Surrogate models in convection-dominated fault systems: considerations for efficient and reliable realizations

Efficiently solving partial differential equations in geothermal systems is increasingly important, particularly for coupled processes. Accurately describing these systems usually involves high-dimensional parameter spaces and computationally expensive forward simulations, which makes the exploration of multiple scenarios for uncertainty quantification or sensitivity analysis challenging. Surrogate modeling helps overcome this barrier by significantly reducing the computation time. However, the partial differential equations can exhibit non-linear and chaotic behavior when natural convection occurs, which might complicate surrogate modeling. In geothermal systems, where fault zones act as preferential fluid pathways leading to convection, geological conditions and physical properties sometimes allow multiple numerical solutions for the same external conditions. Slight variations in parameters or numerical schemes can produce distinct convection regimes, resulting in both physical and numerical challenges. In this study, we construct surrogate models of an idealized thermo-hydraulic fault model using the non-intrusive reduced basis method, which integrates physics-based and data-driven approaches. By incorporating physical preconditioning, exploring possible bifurcation points, and using entropy generation-based surrogates, we demonstrate enhanced surrogate model accuracy. This work highlights key considerations for constructing effective surrogate models in convection-dominated systems.