Hybrid neural networks for improved chemical process modeling: Bridging data-driven insights with physical consistency

• Proposal of a hybrid model that ensures accuracy and physical consistency in modeling. • Benchmark models assess constraint enforcement and predictive reliability against proposed approach. • The hybrid approach demonstrates robustness, scalability, and computational efficiency. • Comparative analysis highlights the balance between accuracy and physical laws. The increasing reliance on neural networks (NN) in chemical process modeling highlights their capability for accurate predictions, yet their standalone application often struggles to adhere to fundamental physical laws such as equilibrium constraints and mass balance. Addressing this limitation, hybrid methods that integrate data-driven insights with physical consistency have gained prominence. This study systematically explores the integration of NNs with nonlinear data reconciliation (NDR) across multiple testing dimensions, including a Gibbs reactor, data robustness evaluations, and reactor-distillation system integration. Hybrid methodologies such as NN + NDR, NN + KKT (Karush-Kuhn-Tucker), and KKT + PINN (Physics-Informed Neural Networks with KKT conditions) are comparatively assessed. The proposed NN + NDR framework demonstrates superior performance in minimizing errors and enforcing physical laws, with minimal computational overhead. This work emphasizes the scalability, robustness, and transformative potential of modular hybrid strategies in advancing reliable, physically consistent chemical process modeling.