Generalization of Urban Wind Field Using Fourier Neural Operators Across Different Wind Directions and Cities

In urban environments, the most common forms of air transportation are helicopters and unmanned aerial vehicles (UAVs). There is a high demand for air transport of small and medium sized aircraft, including UAVs. Wind field simulations in urban environments are typically performed using computational fluid dynamics (CFD), and most of these models fall into the categories of direct numerical simulation (DNS) and large eddy simulation (LES). Although these models are accurate, they are time-consuming, so there is a need to develop a more convenient method to replace the traditional CFD methods. In recent years, with the rapid development of artificial intelligence technology and graphics processing unit (GPU) hardware, a promising research direction has emerged. Currently, many studies are using artificial intelligence-based deep learning techniques to transform the computational processes associated with wind field simulation. The goal of these studies is not only to achieve the accuracy of traditional CFD models, but to surpass them while significantly accelerating the computational process. In this paper, we apply the Fourier Neural Operator (FNO) method based on deep learning technology to simulate the wind field in a two-dimensional urban environment. The method uses a Fourier module to extract and learn features in the Fourier frequency domain of the input data. Compared to traditional convolutional neural network (CNN) modules, Fourier modules aim to learn global features in the Fourier frequency domain of the input data. In contrast, a convolutional neural network (CNN) module performs feature learning in the local spatial domain of the input features. In addition, the input features are processed by a Multi- Layer Perceptron (MLP) module, and the feature output of the MLP module is added to the feature output of the Fourier module. This structure is based on a residual network (ResNet), which can mitigate the phenomenon of gradient vanishing or gradient explosion that occurs when input data propagates through a multilayer network. The FNO model ultimately maps the input features (i.e., the input wind field) to the desired output features (i.e., the output wind field dimensions). Gradients are updated through back propagation to reduce the discrepancy between the FNO model’s output wind field and the actual wind field, thus facilitating the deep learning process. After a series of experiments, the optimal settings for the Fourier layer number and the intermediate feature dimensions of the MLP in the FNO model were determined. In this context, “intermediate feature dimensions” refers to the number of features extracted by the MLP module. These settings ensure that the FNO model achieves the best results on the dataset while minimizing computational overhead and resource consumption. The training phase utilized wind field data from Niigata with westerly winds, with a time step of 0.1 seconds, and the output consisted of wind fields at the same location with a time step of 1 second (i.e. 10 time steps). Experimental results demonstrated that the FNO model could predict the wind field over the entire Niigata urban area for the next 7 seconds (i.e. 70 time i steps), with an average absolute error of less than 0.5 m/s. Importantly, the FNO exhibited strong generalization capabilities in different wind conditions: although the training data consisted of westerly wind data from Niigata, the model performed well in tests with northerly winds. Further validation across different urban geometries revealed that the FNO model could accurately predict 70 time steps (7 seconds) of wind fields in the vertically flipped version of Niigata, indicating that it generalizes well when the geometry is similar to the training data. However, in Montreal, which has a significantly different urban geometry, the model’s accuracy diminished after 10 time steps. This highlights the significance of urban geometry in wind field prediction. During this process, the FNO’s wind field simulation was 300 times faster than that of the CityFFD model we employed, with CityFFD requiring 2.2 seconds per step, whereas FNO took only 0.006 seconds. This further underscores the potential of the FNO model for practical applications in wind field simulation. Although it is premature to use FNO directly to replace wind field simulation due to the exponential growth of errors with time, it is possible to use it in conjunction with CityFFD and other technologies as a complementary model. For example, the wind field output by CityFFD at a given time step can be used as input to FNO, which can generate the wind field in the same area at subsequent time steps. The final output wind field can be used as input to CityFFD, thus reducing the intermediate computation time of CityFFD.

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