Physics-Informed Neural Network Surrogates for Chemical Processes Governed by Partial Differential Equations: From Static Simulation to Real-Time Applications

Abstract Partial differential equation (PDE) models are core first-principles tools for many chemical process design, optimization, and control problems. However, their computational cost may limit their use in settings requiring rapid, repeated evaluations. Consequently, developing efficient surrogate models is essential for applications such as digital-twin development, real-time optimization, and process control. This work presents two Physics-Informed Neural Network (PINN)-based surrogate frameworks tailored to distinct applications. The Simulation-PINN targets offline applications and is conditioned on static boundary conditions and PDE parameters, generating full spatiotemporal solutions in a single neural network forward pass. The PCA–PINN targets real-time applications and is additionally conditioned on the current system state, encoded via Principal Component Analysis (PCA), to predict the solution at the next time step, thereby accommodating time-varying input profiles by holding the inputs constant over each time interval. Both frameworks are validated on isothermal and non-isothermal axial-dispersion tubular reactors, achieving speedups exceeding three orders of magnitude over a conventional numerical solver, with sub-percent mean absolute percentage errors and strong generalization to extrapolated inputs beyond their training domain.