Current physics models used to interpret experimental measurements of particle beams require either simplifying assumptions to be made in order to ensure analytical tractability, or black box optimization methods to perform model based inference. This reduces the quantity and quality of information gained from experimental measurements, in a system where measurements have a limited availability. However differentiable physics modeling, combined with machine learning techniques, can overcome these analysis limitations, enabling accurate, detailed model creation of physical accelerators. Here we examine two applications of differentiable modeling, first to characterize beam responses to accelerator elements exhibiting hysteretic behavior, and second to characterize beam distributions in high dimensional phase spaces.