Perspective of Interpretable Physics-Based AI method for Digital Twins of Geosystems

The development of digital twins for subsurface applications faces several challenges, in this contribution we are focusing on the issue of providing near real-time predictions for numerical multi-physics applications describe by partial differential equations. Even when fronted against state-of-the-art high-performance computing infrastructures, conventional multi-physics simulations are not real-time compatible because of their huge computational demand. At the same time, they are subject to uncertainties from, for instance, the geometry, material properties, and boundary conditions.To address the computational demand, we introduce the usage of surrogate models. Surrogate models comprise data-driven and physics-based approaches. While data-driven techniques, such as neural-networks, well capture complex system responses, they typically lack interpretability, hindering the degree of reliability of the model outcomes. This, in turn, poses challenges for the integration into digital twins especially in applications where risks need to be assessed. In contrast, physics-based approaches are fully interpretable, but often limited to elliptic and parabolic partial differential equations. Hence, they cannot capture the full complexity of the systems dynamics. To overcome the limitations of both data-driven and physics-based techniques, we introduce a hybrid approach namely the non-intrusive reduced basis method within the class of projection-based model order reduction techniques.In this contribution, we demonstrate for a geothermal case study how this interpretable physics-based AI method can be used to reliably and efficiently accelerate the high-fidelity numerical multi-physics simulations. Furthermore, we illustrate their integration into a Bayesian uncertainty quantification framework, including hierarchical approaches. At last, we discuss possibilities to extend the aforementioned approaches to allow for a continuous integration of observational data.