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

2025-07-23

AI Summary

To address the limited spatial resolution of satellite-derived ocean current data—which hinders high-precision coastal management and maritime safety—this paper proposes a multi-scale PDE surrogate model based on neural differential equation operators. The model embeds physical constraints into a deep neural operator architecture, enabling end-to-end cross-resolution modeling and arbitrary-scale super-resolution reconstruction. By jointly incorporating Navier–Stokes equation priors and synthetic-data-driven training, it achieves superior performance on real-world Copernicus ocean current measurements, outperforming conventional interpolation and state-of-the-art deep learning baselines by over 3.2 dB in PSNR. It further demonstrates strong generalization and continuous field representation capability. The key innovation lies in the first application of neural differential operators to physics-consistent, multi-scale downscaling of ocean current fields—establishing a novel paradigm for high-fidelity, interpretable ocean dynamical modeling.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

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.

Problem

• Predict ocean currents at arbitrary resolution
• Downscale low-resolution satellite ocean data
• Model surrogate PDEs for scientific computing

Innovation

• Supervised deep learning for PDE solutions
• Neural operators enable arbitrary resolution
• Downscaling models for ocean current data