Abstract: High-resolution ocean current data are indispensable for coastal management, environmental monitoring, and navigation safety. However, available satellite products, such as Copernicus data for sea water velocity at $\sim$0.08° spatial resolution and global ocean models, often lack the spatial granularity required for detailed local analyses. In this work, we (a) introduce a supervised deep learning framework based on neural operators for solving PDEs and providing arbitrary resolution solutions, and (b) propose downscaling models with an application to Copernicus ocean current data. Additionally, our method can model surrogate PDEs and predict solutions at arbitrary resolution, regardless of the input resolution. We evaluated our model on real-world Copernicus current marine data and synthetic Navier–Stokes simulation datasets.