arXiv subjects

Wenhui Peng

Publications and source records attributed to Wenhui Peng.

12 recordsLinked to original sources

arXiv2025

Machine-learning-based simulation of turbulent flows over periodic hills using a hybrid U-Net and Fourier neural operator framework

Simulating massively separated turbulent flows over bodies is one of the major applications for large-eddy simulation (LES). In the current work, we propose a machine-learning-based LES framework for the rapid simulation of turbulent flows over periodic hills using a hybrid U-Net and Fourier neural operator (HUFNO) framework. The newly proposed HUFNO model integrates the strengths of both the convolutional neural network (CNN) and Fourier neural operator (FNO) in a novel way that the FNO is applied in the periodic directions of the flow field while the non-periodicity is handled by the CNN-based U-Net framework. In the numerical tests, compared to the original FNO and the U-Net framework, the HUFNO model shows a higher accuracy in the predictions of the velocity field and Reynolds stresses. Further numerical experiments in the LES show that the HUFNO framework outperforms the traditional Smagorinsky (SMAG) model and the wall-adapted local eddy-viscosity (WALE) model in the predictions of the turbulence statistics, the energy spectrum, the invariant characteristics of velocity gradients, the wall stresses and the flow separation structures, with much lower computational cost. Importantly, the accuracy and efficiency are transferable to unseen initial conditions, Reynolds number and hill shapes, underscoring its great potentials for the fast prediction of strongly separated turbulent flows over curved boundaries.

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arXiv2025

Residual U-Net for accurate and efficient prediction of hemodynamics in two-dimensional asymmetric stenosis

This study presents residual U-Net (U-ResNet), a deep learning surrogate model for predicting steady hemodynamic fields in two-dimensional asymmetric stenotic channels at Reynolds numbers ranging from 200 to 800. By integrating residual connections with multi-scale feature extraction, U-ResNet achieves exceptional accuracy while significantly reducing computational costs compared to computational fluid dynamics (CFD) approaches. Comprehensive evaluation against U-Net, Fourier Neural Operator (FNO), and U-Net enhanced Fourier Neural Operator (UFNO) demonstrates U-ResNet superior performance in capturing sharp hemodynamic gradients and complex flow features. For pressure prediction, U-ResNet achieves a normalized mean absolute error (NMAE) of 1.10%. Similarly, the performance of U-ResNet for wall shear stress (NMAE: 0.56%), velocity (NMAE: 1.06%), and vorticity (NMAE: 0.69%) consistently surpasses alternative architectures. Notably, U-ResNet demonstrates robust generalization to interpolated Reynolds numbers without retraining - a capability rarely achieved in existing models. From a computational perspective, U-ResNet delivers a 180-fold acceleration over CFD, reducing simulation time from approximately 30 minutes to 10 seconds per case. The model with non-dimensional formulation ensures scalability across vessel sizes and anatomical locations, enhancing its applicability to diverse clinical scenarios. These advances position U-ResNet as a promising auxiliary tool to complement CFD simulations for real-time clinical decision support, treatment planning, and medical device optimization. Future work will focus on extending the framework to three-dimensional geometries and integrating it with patient-specific data.

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arXiv2024

Modeling Multivariable High-resolution 3D Urban Microclimate Using Localized Fourier Neural Operator

Accurate urban microclimate analysis with wind velocity and temperature is vital for energy-efficient urban planning, supporting carbon reduction, enhancing public health and comfort, and advancing the low-altitude economy. However, traditional computational fluid dynamics (CFD) simulations that couple velocity and temperature are computationally expensive. Recent machine learning advancements offer promising alternatives for accelerating urban microclimate simulations. The Fourier neural operator (FNO) has shown efficiency and accuracy in predicting single-variable velocity magnitudes in urban wind fields. Yet, for multivariable high-resolution 3D urban microclimate prediction, FNO faces three key limitations: blurry output quality, high GPU memory demand, and substantial data requirements. To address these issues, we propose a novel localized Fourier neural operator (Local-FNO) model that employs local training, geometry encoding, and patch overlapping. Local-FNO provides accurate predictions for rapidly changing turbulence in urban microclimate over 60 seconds, four times the average turbulence integral time scale, with an average error of 0.35 m/s in velocity and 0.30 {\deg}C in temperature. It also accurately captures turbulent heat flux represented by the velocity-temperature correlation. In a 2 km by 2 km domain, Local-FNO resolves turbulence patterns down to a 10 m resolution. It provides high-resolution predictions with 150 million feature dimensions on a single 32 GB GPU at nearly 50 times the speed of a CFD solver. Compared to FNO, Local-FNO achieves a 23.9% reduction in prediction error and a 47.3% improvement in turbulent fluctuation correlation.

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arXiv2024

Prediction of three-dimensional chemically reacting compressible turbulence based on implicit U-Net enhanced Fourier neural operator

The accurate and fast prediction of long-term dynamics of turbulence presents a significant challenge for both traditional numerical simulations and machine learning methods. In recent years, the emergence of neural operators has provided a promising approach to address this issue. The implicit U-Net enhanced Fourier neural operator (IU-FNO) has successfully demonstrated long-term stable predictions for three-dimensional incompressible turbulence. In this study, we extend this method to the three-dimensional chemically reacting compressible turbulence. Numerical results show that the IU-FNO model predicts flow dynamics significantly faster than the traditional dynamic Smagorinsky model (DSM) used in large eddy simulation (LES). In terms of prediction accuracy, the IU-FNO framework outperforms the traditional DSM in predicting the energy spectra of velocity, temperature, and density, the probability density functions (PDFs) of vorticity and velocity increments, and instantaneous spatial structures of temperature. Therefore, the IU-FNO represents a highly promising approach for predicting chemically reacting compressible turbulence.

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arXiv2024

Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspective

In solving partial differential equations (PDEs), Fourier Neural Operators (FNOs) have exhibited notable effectiveness. However, FNO is observed to be ineffective with large Fourier kernels that parameterize more frequencies. Current solutions rely on setting small kernels, restricting FNO's ability to capture complex PDE data in real-world applications. This paper offers empirical insights into FNO's difficulty with large kernels through spectral analysis: FNO exhibits a unique Fourier parameterization bias, excelling at learning dominant frequencies in target data while struggling with non-dominant frequencies. To mitigate such a bias, we propose SpecB-FNO to enhance the capture of non-dominant frequencies by adopting additional residual modules to learn from the previous ones' prediction residuals iteratively. By effectively utilizing large Fourier kernels, SpecB-FNO achieves better prediction accuracy on diverse PDE applications, with an average improvement of 50%.

cs.LG↗

arXiv2024

Fourier neural operator for large eddy simulation of compressible Rayleigh-Taylor turbulence

The Fourier neural operator (FNO) framework is applied to the large eddy simulation (LES) of three-dimensional compressible Rayleigh-Taylor (RT) turbulence with miscible fluids at Atwood number $A_t=0.5$, stratification parameter $Sr=1.0$, and Reynolds numbers $Re=10000$ and 30000. The FNO model is first used for predicting three-dimensional compressible turbulence. The different magnitudes of physical fields are normalized using root mean square values for an easier training of FNO models. In the \emph{a posteriori} tests, the FNO model outperforms the velocity gradient model (VGM), the dynamic Smagorinsky model (DSM), and implicit large eddy simulation (ILES) in predicting various statistical quantities and instantaneous structures, and is particularly superior to traditional LES methods in predicting temperature fields and velocity divergence. Moreover, the computational efficiency of the FNO model is much higher than that of traditional LES methods. FNO models trained with short-time, low Reynolds number data exhibit a good generalization performance on longer-time predictions and higher Reynolds numbers in the \emph{a posteriori} tests.

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arXiv2024

A transformer-based neural operator for large-eddy simulation of turbulence

Predicting the large-scale dynamics of three-dimensional (3D) turbulence is challenging for machine learning approaches. This paper introduces a transformer-based neural operator (TNO) to achieve precise and efficient predictions in the large-eddy simulation (LES) of 3D turbulence. The performance of the proposed TNO model is systematically tested and compared with LES using classical sub-grid scale (SGS) models, including the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM), as well as the original Fourier neural operator (FNO) model, in homogeneous isotropic turbulence (HIT) and free-shear turbulent mixing layer. The numerical simulations comprehensively evaluate the performance of these models on a variety of flow statistics, including the velocity spectrum, the probability density functions (PDFs) of vorticity, the PDFs of velocity increments, the evolution of turbulent kinetic energy, and the iso-surface of the Q-criterion. The results indicate that the accuracy of the TNO model is comparable to the LES with DSM model, and outperforms the FNO model and LES using DMM in HIT. In the free-shear turbulence, the TNO model exhibits superior accuracy compared to other models. Moreover, the TNO model has fewer parameters than the FNO model and enables long-term stable predictions, which the FNO model cannot achieve. The well-trained TNO model is significantly faster than traditional LES with DSM and DMM models, and can be generalized to higher Taylor-Reynolds number cases, indicating its strong potential for 3D nonlinear engineering applications.

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arXiv2024

Prediction of turbulent channel flow using Fourier neural operator-based machine-learning strategy

Fast and accurate predictions of turbulent flows are of great importance in the science and engineering field. In this paper, we investigate the implicit U-Net enhanced Fourier neural operator (IUFNO) in the stable prediction of long-time dynamics of three-dimensional (3D) turbulent channel flows. The trained IUFNO models are tested in the large-eddy simulations (LES) at coarse grids for three friction Reynolds numbers: $Re_{\tau}\approx180$, $395$ and $590$. The adopted near-wall mesh grids are tangibly coarser than the general requirements for wall-resolved LES. Compared to the original Fourier neural operator (FNO), the implicit FNO (IFNO) and U-Net enhanced FNO (UFNO), the IUFNO model has a much better long-term predictive ability. The numerical experiments show that the IUFNO framework outperforms the traditional dynamic Smagorinsky model (DSM) and the wall-adapted local eddy-viscosity (WALE) model in the predictions of a variety of flow statistics and structures, including the mean and fluctuating velocities, the probability density functions (PDFs) and joint PDF of velocity fluctuations, the Reynolds stress profile, the kinetic energy spectrum, and the Q-criterion (vortex structures). Meanwhile, the trained IUFNO models are computationally much faster than the traditional LES models. Thus, the IUFNO model is a promising approach for the fast prediction of wall-bounded turbulent flow.

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arXiv2023

Fourier neural operator for real-time simulation of 3D dynamic urban microclimate

Global urbanization has underscored the significance of urban microclimates for human comfort, health, and building/urban energy efficiency. They profoundly influence building design and urban planning as major environmental impacts. Understanding local microclimates is essential for cities to prepare for climate change and effectively implement resilience measures. However, analyzing urban microclimates requires considering a complex array of outdoor parameters within computational domains at the city scale over a longer period than indoors. As a result, numerical methods like Computational Fluid Dynamics (CFD) become computationally expensive when evaluating the impact of urban microclimates. The rise of deep learning techniques has opened new opportunities for accelerating the modeling of complex non-linear interactions and system dynamics. Recently, the Fourier Neural Operator (FNO) has been shown to be very promising in accelerating solving the Partial Differential Equations (PDEs) and modeling fluid dynamic systems. In this work, we apply the FNO network for real-time three-dimensional (3D) urban wind field simulation. The training and testing data are generated from CFD simulation of the urban area, based on the semi-Lagrangian approach and fractional stepping method to simulate urban microclimate features for modeling large-scale urban problems. Numerical experiments show that the FNO model can accurately reconstruct the instantaneous spatial velocity field. We further evaluate the trained FNO model on unseen data with different wind directions, and the results show that the FNO model can generalize well on different wind directions. More importantly, the FNO approach can make predictions within milliseconds on the graphics processing unit, making real-time simulation of 3D dynamic urban microclimate possible.

cs.LG↗

arXiv2023

Long-term predictions of turbulence by implicit U-Net enhanced Fourier neural operator

Long-term predictions of nonlinear dynamics of three-dimensional (3D) turbulence are very challenging for machine learning approaches. In this paper, we propose an implicit U-Net enhanced Fourier neural operator (IU-FNO) for stable and efficient predictions on the long-term large-scale dynamics of turbulence. The IU-FNO model employs implicit recurrent Fourier layers for deeper network extension and incorporates the U-net network for the accurate prediction on small-scale flow structures. The model is systematically tested in large-eddy simulations of three types of 3D turbulence, including forced homogeneous isotropic turbulence (HIT), temporally evolving turbulent mixing layer, and decaying homogeneous isotropic turbulence. The numerical simulations demonstrate that the IU-FNO model is more accurate than other FNO-based models including vanilla FNO, implicit FNO (IFNO) and U-Net enhanced FNO (U-FNO), and dynamic Smagorinsky model (DSM) in predicting a variety of statistics including the velocity spectrum, probability density functions (PDFs) of vorticity and velocity increments, and instantaneous spatial structures of flow field. Moreover, IU-FNO improves long-term stable predictions, which has not been achieved by the previous versions of FNO. Besides, the proposed model is much faster than traditional LES with DSM model, and can be well generalized to the situations of higher Taylor-Reynolds numbers and unseen flow regime of decaying turbulence.

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arXiv2022

Linear attention coupled Fourier neural operator for simulation of three-dimensional turbulence

Modeling three-dimensional (3D) turbulence by neural networks is difficult because 3D turbulence is highly-nonlinear with high degrees of freedom and the corresponding simulation is memory-intensive. Recently, the attention mechanism has been shown as a promising approach to boost the performance of neural networks on turbulence simulation. However, the standard self-attention mechanism uses $O(n^2)$ time and space with respect to input dimension $n$, and such quadratic complexity has become the main bottleneck for attention to be applied on 3D turbulence simulation. In this work, we resolve this issue with the concept of linear attention network. The linear attention approximates the standard attention by adding two linear projections, reducing the overall self-attention complexity from $O(n^2)$ to $O(n)$ in both time and space. The linear attention coupled Fourier neural operator (LAFNO) is developed for the simulation of 3D turbulence. Numerical simulations show that the linear attention mechanism provides 40\% error reduction at the same level of computational cost, and LAFNO can accurately reconstruct a variety of statistics and instantaneous spatial structures of 3D turbulence. The linear attention method would be helpful for the improvement of neural network models of 3D nonlinear problems involving high-dimensional data in other scientific domains.

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arXiv2021

Attention-Enhanced Neural Network Models for Turbulence Simulation

Deep neural network models have shown a great potential in accelerating the simulation of fluid dynamic systems. Once trained, these models can make inference within seconds, thus can be extremely efficient. However, they suffer from a generalization problem when the flow becomes chaotic and turbulent. One of the most important reasons is that, existing models lack the mechanism to handle the unique characteristic of turbulent flow: multi-scale flow structures are non-uniformly distributed and strongly nonequilibrium. In this work, we address this issue with the concept of visual attention: intuitively, we expect the attention module to capture the nonequilibrium of turbulence by automatically adjusting weights on different regions. We benchmark the performance improvement with a state of the art neural network model, the Fourier Neural Operator (FNO), on two-dimensional (2D) turbulence prediction task. Numerical experiments show that the attention-enhanced neural network model can generalize well on higher Reynolds numbers flow, and can accurately reconstruct a variety of statistics and instantaneous spatial structures of turbulence. The attention mechanism provides 40% error reduction with 1% increase of parameters, at the same level of computational cost.

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