Data-driven reduced order modeling of a two-layer quasi-geostrophic ocean model

The two-layer quasi-geostrophic equations (2QGE) are a simplified model that describes the dynamics of a stratified, wind-driven ocean in terms of potential vorticity and stream function. Its numerical simulation is plagued by a high computational cost due to the size of the typical computational domain and the need for high resolution to capture the full spectrum of turbulent scales. In this paper, we present a data-driven reduced order model (ROM) for the 2QGE that drastically reduces the computational time to predict ocean dynamics, especially when there are variable physical parameters. The main building blocks of our ROM are: i) proper orthogonal decomposition (POD) and ii) long short-term memory (LSTM) recurrent neural networks. Snapshots data are collected from a high-resolution simulation for part of the time interval of interest and for given parameter values in the case of variable parameters. POD is applied to each field variable to extract the dominant modes and a LSTM model is trained on the modal coefficients associated with the snapshots for each variable. Then, the trained LSTM models predict the modal coefficients for the remaining part of the time interval of interest and for a new parameter value. To illustrate the predictive performance of our POD-LSTM ROM and the corresponding time savings, we consider an extension of the so-called double-gyre wind forcing test. We show that the POD-LSTM ROM is accurate in predicting both time-averaged fields and time-dependent quantities (modal coefficients, enstrophy, and kinetic energy), even when retaining only 10-20% of the singular value energy of the system. The computational speed up for the prediction is about up to 1E+07 compared to a finite volume based full order method.