Shaoxiang Qin

Shaoxiang Qin, Fuyuan Lyu, Wenhui Peng et al.

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%.

Cheng Chen, Geng Tian, Shaoxiang Qin et al.

Simulation of urban wind environments is crucial for urban planning, pollution control, and renewable energy utilization. However, the computational requirements of high-fidelity computational fluid dynamics (CFD) methods make them impractical for real cities. To address these limitations, this study investigates the effectiveness of the Fourier Neural Operator (FNO) model in predicting flow fields under different wind directions and urban layouts. In this study, we investigate the effectiveness of the Fourier Neural Operator (FNO) model in predicting urban wind conditions under different wind directions and urban layouts. By training the model on velocity data from large eddy simulation data, we evaluate the performance of the model under different urban configurations and wind conditions. The results show that the FNO model can provide accurate predictions while significantly reducing the computational time by 99%. Our innovative approach of dividing the wind field into smaller spatial blocks for training improves the ability of the FNO model to capture wind frequency features effectively. The SDF data also provides important spatial building information, enhancing the model's ability to recognize physical boundaries and generate more realistic predictions. The proposed FNO approach enhances the AI model's generalizability for different wind directions and urban layouts.