Multiscale Neural PDE Surrogates for Prediction and Downscaling: Application to Ocean Currents
This work addresses the need for high-resolution ocean current data for coastal management and environmental monitoring, representing an incremental advancement in neural PDE surrogates.
The paper tackles the problem of low-resolution ocean current data by introducing a supervised deep learning framework based on neural operators to provide arbitrary resolution solutions and downscaling models, applied to Copernicus data and synthetic datasets.
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, available satellite products, such as Copernicus data for sea water velocity at ~0.08 degrees 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 ocean current data and synthetic Navier-Stokes simulation datasets.