Sleep impairment significantly alters human brain structure and cognitive function, but available evidence suggests that adults in developed nations are sleeping less. A growing body of research has sought to use sleep to forecast cognitive performance by modeling the relationship between the two, but has generally focused on vigilance rather than other cognitive constructs affected by sleep, such as reaction time, executive function, and working memory. Previous modeling efforts have also utilized subjective, self-reported sleep durations and were restricted to laboratory environments. In the current effort, we addressed these limitations by employing wearable systems and mobile applications to gather objective sleep information, assess multi-construct cognitive performance, and model/predict changes to mental acuity. Thirty participants were recruited for participation in the study, which lasted 1 week. Using the Fitbit Charge HR and a mobile version of the automated neuropsychological assessment metric called CogGauge, we gathered a series of features and utilized the unified model of performance to predict mental acuity based on sleep records. Our results suggest that individuals poorly rate their sleep duration, supporting the need for objective sleep metrics to model circadian changes to mental acuity. Participant compliance in using the wearable throughout the week and responding to the CogGauge assessments was 80%. Specific biases were identified in temporal metrics across mobile devices and operating systems and were excluded from the mental acuity metric development. Individualized prediction of mental acuity consistently outperformed group modeling. This effort indicates the feasibility of creating an individualized, mobile assessment and prediction of mental acuity, compatible with the majority of current mobile devices.