Physics-Informed Neural Networks for process systems: Estimating the unknown dynamics

This work proposes a Physics-Informed Neural Network framework for process modeling in situations where the governing dynamics are only partially known, and the available data are noisy and limited. The approach incorporates only the known part of the system dynamics into the physics-based loss, enforcing essential physical consistency while utilizing a second neural network to learn the missing part of the dynamics (i.e., reaction rate) from data. The approach particularly addresses situations where informative data from one mode of operation (e.g., batch) is available and is needed to inform operation in another mode (e.g., continuous). Results showed that while purely data-driven models (NARX-ANN and LSTM) achieved acceptable accuracy in the batch-mode, their predictive capability deteriorated significantly when applied to continuous-mode datasets. In contrast, the proposed PINN framework, together with the secondary reaction rate estimator, successfully bridged this gap. Overall, the study demonstrates that the proposed PINN strategy provides a powerful and interpretable modeling framework that respects known physics, makes it possible to estimate the missing reaction rate, and generalizes reliably across different operational modes.