skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


This content will become publicly available on July 1, 2026

Title: Ocean Emulation With Fourier Neural Operators: Double Gyre
Abstract A data‐driven emulator for the baroclinic double gyre ocean simulation is presented in this study. Traditional numerical simulations using partial differential equations (PDEs) often require substantial computational resources, hindering real‐time applications and inhibiting model scalability. This study presents a novel approach employing Fourier neural operators to address these challenges in an idealized double‐gyre ocean simulation. We propose a deep learning approach capable of learning the underlying dynamics of the ocean system, complementing the classical methods. Additionally, we show how Fourier neural operators allow us to train the network at one resolution and generate ensembles at a different resolution. We find that there is an intermediate time scale where the prediction skill is maximized.  more » « less
Award ID(s):
2103942
PAR ID:
10635541
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
AGU
Date Published:
Journal Name:
Journal of Advances in Modeling Earth Systems
Volume:
17
Issue:
7
ISSN:
1942-2466
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract While data-driven approaches demonstrate great potential in atmospheric modeling and weather forecasting, ocean modeling poses distinct challenges due to complex bathymetry, land, vertical structure, and flow non-linearity. This study introduces OceanNet, a principled neural operator-based digital twin for regional sea-suface height emulation. OceanNet uses a Fourier neural operator and predictor-evaluate-corrector integration scheme to mitigate autoregressive error growth and enhance stability over extended time scales. A spectral regularizer counteracts spectral bias at smaller scales. OceanNet is applied to the northwest Atlantic Ocean western boundary current (the Gulf Stream), focusing on the task of seasonal prediction for Loop Current eddies and the Gulf Stream meander. Trained using historical sea surface height (SSH) data, OceanNet demonstrates competitive forecast skill compared to a state-of-the-art dynamical ocean model forecast, reducing computation by 500,000 times. These accomplishments demonstrate initial steps for physics-inspired deep neural operators as cost-effective alternatives to high-resolution numerical ocean models. 
    more » « less
  2. The computational efficiency of many neural operators, widely used for learning solutions of PDEs, relies on the fast Fourier transform (FFT) for performing spectral computations. As the FFT is limited to equispaced (rectangular) grids, this limits the efficiency of such neural operators when applied to problems where the input and output functions need to be processed on general non-equispaced point distributions. Leveraging the observation that a limited set of Fourier (Spectral) modes suffice to provide the required expressivity of a neural operator, we propose a simple method, based on the efficient direct evaluation of the underlying spectral transformation, to extend neural operators to arbitrary domains. An efficient implementation of such direct spectral evaluations is coupled with existing neural operator models to allow the processing of data on arbitrary non-equispaced distributions of points. With extensive empirical evaluation, we demonstrate that the proposed method allows us to extend neural operators to arbitrary point distributions with significant gains in training speed over baselines, while retaining or improving the accuracy of Fourier neural operators (FNOs) and related neural operators. 
    more » « less
  3. The computational efficiency of many neural operators, widely used for learning solutions of PDEs, relies on the fast Fourier transform (FFT) for performing spectral computations. As the FFT is limited to equispaced (rectangular) grids, this limits the efficiency of such neural operators when applied to problems where the input and output functions need to be processed on general non-equispaced point distributions. Leveraging the observation that a limited set of Fourier (Spectral) modes suffice to provide the required expressivity of a neural operator, we propose a simple method, based on the efficient direct evaluation of the underlying spectral transformation, to extend neural operators to arbitrary domains. An efficient implementation of such direct spectral evaluations is coupled with existing neural operator models to allow the processing of data on arbitrary non-equispaced distributions of points. With extensive empirical evaluation, we demonstrate that the proposed method allows us to extend neural operators to arbitrary point distributions with significant gains in training speed over baselines, while retaining or improving the accuracy of Fourier neural operators (FNOs) and related neural operators. 
    more » « less
  4. Abstract The resolution of climate models is limited by computational cost. Therefore, we must rely on parameterizations to represent processes occurring below the scale resolved by the models. Here, we focus on parameterizations of ocean mesoscale eddies and employ machine learning (ML), namely, relevance vector machines (RVMs) and convolutional neural networks (CNNs), to derive computationally efficient parameterizations from data, which are interpretable and/or encapsulate physics. In particular, we demonstrate the usefulness of the RVM algorithm to reveal closed‐form equations for eddy parameterizations with embedded conservation laws. When implemented in an idealized ocean model, all parameterizations improve the statistics of the coarse‐resolution simulation. The CNN is more stable than the RVM such that its skill in reproducing the high‐resolution simulation is higher than the other schemes; however, the RVM scheme is interpretable. This work shows the potential for new physics‐aware interpretable ML turbulence parameterizations for use in ocean climate models. 
    more » « less
  5. Two elementary models of ocean circulation, the well-known double-gyre stream function model and a single-layer quasi-geostrophic (QG) basin model, are used to generate flow data that sample a range of possible dynamical behavior for particular flow parameters. A reservoir computing (RC) machine learning algorithm then learns these models from the stream function time series. In the case of the QG model, a system of partial differential equations with three physically relevant dimensionless parameters is solved, including Munk- and Stommel-type solutions. The effectiveness of a RC approach to learning these ocean circulation models is evident from its ability to capture the characteristics of these ocean circulation models with limited data including predictive forecasts. Further assessment of the accuracy and usefulness of the RC approach is conducted by evaluating the role of both physical and numerical parameters and by comparison with particle trajectories and with well-established quantitative assessments, including finite-time Lyapunov exponents and proper orthogonal decomposition. The results show the capability of the methods outlined in this article to be applied to key research problems on ocean transport, such as predictive modeling or control. 
    more » « less