduction of a recurrent framework offers the model's ability to capture the temporal characteristics and handle noisy inputs. As a surrogate model that extends the measurement capabilities within reactive flow systems, the model introduced in this study holds noticeable engineering significance.

A finite element implementation of the incompressible Schrödinger flow method

As first proposed by Madelung in 1926, the analogy between quantum mechanics and hydrodynamics has been known for a long time; however, its potentialities and the possibility of using the characteristic equations of quantum mechanics to simulate the behavior of inviscid fluids have not been thoroughly investigated in the past. In this methodology, the incompressible Euler equations are thus substituted by the Schrödinger equation, turning a quasi-linear Partial Differential Equation into a linear one, an algorithm known in the literature as Incompressible Schrödinger Flow. Previous works on the subject used the Fast Fourier Transform method to solve this problem, obtaining promising results, especially in predicting vortex dynamics; this paper aims to implement this novel approach into a Finite Element framework to find a more general formulation better suited for future application on complex geometries and on test cases closer to real-world applications. Simple case studies are presented in this work to analyze the potentialities of this method: the results obtained confirm that this method could potentially have some advantages over traditional Computational Fluid Dynamics method, especially for what concerns computational savings related to the required time discretization, whilst also introducing new aspects of the algorithm, mainly related to boundary conditions, not addressed in previous works.

Stacked Deep Learning Models for Fast Approximations of Steady-State Navier–Stokes Equations for Low Re Flow

Computational fluid dynamics (CFD) simulations are broadly used in many engineering and physics fields. CFD requires the solution of the Navier–Stokes (N-S) equations under complex flow and boundary conditions. However, applications of CFD simulations are computationally limited by the availability, speed, and parallelism of high-performance computing. To address this, machine learning techniques have been employed to create data-driven approximations for CFD to accelerate computational efficiency. Unfortunately, these methods predominantly depend on large labeled CFD datasets, which are costly to procure at the scale required for robust model development. In response, we introduce a weakly supervised approach that, through a multichannel input capturing boundary and geometric conditions, solves steady-state N-S equations. Our method achieves state-of-the-art results without relying on labeled simulation data, instead using a custom data-driven and physics-informed loss function and small-scale solutions to prime the model for solving the N-S equations. By training stacked models, we enhance resolution and predictability, yielding high-quality numerical solutions to N-S equations without hefty computational demands. Remarkably, our model, being highly adaptable, produces solutions on a 512 × 512 domain in a swift 7 ms, outpacing traditional CFD solvers by a factor of 1,000. This paves the way for real-time predictions on consumer hardware and Internet of Things devices, thereby boosting the scope, speed, and cost-efficiency of solving boundary-value fluid problems.

Data driven reduced modeling for fluidized bed with immersed tubes based on PCA and Bi-LSTM neural networks

The fast and accurate reduced-order modeling of fluidized beds is a challenging task in the field of fluid dynamics, owing to their high dimensionality and nonlinear dynamic behavior. In this study, a nonintrusive reduced order modeling method, the reduced order model based on principal component analysis and bidirectional long short-term memory networks (PBLSTM ROM), was developed to capture complex spatio-temporal dynamics of fluidized beds. By combining principal component analysis and Bidirectional long- short-term memory networks, the PBLSTM ROM effectively extracted dynamic evolution information without any prior knowledge of governing equations, enabling reduced-order modeling of unsteady flow fields. The PBLSTM ROM was validated using the solid volume fraction and gas velocity flow fields of a fluidized bed with immersed tubes, showing superior performance over both the PLSTM and PANN ROMs in accurately capturing temporal changes in the fluidization fields, especially in the region near immersed tubes where severe fluctuations appear. Moreover, the PBLSTM ROM improved the simulation speed by five orders of magnitude compared to traditional computational fluid dynamics simulations. These findings suggest that the PBLSTM ROM presents a promising approach for analyzing the complex fluid flows in engineering practice.

Physics-informed neural networks for heat transfer prediction in two-phase flows

This paper presents data-driven simulations of two-phase fluid processes with heat transfer. A Physics-Informed Neural Network (PINN) was applied to capture the behaviour of phase interfaces in two-phase flows and model the hydrodynamics and heat transfer of flow configurations representative of established numerical test cases. The developed PINN approach was trained on simulation data derived from physically based Computational Fluid Dynamics (CFD) simulations with interface capturing. The present study considers fundamental problems, including tracking the rise of a single gas bubble in a denser fluid and exploring the heat transfer in the wake of a bubble rising close to a heated wall. Tracking of a rising bubble phase interface of fluids with disparate properties was performed, revealing a maximum error of only 5.2% at the interface edge and a maximum error of 2.8% at the position of the centre of mass. Inferred (hidden variable) flows are studied in addition to a purely extrapolative inverse isothermal bubble case. When no velocity data was supplied, velocity field predictions remained accurate. Rise of an inferred isothermal bubble with unseen fluid properties was found to produce a maximum mean-squared error of 0.28 and centre of mass error of 1.25%. For the case of the rising bubble with a hot wall, the maximum error in the temperature domain using specified boundary conditions was 6.8%, while the bubble position analysis reveals a maximum positional error of 3.6%. These results demonstrate that PINN is agnostic to geometry and fluid properties when studying the combined effects of convection and buoyancy on two-phase flows for the first time. This work serves as a starting point for PINN in multiphase cases involving heat transfer over a range of geometries. Eventually, PINN will be used in such cases to provide solutions for forward, inverse, and extrapolative cases. Each of which represent a dramatic saving in computational cost compared to traditional CFD.

Simulation of heavy particles fluidized with non-Newtonian fluids

Aqueous solutions of very fine particles behave as non-Newtonian fluids and are used to fluidize heavy spherical particles creating large bed expansions and inhomogeneities similar to those observed in traditional fluidization of particles with Newtonian fluids. This study attempts to extend the validity of traditional computational fluid dynamics (CFD) models that are routinely used for gas-solids fluidization to non-Newtonian fluids. The modified model incorporates a shear-thinning power law viscosity for the non-Newtonian fluid and a recently published drag correlation derived from direct numerical simulation data of flow around randomly positioned spheres. This validation study compares numerical results obtained in 3D fluidized beds with two independent experimental bed porosity data sets for heavy steel and glass spherical particles. The current CFD results show a better agreement with experimental data obtained over a wide range of porosity and Reynolds number than a previously published semi-empirical correlation.

Validation of Rotating Detonation Combustor Computational Fluid Dynamics Simulations for Predicting Unsteady Supersonic–Subsonic Flow Field at the Exit

Abstract Rotating detonation combustors (RDCs) have gained increased interest for integration with power-generating gas turbines due to the potential to increase thermal efficiency. The unsteady flow field exiting the RDC is fundamentally different compared to traditional swirl-stabilized combustors. Successful integration of RDC with gas turbines will depend on the ability to properly condition the unsteady flow to achieve performance levels comparable to swirl-stabilized combustors. RDC simulations require significant computational resources due to the small spatial and temporal time scales required to resolve the detonation phenomenon. Furthermore, traditional steady-state computational fluid dynamics (CFD) analyses are not possible for RDC simulations. The present study develops and validates a computationally efficient approach for predicting unsteady flow fields exiting the combustor using 2D, transient reacting CFD with periodic boundary conditions in the combustor and a downstream plenum. Validation is performed by comparing the CFD results to various experimental measurements: (i) wave speed obtained from high-speed ion probe and dynamic pressure data, (ii) average wall static pressure measurements, and (iii) time-resolved particle image velocimetry (PIV) at 100 kHz at the RDC exit. Results indicate good agreement between CFD and experiments with respect to velocity field exiting the RDC, detonation wave speed, and static pressure distribution.

Efficient optimization design of flue deflectors through parametric surrogate modeling with physics-informed neural networks

In engineering applications, deflectors play a vital role in regulating the uniformity of flow field distribution in the selective catalytic reduction (SCR) system, and their optimal design is a topic of great concern. However, traditional optimal design methods often suffer from insufficient prediction accuracy or too high computational cost. This paper develops and verifies an efficient and robust parametric surrogate model for SCR systems based on the physics-informed neural networks (PINNs) framework. This study comprises three progressive steps. (1) We predicted the flow field distribution in the original flue based on the PINNs framework and compared the results qualitatively and quantitatively with the traditional computational fluid dynamics (CFD) method. The results show that the maximum relative error of velocity is 12.6%, and the relative error is within 5% in most areas. (2) For the optimal design of the deflector in the SCR system, a parametric surrogate model based on the PINNs framework is developed, and the model inputs include not only the coordinate variables but also the position parameters of the deflector. The accuracy and efficiency of this parametric surrogate model are also compared with the traditional CFD method. (3) Based on the parametric surrogate model developed above, the deflector optimal position for the research object of this study is found through two quantitative indicators (uniformity coefficient and flue gas energy loss). The results demonstrate that the parameterized model based on PINNs can reduce the computational time to about 14% compared to traditional methods. Finally, the sensitivity analysis of the deflector position parameters is carried out. Overall, the results of this study demonstrate that the parametric surrogate model based on the PINNs framework is an efficient and robust tool for system optimization, design, and autonomous control.

A novel compact thermal management model for performance evaluation of tesla-like lithium-ion battery packs

This study presents a compact thermal management model for Li-ion battery packs, with a specific focus on Tesla Model S vehicles. The model, which utilizes a detailed thermal resistance network, provides faster results than traditional Computational Fluid Dynamics (CFD) tools, making it approximately 10.5 times faster without compromising on comprehensive assessment. Key factors such as the C-rate and initial fluid temperature were found to significantly impact battery temperature and the maximum temperature difference. For instance, as the C-rate increases from 0.5 to 5, the average battery temperature rises by 84.5 °C, a condition that would lead to thermal runaway in practical scenarios. Meanwhile, an increase in the initial fluid temperature from 15 °C to 30 °C results in an approximate increase of 13.2 °C in the average battery temperature. The coolant velocity also plays a crucial role in managing heat dissipation from the batteries. The model, offering easy customization and reduced computational complexity, is ideal for modeling and simulations of Li-ion battery modules and packs. This research significantly contributes to improving the efficiency and safety of Li-ion batteries, particularly in electric vehicles, providing valuable insights for the design and analysis of battery thermal management systems (BTMS).

A novel study on forecasting the airfoil self-noise, using a hybrid model based on the combination of CatBoost and Arithmetic Optimization Algorithm

One of the important challenges in aircraft design is the light, inexpensive, and self-noise-free design of airfoil. Since the self-noise generated by rotor blades interacting with turbulent flow produced in their boundary layer can impact how well the system works. Predicting aerofoil self-noise can help shorten computational times and improve cost-effectiveness because traditional computational fluid dynamics methods flow has more time consumption. Therefore, this paper proposes a forecasting approach using the hybrid model of the CatBoost algorithm. In this way, the hyperparameters of the CatBoost are tuned by twelve optimizers to increase precision and speed up forecasting. The precision of the hybrid models is evaluated by statistical evaluation indices such as Coefficient of determination (R2), Root Mean Square Error (RMSE), Mean Absolute Error (MSE), and relative absolute error (MAE). The obtained results show that the CatBoost combination with the Arithmetic Optimization Algorithm better operates optimally and depicts lower error values compared to other optimizers. Also, the values of the coefficient of determination for training and testing data with 0.9999 and 0.9706, respectively, demonstrate that Arithmetic Optimizer is the most precise optimizer among studied metaheuristic algorithms.

Differentiable hybrid neural modeling for fluid-structure interaction

Solving complex fluid-structure interaction (FSI) problems, which are described by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics based solvers are inadequate to handle the increasing demand for large-scale and long-period simulations. The ever-increasing availability of data and rapid advancement in deep learning (DL) have opened new avenues to tackle these challenges through data-enabled modeling. The seamless integration of DL and classic numerical techniques through the differentiable programming framework can significantly improve data-driven modeling performance. In this study, we propose a differentiable hybrid neural modeling framework for efficient simulation of FSI problems, where the numerically discretized FSI physics based on the immersed boundary method is seamlessly integrated with sequential neural networks using differentiable programming. All modules are programmed in JAX, where automatic differentiation enables gradient back-propagation over the entire model rollout trajectory, allowing the hybrid neural FSI model to be trained as a whole in an end-to-end, sequence-to-sequence manner. Through several FSI benchmark cases, we demonstrate the merit and capability of the proposed method in modeling FSI dynamics for both rigid and flexible bodies. The proposed model has also demonstrated its superiority over baseline purely data-driven neural models, weakly-coupled hybrid neural models, and purely numerical FSI solvers in terms of accuracy, robustness, and generalizability.