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

• URL: http://arxiv.org/abs/2507.18067v1
• Date: Thu, 24 Jul 2025 03:42:06 GMT
• Title: Multiscale Neural PDE Surrogates for Prediction and Downscaling: Application to Ocean Currents
• Authors: Abdessamad El-Kabid, Loubna Benabbou, Redouane Lguensat, Alex Hernández-García,
• Abstract summary: High-resolution current data are critical for coastal management, environmental monitoring, and maritime safety.<n>In this work, we introduce a supervised deep learning framework based on neural operators for solving partial differential equations.<n>Our method can model surrogate PDEs and predict solutions at arbitrary resolution, regardless of the input resolution.
• Score: 1.4937633645484905
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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