The structure-property linkages established using the CNN model exhibit better accuracy for predicting diffusivities compared to that using other deep learning models based on physics-inspired approaches. We then use the trained CNN model to perform topology optimization for identifying nanoparticle configurations that can potentially exhibit a wider range of diffusivities. We explore the extent to which the deep learning model captures the relevant physical information influencing cation diffusivity based on the CNN predictions for microstructures with different nanoparticle volume fractions. Lastly, by analyzing the influence of physics-inspired structural descriptors on cation diffusivity, we discuss the structural characteristics of the optimal microstructures and provide a physical rationale for the optimal cation diffusivities exhibited by these structures. While the present study is inspired by the nanoparticle-based electrolyte system, the methods and ideas presented in this work can be easily adapted to establish quantitative structure-property relationships and identify optimal morphologies in other nanoparticle-based systems.