Principled Fourier Neural Operators for High‐Resolution Regional Ocean Modeling

Abstract Reliable and computationally efficient ocean state forecasts are essential for climate resilience, maritime safety, and science‐to‐decision applications. Growing demand has stimulated interest in machine learning approaches as scalable complements to traditional numerical models. Neural operators have emerged as promising tools for learning solution operators of governing partial differential equations in ocean and weather prediction. Despite encouraging progress, challenges remain in maintaining long‐term stability and spectral fidelity, particularly for high‐frequency processes. In this study, we investigate the impact of incorporating temporal structure into operator learning on autoregressive stability in high‐resolution regional ocean emulation. We compare the standard Fourier Neural Operator (FNO) with a modified variant, FNOtD, which incorporates joint spatial–temporal Fourier parameterization to better represent spatiotemporal spectral interactions relevant to unsteady ocean dynamics. Within a controlled regional configuration, FNOtD exhibits substantially improved long‐horizon stability and reduced error growth compared to the standard FNO. Furthermore, training with a multi‐lead‐time objective enhances predictive accuracy and spectral agreement. In the evaluated case study, the modified operator achieves predictive skill comparable to a state‐of‐the‐art high‐resolution numerical ocean model while operating at a fraction of the computational cost. These results demonstrate improved robustness and generalization of the operator learning in a regional setting, despite being trained on a relatively short time span and coarse‐resolution data set. However, further validation across diverse oceanic regimes is required to assess the transferability, generalizability, and operational robustness of FNOtD models.