In this work, we introduce a physics-informed machine learning framework that can build a model of stochastically behaving defects in the gate oxide of an individual scaled transistor device. This is achieved by automated data-driven analysis of low-voltage stress-induced leakage current data constituting convoluted random telegraph noise signals. The decision-making of the framework is guided by defect physics. Furthermore, it was successfully applied to generate statistics on defect properties in multiple devices.