Be it your favorite novel, a newswire article, a cooking recipe or an academic paper – in many daily situations we read the same text more than once. In this work, we ask whether it is possible to automatically determine whether the reader has previously encountered a text based on their eye movement patterns. We introduce two variants of this task and address them with considerable success using both feature-based and neural models. We further introduce a general strategy for enhancing these models with machine generated simulations of eye movements from a cognitive model. Finally, we present an analysis of model performance which on the one hand yields insights on the information used by the models, and on the other hand leverages predictive modeling as an analytic tool for better characterization of the role of memory in repeated reading. Our work advances the understanding of the extent and manner in which eye movements in reading capture memory effects from prior text exposure, and paves the way for future applications that involve predictive modeling of repeated reading.