FANO: Fourier Advection Neural Operator for Weather Prediction

Weather prediction is essential for various societal applications, including disaster management and agricultural planning. Traditional numerical weather prediction (NWP) models, which solve partial differential equations (PDEs) governing atmospheric motion, have achieved remarkable accuracy. However, their effectiveness is often constrained by the complexity of atmospheric dynamics and high computational costs. In recent years, deep learning approaches have emerged as promising alternatives, leveraging data-driven methodologies to capture complex spatiotemporal patterns. Among these, Fourier-based neural models have demonstrated strong capabilities in capturing global spatial correlations using spectral transformations. Despite their success, these methods often overlook key physical principles essential to atmospheric dynamics, limiting their ability to capture physically realistic weather patterns. To address this limitation, we propose the Fourier advection neural operator (FANO), which introduces a well-established physical principle, the advection equation, into the modeling process, enhancing physical consistency while maintaining computational efficiency. Specifically, FANO employs the Fourier spectral method to solve the advection equation directly in the spectral domain, reducing computational complexity by requiring only a single Fourier transform and its inverse. This integration not only embeds physical constraints into the forecasting model but also enables efficient calculation of key differential operators in the advection equation, such as spatial gradients and flow field divergences. Extensive experiments on real-world weather datasets demonstrate that FANO surpasses state-of-the-art NWP models and remains highly competitive with recent state-of-the-art deep learning models, offering both improved prediction accuracy and enhanced physical consistency. These results highlight the potential of physics-informed neural operators in advancing reliable and efficient weather forecasting.