A hybrid modeling approach for coupling reduced order and full order models of the Boussinesq system

Multiphysics solvers addressing problems with different computational costs for the coupled physics are limited by the most computationally expensive routines (e.g., solving the Poisson equation in incompressible flow solvers). In this work, we replace the costly part with an interactive non-intrusive machine learning (ML) model so that we could benefit from the robustness of the ML and accuracy and generalisability of the full order model (FOM) for the focus of the solution. Specifically, we model the evolution of the proper orthogonal decomposition modal amplitudes of the vorticity transport and continuity equations using a long short-term memory (LSTM) neural network, coupled with the FOM solution of the energy equation. This ROM-FOM coupling framework solves the Boussinesq equations for the lock-exchange problem to demonstrate the benefits of this multi-fidelity setup.