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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…

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…

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…

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…

Accurate and efficient prediction of three-dimensional (3D) wall-bounded turbulent flows poses a significant challenge for machine learning methods, particularly in scenarios where flow field data are limited. Physics-informed neural…

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…

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…

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…

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…

Acquisition of large datasets for three-dimensional (3D) partial differential equations (PDE) is usually very expensive. Physics-informed neural operator (PINO) eliminates the high costs associated with generation of training datasets, and…

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)…

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…

We apply Fourier neural operators (FNOs), a state-of-the-art operator learning technique, to forecast the temporal evolution of experimentally measured velocity fields. FNOs are a recently developed machine learning method capable of…

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,…

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…

The recent development of Neural Operator (NeurOp) learning for solutions to the elastic wave equation shows promising results and provides the basis for fast large-scale simulations for different seismological applications. In this paper,…

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…

We train Fourier Neural Operator (FNO) surrogate models for Rayleigh-B\'enard Convection (RBC), a model for convection processes that occur in nature and industrial settings. We compare the prediction accuracy and model properties of FNO…

Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…

Neural Operators (NOs) are a leading method for surrogate modeling of partial differential equations. Unlike traditional neural networks, which approximate individual functions, NOs learn the mappings between function spaces. While NOs have…