Hybrid ML assisted Bayesian Optimal Experimental Design for Thermal Field Monitoring

In the context of geothermal energy development, accurate characterization of the subsurface thermal field is critical for successful exploration, resource assessment, and validation of numerical models. The temperature distribution in the subsurface is strongly influenced by the distribution of heterogeneous material properties, which are often poorly constrained, leading to significant uncertainties in model predictions. A key challenge lies in designing or improving sensor networks that effectively capture the spatial and temporal evolution of the thermal field, while considering related sources of uncertainty. Maximizing the expected information that can be acquired with an improved sensor network would enable a reliable calibration and validation of subsurface models during the exploration phase of geothermal projects. We approach this challenge by using a Bayesian optimal experimental design strategy, which allows an optimization of the sensor placement considering uncertainties in, for the case discussed in this contribution, bulk material properties. Bayesian optimal design has the disadvantage of requiring numerous forward solves, which are often prohibitive for high-fidelity numerical simulations. We address this computational burden through the construction of interpretable physics-based machine learning surrogate models. They allow faster evaluations of coupled thermal numerical models, by combining model-order reduction methods with data-driven techniques, enabling rapid and accurate predictions across large parameter spaces, while retaining interpretability grounded in the underlying physical laws. As an application of the method we address the problem of thermal sensor placement to monitor the subsurface response for (sedimentary) basin-wide applications. Our results aim at identifying optimal locations for a regional observation network that maximizes sensitivity to key subsurface characteristics.