Reduced Order Modeling Assisted by Convolutional Neural Network for Thermal Problems with Nonparametrized Geometrical Variability

Abstract

In this work, we consider a nonlinear transient thermal problem numerically solved by a high-fidelity model. The objective is to derive fast approximations of the solutions to this problem, under nonparametrized variability of the geometry, and the convection and radiation boundary conditions, using physics-based reduced order models (ROM). Nonparametrized geometrical variability is a challenging task in model order reduction, which we propose to address using deep neural networks. First, a convolutional neural network (CNN) is trained to compute the discretization error of a fastly simulated solution on a coarse mesh, under the aforementioned geometry and boundary conditions variability. Then, for a fixed geometry, a ROM is constructed under the boundary conditions variability; the data used to construct the ROM being the coarse solutions and the CNN predicted discretization errors. We illustrate that in all our tested configurations, the reduced order model improves the accuracy of the coarse and CNN predictions.