Orthogonal-by-construction augmentation of physics-based input-output models

Abstract: Model augmentation is a promising approach for integrating first-principles-based models with machine learning components. Augmentation can result in better model accuracy and faster convergence compared to black-box system identification methods, while maintaining interpretability of the models in terms of how the original dynamics are complemented by learning. A widely used augmentation structure in the literature is based on the parallel connection of the physics-based and learning components, for both of which the corresponding parameters are jointly optimized. However, due to overlap in representation of the system dynamics by such an additive structure, estimation often leads to physically unrealistic parameters, compromising model interpretability. To overcome this limitation, this paper introduces a novel orthogonal-by-construction model augmentation structure for input-output models, that guarantees recovery of the physically true parameters under appropriate identifiability conditions.