Nonlinear kinetic modeling, stability, and optimal control of phenol synthesis using physics informed neural networks: applications in pharmaceuticals and polymer industries

Abstract

This study presents a causal Physics Informed Neural Network framework for modeling and predicting the chemical kinetics of phenol synthesis governed by alkaline fusion and acidification reactions. The reaction mechanism involves sodium benzenesulfonate C ₆ H ₅ SO ₃ Na, sodium hydroxide NaOH, sodium phenoxide C ₆ H ₅ ONa, sodium sulfite Na ₂ SO ₃ , hydrochloric acid HCl, phenol C ₆ H ₅ OH, water H ₂ O, and sodium chloride NaCl, and is formulated as a nonlinear system of ordinary differential equations describing the time-dependent evolution of all chemical species. Stoichiometric constraints and governing physical laws are embedded directly into the loss function, enabling stable learning of concentration profiles and accurate estimation of kinetic parameters for stiff and strongly coupled reaction dynamics. The learned parameters show smooth convergence across multiple initial conditions and extended time horizons. At the same time, phase plane and phase space analyses reveal nonlinear species interactions, stability characteristics, and the transition from transient to equilibrium behavior. The proposed framework is robust, data efficient, and scalable, and is directly applicable to pharmaceutical manufacturing, polymer and resin production, and chemical intermediate synthesis, providing a reliable computational tool for stoichiometric analysis, stability assessment, and kinetic modeling of phenol synthesis.