  Physics-guided neural networks (PGNN) is an effective tool that combines the
benefits of data-driven modeling with the interpretability and generalization
of underlying physical information. However, for a classical PGNN, the
penalization of the physics-guided part is at the output level, which leads to
a conservative result as systems with highly similar state-transition
functions, i.e. only slight differences in parameters, can have significantly
different time-series outputs. Furthermore, the classical PGNN cost function
regularizes the model estimate over the entire state space with a constant
trade-off hyperparameter. In this paper, we introduce a novel model
augmentation strategy for nonlinear state-space model identification based on
PGNN, using a weighted function regularization (W-PGNN). The proposed approach
can efficiently augment the prior physics-based state-space models based on
measurement data. A new weighted regularization term is added to the cost
function to penalize the difference between the state and output function of
the baseline physics-based and final identified model. This ensures the
estimated model follows the baseline physics model functions in regions where
the data has low information content, while placing greater trust in the data
when a high informativity is present. The effectiveness of the proposed
strategy over the current PGNN method is demonstrated on a benchmark example.
