Physics-informed neural network for inverse modeling of natural-state geothermal systems

Predicting the temperature, pressure, and permeability at depth is crucial for understanding natural-state geothermal systems. As direct observations of these quantities are limited to well locations, a reliable methodology that predicts the spatial distribution of the quantities from well observations is required. In this study, we developed a physics-informed neural network (PINN), which constrains predictions to satisfy conservation of mass and energy, for predicting spatial distributions of temperature, pressure, and permeability of natural-state hydrothermal systems. We assessed the characteristics of the proposed method by applying it to 2D synthetic models of geothermal systems. Our results showed that the PINN outperformed the conventional neural network in terms of prediction accuracy. Among the PINN-predicted quantities, the errors in the predicted temperatures in the unexplored regions were significantly reduced. Furthermore, we confirmed that the predictions decreased the loss of the conservation laws. Thus, our PINN approach guarantees physical plausibility, which has been impossible using existing machine learning approaches. As permeability investigations in geothermal wells are often limited, we also demonstrate that the resistivity model obtained using the magnetotelluric method is effective in supplementing permeability observations and improving its prediction accuracy. This study demonstrated for the first time the usefulness of the PINN to a geothermal energy problem.