Abstract

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.