Learning constitutive equations of physical components with predefined feasibility conditions

Complete models of physical systems enable a plethora of model-based methods in control, diagnosis or prognosis. Proprietary information and system complexity often hinder building such models. We address here the problem of learning physical representations of components in partially known physical systems. These representations need to be feasible: when included in the system model, at minimum the model has to simulate. We propose mathematical models for the component representations and give necessary and sufficient conditions for their feasibility. We demonstrate our approach on a illustrative example where we learn different representations of an unknown resistor component in an electrical circuit.