Quantifying Geodynamical Influences through Physics-Based Machine Learning: A Case Study from the Alpine Region

Characterizing the influence of geodynamical models is important to improve our understanding of the development and current state of subsurface properties. Which are, in turn, of great societal relevance, for questions such as renewable energy. However, enabling a quantifiable characterization is a major challenge in Geodynamics, due to the high computational cost associated with both the model and the analysis for characterizing the influential parameters. The high cost of the model is caused by a high dimensionality in space, and time and a large number of input parameters. The cost of the probabilistic analyses is related to the large number of individual model solves required for performing the characterization.

To address this computational challenge, we employ the non-intrusive RB method, which combines advanced mathematical algorithms and novel machine learning methods. The method produces models that considerably reduce the dimensionality, yielding an acceleration of several orders of magnitude while maintaining the physical principles. In contrast, to other machine learning methods, the non-intrusive RB method produces explainable models, which is a crucial property for later analyses and predictions.

In this work, we demonstrate how the methodology can be beneficially used for the construction of reliable surrogate models of large-scale geodynamical applications without impacting the underlying physics. Furthermore, we show the benefits of global variance-based sensitivity analysis to quantifiable characterize the influence of the densities and viscosities on both the topography and velocity for the designated case study of the Alpine Region. We employ a global sensitivity analysis to account for possible parameter correlations and nonlinearities.