The two-layer quasi-geostrophic equations (2QGE) serve as a simplified model
for simulating wind-driven, stratified ocean flows. Jedoch, their numerical
simulation remains computationally expensive due to the need for
high-resolution meshes to capture a wide range of turbulent scales. This
becomes especially problematic when several simulations need to be run because
of, e.g., uncertainty in the parameter settings. To address this challenge, we
propose a data-driven reduced order model (ROM) for the 2QGE that leverages
randomized proper orthogonal decomposition (rPOD) and long short-term memory
(LSTM) networks. To efficiently generate the snapshot data required for model
construction, we apply a nonlinear filtering stabilization technique that
allows for the use of larger mesh sizes compared to a direct numerical
simulations (DNS). Thanks to the use of rPOD to extract the dominant modes from
the snapshot matrices, we achieve up to 700 times speedup over the use of
deterministic POD. LSTM networks are trained with the modal coefficients
associated with the snapshots to enable the prediction of the time- Und
parameter-dependent modal coefficients during the online phase, which is
hundreds of thousands of time faster than a DNS. We assess the accuracy and
efficiency of our rPOD-LSTM ROM through an extension of a well-known benchmark
called double-gyre wind forcing test. The dimension of the parameter space in
this test is increased from two to four.

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