Abstract: This application relates to apparatus and methods for determining the integrity of data, such as sensor data, in systems. In some examples, a computing device receives input data for the system, and executes a physics-based model to generate a first output. The physics-based model may include a plurality of surrogate models that simulate various portions of the system. The computing device may further execute a machine learning model that operates on the first output to generate a second output. The computing device may generate a predicted output for the system based on the first output and the second output. In some examples, the computing device determines an error for the system based on the predicted output and sensor data received from sensors for the system. Based on the error, the computing device determines if the sensor data is valid. The computing device may then provide an indication of the determination.