Cells interpret cues from and interact with fibrous microenvironments through the body based on the mechanics and organization of these environments and the phenotypic state of the cell. This in turn regulates mechanoactive pathways, such as the localization of mechanosensitive factors. Here, we leverage the microscale heterogeneity inherent to engineered fiber microenvironments to produce a large morphologic data set, across multiple cells types, while simultaneously measuring mechanobiological response (YAP/TAZ nuclear localization) at the single cell level. This dataset describing a large dynamic range of cell morphologies and responses was coupled with a machine learning approach to predict the mechanobiological state of individual cells from multiple lineages. We also noted that certain cells (e.g., invasive cancer cells) or biochemical perturbations (e.g., modulating contractility) can limit the predictability of cells in a universal context. Leveraging this finding, we developed further models that incorporate biochemical cues for single cell prediction or identify individual cells that do not follow the established rules. The models developed here provide a tool for connecting cell morphology and signaling, incorporating biochemical cues in predictive models, and identifying aberrant cell behavior at the single cell level.