Abstract
Hybrid process models are increasingly used for real-time decision support in dynamic operations, where models must remain reliable under changing operating conditions. In such settings, models are often required to extrapolate beyond previously observed batch trajectories, yet conventional validation strategies may fail to reveal weaknesses in extrapolative behavior. This work investigates the effect of hybrid model structure on extrapolative performance using a pilot-scale batch crystallizer as a test case. A structured set of mechanistic and hybrid models is evaluated using nested batchwise leave-one-out cross-validation (NBLOOCV), in which entire batches are withheld to assess extrapolation across operating regimes. For this specific application, the results show that hybrid models employing simple linear correction terms consistently outperform more flexible neural network-based formulations under extrapolation, despite comparable training performance. For the studied process, the findings highlight the importance of validation strategies that reflect intended model use and demonstrate that modest, physically consistent hybridization provides a robust and interpretable basis for operational decision support.