Pure physics modeling is not enough for particularly complex applications. Once the physics-based VTS is tested, an additional component can be added to the architecture if the required accuracy is not achieved.

In this case, the physics-based ROM tracks the fundamental dynamics, and the additional uncertainties are factored into a discrepancy model.

This peculiar neural network has several benefits:

1. Guarantee of stability;

2. Lightweight;

3. Limited training data required;

4. Allow for high accuracy within complex applications.