Deep learning enhanced numerical simulations of mixed-dimensional models for subsurface flow
Exploiting the subsurface as an energy storage site is a crucial step to meet some of the challenges arising from energy production by renewable sources. For such applications, a proper understanding of the subsurface flow is essential and calls for efficient and effective computational models. The main difficulties in the mathematical modeling arise from the highly varying material parameters as well as the presence of fracture networks, the latter aspect being crucial due to its leading impact on flow characteristics. These features are a leading source of computational complexity, often making it infeasible to use full order simulation models in real-life situations, particularly when there is the need to investigate different scenarios and/or quantify uncertainties.

In this project, I will build on my acquired expertise in mixed-dimensional models of fractured porous media, where fractures are represented as a collection of immersed, lower-dimensional manifolds. Although these models lead to accurate numerical methods, the computational cost remains impractically high. To overcome this, I propose to develop reduced order models for mixed-dimensional flow problems. In particular, I will investigate how to properly capture non-linear dependencies on model parameters such as the fracture network configuration by extending and adapting the deep learning enhanced reduced order modeling techniques recently investigated by researchers of the host institution. 

The combination of research fields is reflected by the composition of the project: the proponent has a strong theoretical background in analyzing and discretizing mixed-dimensional models whereas the supervisor and associated host institute are leading experts in fractured porous media flow and application-driven reduced order modeling. Additionally, the host institution offers the necessary research and complementary skill training for the proponent to further develop and thrive as an independent researcher.