A General Framework for Predicting Permeability in Porous Structures Using Convolutional Neural Networks with Error Estimation

Two major challenges plague permeability prediction with a convolutional neural network (CNN): failure to generalize to external data and the sources of error are not well defined. This study compares five optimized CNN architectures on a training dataset with 4500 images of porous media generated via random sphere-packing, quartet structure generation set, and Voronoi diagrams. An external set of 400 slices of an X-ray tomography from an aluminum foam sample and 300 slices of a 3D reconstruction of a carbon electrode are used for external validation. The permeabilities for all data were calculated using an in-house computational fluid dynamics algorithm. The CNN models were derived from AlexNet, VGG19, DenseNet, ResNet34, and ResNet50 architectures. This work shows that transforming the training data by taking the log of permeability significantly increases the prediction accuracy for all ranges of permeability. The VGG19, ResNet34, and ResNet50 architectures have the highest prediction accuracy, with a mean absolute percent error (MAPE) of 2.64%, 2.61%, and 2.65%, respectively. In the external dataset, the CNNs retained remarkable accuracy, with MAPEs of 1.33%, 1.36%, and 1.44%, respectively. AlexNet and DenseNet performed significantly worse on both datasets. A direct link is found between training dataset diversity and generalization, and the study shows that one type of training data is not enough to extrapolate to other types of microstructures. Permeability prediction with an ensemble of the 10 most accurate VGG19 models from the hyperparameter optimization shows significant accuracy increase, with a MAPE of 1.99% in the test set and 1.22% in the external dataset, while also providing a measure of confidence. Performing Monte Carlo dropout on the VGG19 network indicates that the majority of the error from the CNN prediction comes from noise in the training data. These insights pave the way for more general CNN models, which could come to replace empirical relations as an on-demand alternative to permeability estimation.