Multiscale Neural PDE Surrogates for Prediction and Downscaling: Application to Ocean Currents

Accurate modeling of physical systems governed by partial differential equations is a central challenge in scientific computing. In oceanography, high-resolution current data are critical for coastal management, environmental monitoring, and maritime safety. However, widely used satellite products, such as Copernicus sea-surface velocity at $\sim 0.08^\circ$ resolution and global ocean models, often lack the spatial granularity required for detailed local analyses. We (a) introduce a supervised deep learning framework based on neural operators for solving PDEs and producing arbitrary-resolution solutions, and (b) propose downscaling models applied to Copernicus ocean current data. Additionally, our method serves as a surrogate PDE model that predicts solutions at arbitrary resolution, regardless of the input resolution. We evaluate on real-world Copernicus ocean current data and synthetic Navier--Stokes simulation datasets.