OceanNet: A principled neural operator-based digital twin for regional oceans

TL;DR

OceanNet, a principled neural operator-based digital twin for regional sea-suface height emulation, uses a Fourier neural operator and predictor-evaluate-corrector integration scheme to mitigate autoregressive error growth and enhance stability over extended time scales.

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 ocean circulation. 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 by outperforming SSH predictions by an uncoupled, state-of-the-art dynamical ocean model forecast, reducing computation by 500,000 times. These accomplishments demonstrate the potential of physics-inspired deep neural operators as cost-effective alternatives to high-resolution numerical ocean models.

Figures (4)

• Figure 1: The domain for the reanalysis data covering the northwestern Atlantic (a). The two subdomains used to develop OceanNet, specifically (b) the GS separation from the central US east coast to 60$^{\circ}$W and (c) the LC eddy-shedding region in the eastern GoM, extending from 92$^{\circ}$W into the Atlantic 75$^{\circ}$W. The mean SSH from from 1993-2020 in the reanalysis data is shown in (a), while (b) and (c) depict daily mean SSH on May 1, 2019, and July 10, 2019, respectively. All three domains share the same color scale.
• Figure 2: OceanNet performance metrics in the GoM: RMSE (a-c), CC (d-f), and MHD (g-i). In the left column, probability density functions (PDFs) are presented for 1,000 random pairs sourced from the training data spanning 1993-2018 (means shown by black horizontal lines). The performance statistics, calculated based on forecasts of 0-120 days for eddies Sverdrup (middle column) and Thor (right column), are displayed as mean values (lines) with standard deviations (shading). The black horizontal dashed lines in these columns denote saturation values determined as 95% of the means derived from the random pairs. In the middle and right columns, solid blue lines are OceanNet, dashed red lines are the regional ocean dynamical forecast model, and gray dots are persistence. These representations illustrate how each method’s statistics compare with the target SSH from the reanalysis dataset. The shading is obtained from the standard deviation due to the choice of different initial conditions to evluate the forecast skill.
• Figure 3: OceanNet’s performance metrics in the northwest Atlantic: RMSE (top), CC (middle), and MHD (bottom), compared to the persistence forecast and regional ocean dynamical model forecast. In the left column, probability density functions (PDFs) are presented, derived from 1,000 random pairs sourced from the training data spanning 1993-2018 (means shown by black horizontal lines). The performance statistics, calculated based on forecasts of 0-120 days, are displayed as mean values (lines) with standard deviations (shading). The black horizontal dashed lines denote saturation values, which are determined as 95% of the means derived from the random pairs. Solid blue lines are OceanNet, dashed red lines are the regional ocean dynamical forecast model, and gray dots are persistence. These representations illustrate how each method’s statistics compare with the target SSH from the reanalysis dataset. The shading is obtained from the standard deviation due to the choice of different initial conditions to evluate the forecast skill.
• Figure 4: (a) A schematic of the OceanNet model. (b) The Fourier Neural Operator, depicted as $\mathcal{N}$. The neural operator uplifts the input state, $X(t)$ to a high-dimensional space using two convolutional layers. The uplifted state then undergoes a Fourier transform, subsequent coarse-graining by removing the high-wavenumber modes, and then undergoes an inverse Fourier transform. Finally a bias layer is also added to account for aperiodicity in the data. Finally, two more convolutional layers are added to preserve the dimension of the final output, $X(t+k\Delta t)$. (c) 2-time-step training scheme. (d) The loss function used. Here, $X$ is the state of the system that is predicted, and $\mathbf{H}$ is the PEC-based convergent integration scheme used.