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This paper explores Neural Operators to predict turbulent flows, focusing on the Fourier Neural Operator (FNO) model. It aims to develop reduced-order/surrogate models for turbulent flow simulations using Machine Learning. Different model…
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…
High-fidelity direct numerical simulation of turbulent flows for most real-world applications remains an outstanding computational challenge. Several machine learning approaches have recently been proposed to alleviate the computational…
Long-term prediction of three-dimensional (3D) turbulent flows is one of the most challenging problems for machine learning approaches. Although some existing machine learning approaches such as implicit U-net enhanced Fourier neural…
Accurately autoregressive prediction of three-dimensional (3D) turbulence has been one of the most challenging problems for machine learning approaches. Diffusion models have demonstrated high accuracy in predicting two-dimensional (2D)…
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…
Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically…
Turbulence poses challenges for numerical simulation due to its chaotic, multiscale nature and high computational cost. Traditional turbulence modeling often struggles with accuracy and long-term stability. Recent scientific machine…
Fourier Neural Operators (FNOs) have demonstrated exceptional accuracy in mapping functional spaces by leveraging Fourier transforms to establish a connection with underlying physical principles. However, their opaque inner workings often…
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…
Modeling complex fluid systems, especially turbulence governed by partial differential equations (PDEs), remains a fundamental challenge in science and engineering. Recently, diffusion-based generative models have gained attention as a…
The random Fourier method (RFM) is widely employed for synthetic turbulence due to its mathematical clarity and simplicity. However, deviations remain between prescribed inputs and synthetic results, and the origin of these errors has not…
We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the…
Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing differential equations…
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,…
Fourier neural operators (FNOs) provide a mesh-independent way to learn solution operators for partial differential equations, yet their efficacy for magnetized turbulence is largely unexplored. Here we train an FNO surrogate for the 2-D…
Neural operators are a new type of models that can map between function spaces, allowing trained models to emulate the solution operators of partial differential equations (PDEs). This paper proposes a multigrid Fourier neural operator…
Spatio-temporal process models are often used for modeling dynamic physical and biological phenomena that evolve across space and time. These phenomena may exhibit environmental heterogeneity and complex interactions that are difficult to…
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 $Sr=1.0$,…
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…