Supported precious metal nanoparticles are important heterogeneous catalysts for both industrial processes and commercial products. Their high catalytic activity stems from their high surface free energy and under-coordinated surfaces, however these same properties destabilize the particles and cause them to grow and deactivate. While research studying the degradation of supported catalysts has been undertaken for decades, the exact mechanisms at play, and how the vary with reaction conditions, are not well understood. Advances in experimental instrumentation have positioned Transmission Electron Microscopy (TEM) as an ideal tool for characterizing the dynamic evolution of these nanoscale systems with both high spatial and temporal resolution. However, the difficulty of manually analyzing large in situ datasets to quantify nanostructural evolution remains a challenge. This dissertation focuses on combining in situ experimental observations with machine learning and data analytics to quantify image data and understand nanoparticle coarsening. The first thrust of this research is developing a machine-learning pipeline for automated image segmentation. By optimizing state-of-the-art deep learning segmentation models, we were able to rapidly segment and measure particles from thousands of TEM images in a reliable and reproducible fashion. Utilizing this automated image processing pipeline, we observed the evolution of a model catalyst at high temperature and assessed the competition between coarsening by evaporation and surface diffusion as a function of particle size and temperature. After developing a physical model to describe each mechanism, we were able to characterize particle interactions along the support and to identify a critical particle size which avoids degradation. Finally, we used a combination of temperature-dependent in situ experiments and Kinetic Monte Carlo simulations to understand how the rate of nanoparticle evaporation depends on nanoparticle morphology. Our mechanistic model allows us to understand how random structural fluctuations and surface roughening contribute to the evaporation process. In all, this research aims at developing techniques and data-rich quantitative methods for understanding how supported nanocatalysts can be engineered for optimal activity and lifetime.