Intrusive and non-intrusive reduced order modeling of the rotating thermal shallow water equation

TL;DR

This paper compares intrusive and non-intrusive reduced order modeling techniques for the rotating thermal shallow water equations, demonstrating accurate, stable, and computationally efficient models that preserve physical properties.

Contribution

It introduces a combined analysis of POD-G and operator inference methods for RTSWE, highlighting their ability to maintain physical invariants and perform well in parametric settings.

Findings

Both ROMs achieve significant speedup over FOM.

ROMs accurately predict system behavior and preserve conserved quantities.

Models are robust to parameter variations and suitable for long-term simulations.

Abstract

In this paper, we investigate projection-based intrusive and data-driven non-intrusive model order reduction methods 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 for non-intrusive reduced-order modeling. 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 similar and are able to accurately predict the test and training data and capture system behavior in the prediction phase with several orders of computational speedup over the FOM. The preservation of system physics such as the conserved quantities of the RTSWE by both ROMs enables that the models fit better to data and stable solutions are obtained in long-term predictions, which are robust to parameter changes.