Convolutional neural network based prediction of effective diffusivity from microscope images

Abstract

This study presents a method to predict the effective diffusivity of porous media from a limited set of scanning electron microscope images using deep learning. The electrodeposited nickel oxide film over carbon nanostructure, meant to provide electrochemical capacitance based on diffusion of ions through the film's pore space, was observed under the scanning electron microscope. Gray scale SEM images were converted to binary images, and the effective diffusivity was found using lattice Boltzmann simulations. A convolutional neural network (CNN) model comprising two sets of convolution and pooling layers and a fully connected layer was trained with lattice Boltzmann method data, where the choices of kernel size and stride were made, keeping the homogeneity of the image in perspective. An initial attempt to train a CNN with 900 training instances predicted effective diffusivity with a relative error of 13.33%, 43.49%, and 36.41% for the training, validation, and test set, respectively. However, it was over-predicting the diffusivities for images with very low connectivity. Isolated pores within the images were identified and were eliminated to solve this issue before using the images to train another CNN. This second network worked well for images with low connectivity and brought down the mean relative error from 36.41% to 25.43% for the test set. The error was found to vary across the images due to highly non-even representation of different image types, increasing by complex pore connectivity at lower porosity for which the number of training instances is the least, and overfitting of networks on medium porosity images that are present in greater numbers. The SEM images were further classified based on porosity as well as pore connectivity. The training was performed with one category of images, and the testing was conducted with images of another category at the other end of the spectrum to evaluate CNN efficacy upon encountering a new category of images. The results show the ability of the network to extend the prediction to an unknown electrode morphology, which is critical for the analysis of SEM images.