Learning Constitutive Equations Of Physical Components With Constraints Discovery

We address the problem of learning constitutive equations of acausal physical components in partially known physical systems. The parameters of the constitutive equations satisfy a set of unknown constraints. We propose an iterative procedure for joint parameters and constraints learning and discuss practical aspects of its implementation. The procedure favors exploration during the first iterations. This enables learning a model for the constraints. As the constraints learning advances more weight is given to finding the constitutive equations. We test our method on a demonstrative example in which the model of a nonlinear resistor is learned.