Modeling transient natural convection in heterogeneous porous media with Convolutional Neural Networks

Convolutional Neural Networks (CNNs) are gaining significant attention in applications related to coupled flow and transfer processes in porous media, especially when dealing with image-like data. In this context, the most important applications are related to surrogate modeling, where data obtained from simulators is used to train a CNN model. CNNs are also used as optimizers for inverse modeling or parameter estimation. For natural convection in porous media, applications of CNNs are scarce and limited to steady-state data. The main goal of this paper is to extend the applications of CNNs to transient data, by developing new CNN models that allow for integrating time-variant images. Thus, we suggest using an Encoder-Decoder CNN (ED-CNN) for surrogate modeling and a 3D-CNN for inverse modeling. Besides surrogate and inverse modeling, we suggest using CNN for time prediction by coupling it with long short-term memory (LSTM). The performances of these suggested approaches are investigated by applying them to the benchmark of natural convection in porous cavity with heterogeneous property fields, and by comparing the suggested approaches to other alternatives such as standard deep neural network (DNN) and 2D-CNN trained on steady-state data. The results show that, for surrogate modeling, with the same amount of data and equivalent training times, ED-CNN is more practical than DNN because it provides spatially distributed prediction while DNN is limited to local data. The transient data allows for improving the performance of CNN in inverse modeling because it provides more information about heat transfer across the different material zones and thus heterogeneity. The 3D-CNN approach is more efficient than 2D-CNN as it allows for considering the time progress in the training. For instance, the error with 3D-CNN and transient data is about 11 %, while it is about 18 % with 2D-CNN. Coupling CNN with LSTM allows for improving the performance of CNN in time series prediction.