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Evaluation of Deep Neural Operator Models toward Ocean Forecasting

Ellery Rajagopal, Anantha N. S. Babu, Tony Ryu, Patrick J. Haley, Chris Mirabito, Pierre F. J. Lermusiaux

TL;DR

<3-5 sentence high-level summary>This paper benchmarks deep neural operator models for forecasting dynamical systems, starting with a canonical 2D flow past a cylinder and extending to realistic ocean surface flows. It compares DeepONet and kernel-based operator approaches, including Fourier/AFNO-based variants, and outlines training strategies (single-step vs multi-step predictions). Using high-resolution, data-assimilative simulations from the MSEAS-PE system in the Middle Atlantic Bight and Massachusetts Bay, the study demonstrates that these models can reproduce key features like vortex shedding and tidal dynamics, with varying levels of forecast skill and sensitivity to architecture and hyperparameters. The results highlight the potential of discretization-invariant neural operators for efficient, data-driven ocean forecasting and motivate further development for operational-like applications.

Abstract

Data-driven, deep-learning modeling frameworks have been recently developed for forecasting time series data. Such machine learning models may be useful in multiple domains including the atmospheric and oceanic ones, and in general, the larger fluids community. The present work investigates the possible effectiveness of such deep neural operator models for reproducing and predicting classic fluid flows and simulations of realistic ocean dynamics. We first briefly evaluate the capabilities of such deep neural operator models when trained on a simulated two-dimensional fluid flow past a cylinder. We then investigate their application to forecasting ocean surface circulation in the Middle Atlantic Bight and Massachusetts Bay, learning from high-resolution data-assimilative simulations employed for real sea experiments. We confirm that trained deep neural operator models are capable of predicting idealized periodic eddy shedding. For realistic ocean surface flows and our preliminary study, they can predict several of the features and show some skill, providing potential for future research and applications.

Evaluation of Deep Neural Operator Models toward Ocean Forecasting

TL;DR

<3-5 sentence high-level summary>This paper benchmarks deep neural operator models for forecasting dynamical systems, starting with a canonical 2D flow past a cylinder and extending to realistic ocean surface flows. It compares DeepONet and kernel-based operator approaches, including Fourier/AFNO-based variants, and outlines training strategies (single-step vs multi-step predictions). Using high-resolution, data-assimilative simulations from the MSEAS-PE system in the Middle Atlantic Bight and Massachusetts Bay, the study demonstrates that these models can reproduce key features like vortex shedding and tidal dynamics, with varying levels of forecast skill and sensitivity to architecture and hyperparameters. The results highlight the potential of discretization-invariant neural operators for efficient, data-driven ocean forecasting and motivate further development for operational-like applications.

Abstract

Data-driven, deep-learning modeling frameworks have been recently developed for forecasting time series data. Such machine learning models may be useful in multiple domains including the atmospheric and oceanic ones, and in general, the larger fluids community. The present work investigates the possible effectiveness of such deep neural operator models for reproducing and predicting classic fluid flows and simulations of realistic ocean dynamics. We first briefly evaluate the capabilities of such deep neural operator models when trained on a simulated two-dimensional fluid flow past a cylinder. We then investigate their application to forecasting ocean surface circulation in the Middle Atlantic Bight and Massachusetts Bay, learning from high-resolution data-assimilative simulations employed for real sea experiments. We confirm that trained deep neural operator models are capable of predicting idealized periodic eddy shedding. For realistic ocean surface flows and our preliminary study, they can predict several of the features and show some skill, providing potential for future research and applications.
Paper Structure (16 sections, 7 equations, 4 figures)

This paper contains 16 sections, 7 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Deep Neural Operator Models
  3. DeepONet
  4. Kernel-Based Neural Operator Models
  5. Model Inputs and Outputs, and Training
  6. Flow Past a Cylinder
  7. Test Case Description
  8. Learning Results
  9. Realistic Ocean Surface Flows
  10. Middle Atlantic Bight (MAB)
  11. Test Case Description
  12. Learning Results
  13. Massachusetts Bay (MB)
  14. Test Case Description
  15. Learning Results
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Applying FCN in the MAB. Surface velocity field amplitudes overlaid with curved velocity vectors. Ground truth from the MSEAS-PE forecast (top row), FCN predictions for training-run 246 (middle row), and error fields (bottom row) for five different forecast times: 2006 Sep 18 09Z and 6, 12, 24, and 28 hours later.
  • Figure 2: Applying FCN in the MAB. Errors (RMSE) of FCN forecasts of surface velocity for 0 to 29h forecast lead times (2006 Sep 18 08Z to Sep 19 13Z). The FNC forecasts correspond to ten MAB training-runs with different hyperparameter values.
  • Figure 3: Applying FCN in MB. Surface velocity field amplitudes overlaid with curved velocity vectors. Ground truth from the MSEAS-PE forecast (top row), FCN predictions for training-run 264 (middle row), and error fields (bottom row) for five different forecast times: 2019 Sep 3 09Z and 6, 12, 24, and 28 hours later.
  • Figure 4: Applying FCN in MB. Errors (RMSE) of FCN forecasts of surface velocity for 0 to 29h forecast lead times (2019 Sep 3 08Z to Sep 4 13Z). The FNC forecasts correspond to ten MAB training-runs with different hyperparameter values.