Structure-Promoting Hybrid Modeling for Well-Posed Parameter Identification: Application to Non-Isothermal Continuous Stirred Tank Reactor Systems

High Resolution Image Download MS PowerPoint Slide Hybrid modeling combines mechanistic knowledge with data-driven components to address system-model mismatch in complex dynamical systems. While such models often achieve accurate trajectory prediction, the inferred data-driven components are not guaranteed to be unique, identifiable, or robust to perturbations. Consequently, multiple hybrid structures can yield nearly identical prediction errors while corresponding to fundamentally different physical interpretations. In this work, we propose a structure-promoting hybrid model training framework that combines predictive accuracy with regularization of the parameter-identification problem. Monotonicity penalties are introduced as structural priors to restrict the admissible space of latent-parameter trajectories and to eliminate nonphysical oscillatory solutions during early training. To resolve parameter ambiguity, sensitivity-based identifiability penalties are formulated using the smallest singular value and condition number of the parameter sensitivity matrix, thereby improving the conditioning of the inverse mapping. In addition, stability-based regularization is incorporated to promote the robustness of estimated parameters with respect to measurement perturbations. A staged training strategy is developed in which monotonicity is weighted strongly during early optimization and gradually relaxed, allowing identifiability and stability penalties to refine the solution without introducing bias. The framework is demonstrated on a nonlinear reactor case study with multiple candidate hybrid architectures. Results show that while conventional hybrid models achieve similar prediction accuracy, the proposed approach reduces ambiguous parametrizations and promotes parameter trajectories that are identifiable, robust, and physically interpretable. This work establishes a principled framework for hybrid model selection based on structural well-posedness, moving beyond prediction-error minimization toward reliable and interpretable model discovery.