Simulating ocean surface waves is essential for understanding Earth's climate and marine environments, but traditional numerical wave models remain computationally prohibitive for global, long-term applications. Conversely, current deep learning approaches struggle to capture fundamental wave physics, failing to generalize beyond their specific training domains. We present the Neural Spectral Wave Model (NSWM), a hybrid physics-AI framework that bridges this divide. By embedding a differentiable numerical solver to govern universal wave propagation alongside a neural network that learns complex energy source terms, NSWM efficiently evolves full directional wave spectra. Remarkably, the model demonstrates true zero-shot transferability: trained exclusively on a semi-enclosed sea, it accurately predicts wave dynamics in the unlimited-fetch Southern Ocean. Validated against satellite altimetry, NSWM maintains operational-grade accuracy at a fraction of traditional computational costs. By seamlessly fusing inviolable physical laws with data-driven efficiency, this architecture provides a scalable foundation for integrating explicit wave dynamics into global Earth system models.