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

arXiv: https://arxiv.org/abs/2507.18067 · HTML: https://mlsanity.com/paper/2507.18067/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 16 references that are in the map.
- First posted on arXiv 24 Jul 2025.

## Builds on (most cited first, 9 of 9)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Scalable Transformer for PDE Surrogate Modeling](https://mlsanity.com/paper/2305.17560/) (2023)
- [Solving High-Dimensional PDEs with Latent Spectral Models](https://mlsanity.com/paper/2301.12664/) (2023)
- [Physics-Guided Architecture (PGA) of Neural Networks for Quantifying Uncertainty in Lake Temperature Modeling](https://mlsanity.com/paper/1911.02682/) (2019)
- [Fourier Neural Operators for Arbitrary Resolution Climate Data Downscaling](https://mlsanity.com/paper/2305.14452/) (2023)
- [Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspective](https://mlsanity.com/paper/2404.07200/) (2024)
- [Streamlining Ocean Dynamics Modeling with Fourier Neural Operators: A Multiobjective Hyperparameter and Architecture Optimization Approach](https://mlsanity.com/paper/2404.05768/) (2024)

## Abstract (arXiv)

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.