Many techniques exist to train neural networks to approximate a complex systems, such as deep learning methods. It is well known that despite their robustness with respect to over-fitting, such trained models may be brittle as some fundamental principles of the systems are missing. For many engineering applications, the model class may be derived from first principles (or fundamental principles). In this paper, ideas from both methodologies are combined to arrive at a robust model that is interpretable from first principles, but goes beyond this by capturing structure from the available data. The paper presents two examples to illustrate the ideas. First a synthetic data set based on simulations is used. Next a well known data set from functional magnetic resonance imaging (fMRI) is used. In these two examples, a few representative neural networks are used in combination with model information coming from first principles. The preliminary results show that the framework is highly beneficial and yields excellent system identification fidelity.