Physics-Informed Graph Neural Networks for Modeling Spatially Distributed Dynamically Operated Processes

Modeling process systems by use of partial differential equations is often complex and computationally expensive, especially for inverse problems such as optimization, state identification, or parameter estimation. Data-driven methods typically provide efficient alternatives with lower computational cost. One such method is Graph Neural Networks (GNNs), which can be used to model dynamical systems as graphs. However, dynamic GNNs often face challenges with extrapolation and representability. Integrating mechanistic insights in surrogate models can improve both prediction accuracy and interpretability. This study compares different strategies for embedding physics-based insights into GNNs to model the dynamic behavior of a catalytic CO2 methanation reactor. The hybrid integration of physics-informed GNNs aims to improve the predictive ability and interpretability while reducing the model development time, thereby facilitating faster deployment. Results show that penalizing the predicted change in reactor states from one time step to the next during training reduces the Frobenius error norm of GNN predictions from about 2.2�% to 1.4�%. In contrast, using a traditional physics-based loss function during training results in a Frobenius norm as high as 8.7�%. This highlights the importance of comparing different strategies for embedding physical laws into data-driven models.