APro, a modularized process-based total system performance assessment framework, was developed at the Korea Atomic Energy Research Institute (KAERI) to simulate radionuclide transport considering coupled thermal-hydraulic-mechanicalchemical processes occurring in a geological disposal system. For reactive transport simulation considering geochemical reactions, COMSOL and PHREEQC are coupled with MATLAB in APro using an operator splitting scheme. Conventionally, coupling is performed within a MATLAB interface so that COMSOL stops the calculation to deliver the solution to PHREEQC and restarts to continue the simulation after receiving the solution from PHREEQC at every time step. This is inefficient when the solution is frequently interchanged because restarting the simulation in COMSOL requires an unnecessary setup process. To overcome this issue, a coupling scheme that calls PHREEQC inside COMSOL was developed. In this technique, PHREEQC is called through the “MATLAB function” feature, and PHREEQC results are updated using the COMSOL “Pointwise Constraint” feature. For the one-dimensional advection-reaction-dispersion problem, the proposed coupling technique was verified by comparison with the conventional coupling technique, and it improved the computation time for all test cases. Specifically, the more frequent the link between COMSOL and PHREEQC, the more pronounced was the performance improvement using the proposed technique.

APro, a modularized framework of the process-based total system performance assessment, has been developed by KAERI to simulate the radionuclide transport in geological disposal system considering multi-physics phenomena. However, the target problem including more than 10,000 boreholes and over 100,000 years of simulation time is computationally challenging to deal with numerical solvers provided by COMSOL Multiphysics constituting APro. To alleviate the computational burden, machine learning (ML) techniques have been studied to develop a surrogate model replacing the heavy computation part. In recent studies, attempts have been made to integrate the knowledge of physics and numerical methods into the ML model for partial differential equations (PDEs). Unlike conventional ML approaches solely relying on data-driven method, the integration can help to make the ML model more specialized for solving PDEs. The hybrid neural network (NN) solver method is one of the strategies to develop more efficient PDE solver by interleaving NN with numerical solvers like finite element method (FEM). The hybrid NN model on the premise of numerical solver is easier to train and more stable than the purely data-driven model. For example, one previous study has used the hybrid NN model as a corrector for an incomplete numerical solver for the advection-diffusion problem. In every time step of simulation, NN corrects the error of incomplete solution obtained by a relaxed numerical solver with coarse meshing. The simulation in the next time step starts from the corrected solution, so NN interacts with the numerical solver iteratively. If the corrector is successfully trained, the incomplete but fast solver with corrector can provide reliable results comparable to the original massive solver. This study adopts the hybrid concept to develop a surrogate model for the near-field region, which is the heavy computation part in the simulation of geological disposal system. Various incomplete models such as coarse meshing or emptying the borehole domain are studied to construct a hybrid NN solver. This study also covers how to embed the hybrid NN in COMSOL Multiphysics to train and use it during the simulation.