Stoichiometric Modeling and Stability Analysis of Synthesis of Alkane Reactions Using PINNs with PDFP Optimization: Applications in Pharmaceutical, Rubber, and Fuel

In this study, we present a physics-informed neural network for stoichiometric modeling and stability analysis of synthesis of alkane reactions with optimal control, motivated by applications in the pharmaceutical, rubber, and fuel industries. The reaction in this study mechanism consisting of 12 chemical species and is modeled as a strongly nonlinear mathematical system of ordinary differential equations that represents decarboxylation, radical formation, recombination, and potassium regeneration processes. Fundamental properties, including well-posedness, equilibrium behavior, stability, and parameter sensitivity, are systematically analyzed. An optimal control formulation with bounded time-dependent control inputs is incorporated to regulate reactive intermediates and suppress undesirable reaction pathways. The controlled kinetic system is solved using a PINNs-based approach that provides simultaneous state prediction and parameter identification without conventional time marching. A preconditioned Davidon Fletcher Powell optimizer is employed to increase the convergence and numerical stability for these dynamics. Numerical experiments and phase space analyses confirm accurate stoichiometric balance, stable controlled trajectories, and strong generalization capability of the model.