State-of-the-art physics-based machine learning for hydro-mechanical simulation in geothermal applications

Geothermal energy plays an important role in the future energy mix by providing a renewable energy source with a low carbon footprint. This paper presents state of-the-art physics-based surrogate models for geothermal applications, providing predictions for the safe and efficient use of geothermal energy. A proper characterization of the subsurface is subject to high uncertainties, which are often estimated on the basis of probabilistic simulations. However, when dealing with complex, nonlinear physical simulations, a probabilistic approach is often infeasible due to long computing times. In this contribution, we discuss an alternative approach, based on physics-based and data driven machine learning methods in order to reduce computing times, hence, enabling probabilistic analysis including uncertainty quantification. The methods considered comprise the Physics Informed Neural Network (PINN) and the non-intrusive reduced-basis (NI-RB) method as physics-based machine learning approaches, while we rely on a Neural Network (NN) as the data-driven method. We make use of a hydro mechanical (HM) problem to compare their performances based on accuracy and efficiency at both the construction and prediction stage. We find that PINNs are less suitable than NI-RB methods for geothermal applications, especially in situations when only limited measurement data is available. NN requires a large number of training samples to achieve comparable accuracies in the models constructed by both PINN and NI-RB. The NI-RB method delivers the highest accuracy and physical consistency even for a small number of training samples. Therefore, we recommend the NI-RB method for geothermal simulations. With this study, we would like to raise the awareness of the geothermal communities about the careful deployment of machine learning.