Automated and robust system discovery in electrical dynamical systems using Scientific Machine Learning

In this paper we introduce an end-to-end approach for robust system discovery for a class of electrical dynamical systems with polynomial dynamics. To that end, we provide theoretical analysis of the problem setting and the solution approach using a particular Scientific Machine Learning method called Physics-Informed Machine Learning. We introduce model architecture and training and validation methods for deterministic as well as probabilistic approaches to predict the solution to pertinent inverse problems and propose a sampling method to make the predictions robust to the data sparsity. With empirical evidence drawn from examples of Burger equations arising in electrical dynamical systems and a case study of thermal modeling of electrical induction machines, we establish the merits of the proposed method and discuss the implication of this research on possible future directions.