Analyzing the efficiency and robustness of deep convolutional neural networks for modeling natural convection in heterogeneous porous media

Natural convection in porous media (NCPM) is governed by highly nonlinear dynamics due to the dependence of fluid density and viscosity to temperature. Given the high computational cost associated with numerical modeling of NCPM, data-driven metamodels are commonly used to reduce the computational time in applications that require repetitive model runs. However, to various degrees, all metamodels previously used in this context struggle at scaling to high dimensional input and output problems. This work aims at investigating the performance of encoder-decoder convolutional neural networks (ED-CNNs), as a specialized deep learning architecture, in assisting the procedure of numerical modeling of NCPM. Our interest is directed to image-to-image regression tasks in which both the inputs and outputs of the model are high-dimensional, often high resolution, spatial distributions of the features. Large datasets of images (for e.g. heat map) can be generated by numerical modeling of NCPM, and also through high-resolution imaging and non-destructive scanning techniques. Hence, we apply ED-CNNs to develop a methodology for image-to-image regression. The goals are twofold: (1) to assess the robustness of ED-CNNs in metamodeling and uncertainty propagation analysis, and (2) to evaluate the performance of ED-CNNs as optimizer in input parameter estimation. To do so, we apply the ED-CNNs to the common benchmark of natural convection in a porous cavity. Numerical experiments highlight the robustness and efficiency of the ED-CNNs in handling heterogeneous domains.