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

Abstract

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).

Authors 6

1. Denise Degen corresponding Aachen Computational Geoscience

   RWTH Aachen University

   Affiliation as printed

   Computational Geoscience, Geothermics and Reservoir Geophysics (CG3), RWTH Aachen University, 52074 Aachen, Germany

2. Moritz Ziegler

   GFZ Helmholtz Centre for Geosciences · Technical University of Munich

   Affiliation as printed

   Helmholtz Zentrum Potsdam, Deutsches GeoForschungsZentrum GFZ, 14473 Potsdam, Germany

   Professorship of Geothermal Technologies, TU Munich, Arcisstr. 21, 80333 Munich, Germany

3. Oliver Heidbach

   GFZ Helmholtz Centre for Geosciences · Technische Universität Berlin

   Affiliation as printed

   Helmholtz Zentrum Potsdam, Deutsches GeoForschungsZentrum GFZ, 14473 Potsdam, Germany

   Institute of Applied Geosciences, TU Berlin, 10587 Berlin, Germany

4. Andreas Henk

   Technische Universität Darmstadt

   Affiliation as printed

   Institute of Applied Geosciences, TU Darmstadt, 64287 Darmstadt, Germany

5. Karsten Reiter

   Technische Universität Darmstadt

   Affiliation as printed

   Institute of Applied Geosciences, TU Darmstadt, 64287 Darmstadt, Germany

6. Florian Wellmann Aachen Computational Geoscience

   Fraunhofer Research Institution for Energy Infrastructures and Geotechnologies IEG · RWTH Aachen University

   Affiliation as printed

   Computational Geoscience, Geothermics and Reservoir Geophysics (CG3), RWTH Aachen University, 52074 Aachen, Germany

   Fraunhofer Research Institution for Energy Infrastructures and Geothermal Systems (IEG), 44801 Bochum, Germany