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

This paper proposes a novel orthogonal-by-construction parametrization for augmenting physics-based input–output models with a learning component in an additive sense. The parametrization allows to jointly optimize the parameters of the physics-based model and the learning component. Unlike the commonly applied additive (parallel) augmentation structure, the proposed formulation eliminates overlap in representation of the system dynamics, thereby preserving the uniqueness of the estimated physical parameters, ultimately leading to enhanced model interpretability. By theoretical analysis, we show that, under mild conditions, the method is statistically consistent and guarantees recovery of the true physical parameters. With further analysis regarding the asymptotic covariance matrix of the identified parameters, we also prove that the proposed structure provides a clear separation between the physics-based and learning components of the augmentation structure. The effectiveness of the proposed approach is demonstrated through simulation studies, showing accurate reproduction of the data-generating dynamics without sacrificing consistent estimation of the physical parameters.