<p>System discovery is an important part of the power systems asset management process. 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 a 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 data sparsity. With empirical evidence drawn from a case study of thermal modeling of electrical induction machines, we establish the merits of the proposed method and discuss the implications of this research on possible future directions. In particular, we benchmark our proposed end-to-end method with multiple deterministic and probabilistic approaches and show that it outperforms all but one baseline in terms of performance in a range of 6% to 78% reduction of validation error. The drop in performance (increase in validation error) in our end-to-end probabilistic approach compared to a Bayesian approach is compensated by a large reduction (86%) in the computation time, making our method more balanced in terms of performance and cost. The experimental results establish that our end-to-end approach outperforms the baseline methods by demonstrating consistent balancing among performance and computation cost.</p>