Intrusive and data-driven reduced order modelling of the rotating thermal shallow water equation

In this paper, we investigate projection-based intrusive and data-driven model order reduction in numerical simulation of rotating thermal shallow water equation (RTSWE) in parametric and non-parametric form. Discretization of the RTSWE in space with centered finite differences leads to Hamiltonian system of ordinary differential equations with linear and quadratic terms. The full-order model (FOM) is obtained by applying linearly implicit Kahan’s method in time. Applying proper orthogonal decomposition with Galerkin projection (POD-G), we construct the intrusive reduced-order model (ROM). We apply operator inference (OpInf) with re-projection as data-driven ROM. In the parametric case, we make use of the parameter dependency at the level of the PDE without interpolating between the reduced operators. The least-squares problem of the OpInf is regularized with the minimum norm solution. Both ROMs behave similarly and are able to accurately predict the in the test and training data and capture system behaviour in the prediction phase with several orders of magnitude in computational speed-up over the FOM. The preservation of system physics such as the conserved quantities of the RTSWE by both ROMs enable that the models fit better to data and stable solutions are obtained in long-term predictions which are robust to parameter changes.