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

TL;DR

This paper introduces a neural operator-based deep learning framework for solving PDEs and downscaling ocean current data, enabling high-resolution predictions from low-resolution satellite observations, with applications demonstrated on real-world and synthetic datasets.

Contribution

It presents a novel neural operator approach for PDE surrogates and downscaling, capable of arbitrary resolution predictions, applied to ocean current data.

Findings

Effective downscaling of satellite ocean data to higher resolutions.

Accurate PDE solution predictions at arbitrary resolutions.

Successful application to real-world and synthetic datasets.

Abstract

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.