Interpretable machine learning models: a physics-based view
This work addresses the need for interpretable models in physics and engineering, though it is incremental as it builds on existing formalisms.
The paper tackles the problem of interpretability in machine learning for physical systems by using a physics-based approach with port-Hamiltonian constructs, resulting in models that are both interpretable and numerically stable during training.
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.