Storm surges pose significant threats to coastal populations and livelihoods, and rapid, accurate spatiotemporal forecasting is crucial for mitigating their impacts. In recent years, deep learning models have shown strong forecasting potential, offering new solutions for storm surge prediction. In this study, we developed a storm surge prediction model based on the Adaptive Fourier Neural Operator. The model effectively captures spatiotemporal relationships between meteorological forcing and storm surge dynamics at a spatial resolution of 0.05°. Unlike models that rely solely on historical data, our approach incorporates continuously updated typhoon information as input, allowing it to respond dynamically to changes in storm track and intensity. When tested on Tropical Storm Pulasan (2024) and Typhoon In-Fa (2021), the model achieved 48-hour mean spatial root-mean-square errors (RMSEs) of 0.28 m and 0.27 m, respectively, with correlation coefficients (CORRs) exceeding 0.69 and 0.85 relative to numerical simulations used as the training reference. In addition, validation against observations from multiple tide gauges yielded station-averaged RMSEs of 0.35 m and 0.34 m, CORRs of 0.74 and 0.78, and peak surge errors of 0.18 m and 0.28 m, respectively. These results demonstrate the model's strong potential for operational storm surge forecasting and emergency management.