Hidden Reactive Transport Neural Network: A Physics‐ and Chemistry‐Informed Surrogate Modeling Approach and Application to Pyrite Oxidation

Reactive transport models (RTMs) are essential tools to describe and integrate a wide range of physical and biogeochemical processes in natural and engineered porous media. However, the high computational cost often limits their applications for many practical purposes. These challenges mainly stem from the solution of a set of coupled partial differential equations (PDEs), describing multicomponent transport and geochemical reactions along with their multilevel coupling across different spatial and temporal scales. To mitigate this issue, we propose and develop a surrogate modeling approach, hidden reactive transport neural network (HRTNet). The proposed model relies on a flexible architecture based on two networks, which share a common loss function and allows incorporating both data-driven and physics-chemistry-informed contributions. We consider pyrite oxidation in a 1-D geochemically heterogeneous domain as a model example to investigate and demonstrate the capability of HRTNet as well as to analyze the performance of the developed surrogate modeling approach. HRTNet was trained based on the training data generated from the process-based reactive transport simulations, and, successively, the trained model was used as a surrogate to predict the behavior of the reactive transport system. The results reveal that the predictions obtained by the trained surrogate model agree well with those from mechanistic RTMs in a considerably reduced computation time. Furthermore, the physics- and chemistry-informed learning was promising to achieve a good generalization capability, because HRTNet could predict the desired spatio-temporal dynamics for a wide range of initial concentrations beyond the training data sets.