Interpretable machine learning models: a physics-based view

To understand changes in physical systems and facilitate decisions, explaining how model predictions are made is crucial. We use model-based interpretability, where models of physical systems are constructed by composing basic constructs that explain locally how energy is exchanged and transformed. We use the port Hamiltonian (p-H) formalism to describe the basic constructs that contain physically interpretable processes commonly found in the behavior of physical systems. We describe how we can build models out of the p-H constructs and how we can train them. In addition we show how we can impose physical properties such as dissipativity that ensure numerical stability of the training process. We give examples on how to build and train models for describing the behavior of two physical systems: the inverted pendulum and swarm dynamics. I. Introduction The necessity for interpretability comes from the fact that it is not always enough to train and model and get an answer, but is also important to understand why a particular answer was given. A simple but meaningful definition of model interpretability given in [17] relates this notion to the degree to which a human can understand the cause of a decision. In our case, since we care about models that describe the behavior of physical systems, we change the definition to the degree to which a human can understand the physical processes that cause a prediction. Throughout this paper we focus on physically-interpretable models: models that embed physical laws that explain how energy is transformed and exchanged in the system. A physically-interpretable model facilitates learning and updating the model when something unexpected happens. This update is done by finding an explanation for an unexpected event. For example, an electrical motor unexpectedly overheats and we ask ourselves: "Why is the motor overheating?".