To summarize, application of PCA to the dataset of microstructure radial distribution functions from this topology optimization study, together with direct visualization of optimal microstructures, allows us to identify that for the cation transport model considered in this study, nearest neighbor spacing and percolation of nanoparticles are the main structural characteristics significantly influencing the cation diffusivity. However, we recall the results of Section 3.1 which established that 3-and higher-particle correlations have significant consequences for cation transport. Hence, our results in this study point to the observation that while physics-based models can be useful in understanding and predicting the morphology dependencies of different properties, CNN-based deep learning models can potentially expand such capablities and allow us to probe configurations which may not be subsumed within a purely physics-based approach.