Modeling Multivariable High-resolution 3D Urban Microclimate Using Localized Fourier Neural Operator

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, traditional computational fluid dynamics (CFD) simulations that couple velocity and temperature are computationally expensive. Recent machine learning advancements offer promising alternatives for accelerating urban microclimate simulations. The Fourier neural operator (FNO) has shown efficiency and accuracy in predicting single-variable velocity magnitudes in urban wind fields. Yet, for multivariable high-resolution 3D urban microclimate prediction, FNO faces three key limitations: blurry output quality, high GPU memory demand, and substantial data requirements. To address these issues, we propose a novel localized Fourier neural operator (Local-FNO) model that employs local training, geometry encoding, and patch overlapping. Local-FNO provides accurate predictions for rapidly changing turbulence in urban microclimate over 60 seconds, four times the average turbulence integral time scale, with an average error of 0.35 m/s in velocity and 0.30 {\deg}C in temperature. It also accurately captures turbulent heat flux represented by the velocity-temperature correlation. In a 2 km by 2 km domain, Local-FNO resolves turbulence patterns down to a 10 m resolution. It provides high-resolution predictions with 150 million feature dimensions on a single 32 GB GPU at nearly 50 times the speed of a CFD solver. Compared to FNO, Local-FNO achieves a 23.9% reduction in prediction error and a 47.3% improvement in turbulent fluctuation correlation.

Toward a Better Understanding of Fourier Neural Operators: Analysis and Improvement from a Spectral Perspective

In solving partial differential equations (PDEs), Fourier Neural Operators (FNOs) have exhibited notable effectiveness compared to Convolutional Neural Networks (CNNs). This paper presents clear empirical evidence through spectral analysis to elucidate the superiority of FNO over CNNs: FNO is significantly more capable of learning low-frequencies. This empirical evidence also unveils FNO's distinct low-frequency bias, which limits FNO's effectiveness in learning high-frequency information from PDE data. To tackle this challenge, we introduce SpecBoost, an ensemble learning framework that employs multiple FNOs to better capture high-frequency information. Specifically, a secondary FNO is utilized to learn the overlooked high-frequency information from the prediction residual of the initial FNO. Experiments demonstrate that SpecBoost noticeably enhances FNO's prediction accuracy on diverse PDE applications, achieving an up to 71% improvement.