Reducing the computational cost of ocean modeling with data-driven ROM
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The two-layer quasi-geostrophic equations (2QGE) is 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. We propose a framework to reduce the computational cost through a predictive and parametric data-driven reduced order model (ROM). The main building blocks of our ROM are proper orthogonal decomposition (POD) and long short-term memory (LSTM) recurrent neural networks. 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 a time interval of interest and for each new parameter value. The predictive performance of our framework and the corresponding time savings are illustrated with the so-called double-gyre wind forcing test.