About the Trustworthiness of Physics-Based Machine Learning – A Considerations for Geomechanical Applications

Abstract. Model predictions are important to assess the subsurface state distributions (such as the stress), which are essential to, for instance, determine the location of potential nuclear waste disposal sites. Providing these predictions with quantified uncertainties often requires a large number of simulations, which is difficult due to the high CPU time needed. One possibility for addressing the computational burden is surrogate models. Purely data-driven approaches face challenges when operating in data-sparse application fields such as geomechanical modeling or by producing interpretable models. The latter aspect is critical for applications such as nuclear waste disposal, where it is essential to provide trustworthy predictions. To overcome the challenge of trustworthiness, we propose the usage of a novel hybrid machine learning method, namely the non-intrusive reduced basis method. This method resolves both of the above challenges while being orders of magnitude faster than classical finite element models. In the paper, we demonstrate the usage of the non-intrusive reduced basis method for 3-D geomechanical-numerical modeling with a comprehensive sensitivity assessment. The usage of these surrogate geomechanical models yields a speed-up of six orders of magnitude while maintaining global errors in the range of less than 0.01 %. Because of this enormous reduction in computation time, computational demanding methods such as global sensitivity analyses become feasible, which provide valuable information about the contribution of the various model parameters to stress variability. The consequences of these added benefits are demonstrated for a benchmark example and a simplified study for a siting region for a potential nuclear waste repository in Nördlich Lägern (Switzerland).