Fig. 6

(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 \({\textbf{H}}\) is the PEC-based convergent integration scheme used.