A Generalizable Lie Autoencoder for Emulating Barotropic Turbulence

Iuri Gorenstein, Ilana Wainer, Pedro S. Peixoto, Cesar B. Rocha

Numerical ocean models rely on the discretization of primitive equations to simulate ocean dynamics, but their computational cost increases drastically with resolution. As an alternative, recent advances in neural networks (NN) have demonstrated promising applications in climate science, offering orders-of-magnitude faster simulations than traditional models through data-driven algorithms that can be continuously improved with observational data training. However, NN-based approaches for ocean modeling face critical challenges, including stability, physical consistency, and generalizability. This study presents a novel approach to embedding the barotropic dynamics of the Coastal and Regional Ocean COmmunity (CROCO) model, namely the AB3-AM4 algorithm, into a physics-informed NN. By leveraging a Lie auto-encoder, we transform the nonlinear barotropic dynamics into a latent space where they can be evolved using a linear operator. The network is tested on a linear idealized barotropic tsunami, as well as nonlinear geostrophic equilibrium and perturbation test cases. The results demonstrate stable evolution of surface height and barotropic velocities, conserving physical quantities, the expected energy spectra of the simulation and key eddy structures in turbulent flows. Furthermore, although it does not yet exhibit computational efficiency gains, the model is fully generalizable to any domain grid size and demonstrates comparable performance when applied to resolutions equal to or lower than those seen during training. This approach bridges the gap between traditional numerical models and NN algorithms, paving the way for hybrid modeling techniques that enhance ocean simulation beyond computational limitations.