Measurements of neural data require tradeoffs between temporal and spatial resolution and between invasiveness and noninvasiveness. Scalp electroencephalography (EEG) offers a noninvasive approach to measuring neural data with high temporal resolution, but EEG provides poor spatial resolution due to the surface position of a limited number of sensors. As a result, measurement noise arises from spatial filtering of the scalp, temporal interference of nonlocalized synchronous activity, and sensor conductivity fluctuations. Therefore, research on neural signal processing has focused on methods to infer the underlying generative processes of the brain using noisy measurements such as EEG. Source localization using EEG signals aims to increase spatial resolution of the noninvasive measurement and infer underlying brain activity. Existing source localization methods demonstrate the ability to estimate activity several centimeters below the scalp and have even expanded beyond traditional 16-32 channel EEG into high-density (64-128 channels) and ultra-high-density (256+) EEG. Despite their efficacy, current approaches rely on a linear assumption of the relationship between source activity and sensor measurements and on linearity in their dynamics. We propose a data-driven approach for non-linear source localization estimation using Koopman operator theory applied to high-density EEG synchronously recorded during intracortical stimulation. This technique will contribute to the development of diagnostic technologies that may be used to detect and treat neuropsychiatric conditions, including epilepsy, mild traumatic brain injuries, depression, and addiction.