A hybrid physics-based and data-driven approach with autoencoders: Rayleigh-Benard convection

In computational science and engineering, there is always a trade-off between the available computational resources and the desired level of accuracy. Therefore, in many complex multiphysics systems, solvers with varied levels of approximations are applied in different regions of the computational domain. One of the challenges with multi-fidelity computing is the accuracy of low-fidelity solvers and the recent advancement in machine learning can be utilized to build computationally cheap and accurate surrogate model. To this end, we present a coupled full order model (FOM) and reduced-order model (ROM) approach for considering the system of Boussinesq equations, which has application in various geophysical flows. In our approach, we employ a convolutional autoencoder network to recognize spatial patterns and eliminate nonlinear correlations among input features. Then, long short-term memory neural network architecture is utilized to discover temporal patterns in the low-rank space and complete the ROM part for representing the vorticity transport. The temperature evolution is treated in the FOM level, and we present a seamless coupling between FOM and ROM levels. The trade-off between accuracy and efficiency is analysed for solving a canonical Rayleigh-Benard convection system.