A Multilinear Regression Procedure for Solving the Inverse Problem with Physics-Informed Neural Networks: Application to Three Case Studies in Chemical Engineering

Physics-Informed Neural Networks (PINNs) are gaining increasing interest in the field of modeling and simulation as they enhance the extrapolation ability of standard Neural Networks (NNs), which typically fail to predict system behavior beyond the experimental range. Integrating governing equations into the training algorithm leads to physics-driven networks capable of extrapolating system trends from limited training datasets. In this context, this work proposes an innovative approach that employs PINNs to solve inverse problems that arise when the parameters of the governing equations are unknown. Leveraging a multilinear regression procedure, the proposed method analytically computes model parameters during training without burdening the network’s parameter optimization and reducing the risk of getting stuck in local minima. Three case studies are considered for validation: (i) a continuous stirred tank reactor with proportional control, (ii) an autocatalytic process described with a Lotka–Volterra model, and (iii) a plug flow reactor with multiple reactions, which demonstrate the method’s effectiveness in predicting the system behavior and simultaneously identifying model parameters.