Cross-resolution generalization in ocean downscaling by a spectral-physical neural operator

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Abstract High-fidelity downscaling is essential for capturing the complex, multi-scale dynamics of oceanic systems and improving the reliability of marine hazard predictions. While deep learning has emerged as a promising alternative to computationally expensive numerical models, conventional architectures often fail to preserve physical consistency and suffer from catastrophic performance collapse when generalized to unseen, higher-resolution grids. This limitation stems from a fundamental reliance on discrete pixel-based mappings rather than learning the underlying continuous operators. In this work, we introduce the neural operator for downscaling (NODS), a physics-aware framework that achieves robust cross-resolution generalization. NODS integrates hierarchical multi-grid inductive biases with a unique frequency-spatial synergetic completion mechanism. This architecture enables the model to capture global spectral dependencies through the frequency domain while simultaneously refining local geometric textures in physical space, effectively mimicking the multi-scale energy cascade of fluid dynamics. We evaluate the NODS framework using a comprehensive global dataset of significant wave height across complex oceanic regions as a representative case study. Experimental results suggest that NODS exhibits a remarkable capacity for zero-shot resolution extrapolation to ultra-high resolutions (1/8° × 1/8°), outperforming the evaluated spatial and spectral baselines. Quantitatively, NODS reduces scale-induced error inflation by 50%–70% compared to benchmarks within the tested scenarios. Wavenumber spectrum analysis reveals that our approach effectively mitigates non-physical spectral artifacts and maintains structural integrity at intricate land-sea interfaces, achieving a 92.35% recovery ratio of high-wavenumber energy. Furthermore, under extreme sea states, NODS maintains exceptional precision with a root mean square error below 0.2 m and high spectral alignment, ensuring robustness in operational scenarios. By bridging coarse-grained simulations with fine-scale physical consistency, NODS proposes a promising, scalable paradigm for downscaling in Earth system modeling.

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