To understand the exhumation history of the Alpine foreland, it is important to accurately reconstruct its time-temperature evolution. This is often done employing thermokinematic models. One problem of many current approaches is that they are limited to 2-D and do not consider structural or kinematic uncertainties. In this work, we combine 3-D kinematic forward modeling with a systematic random sampling approach to automatically generate an ensemble of kinematic models in the range of assigned geometric uncertainties. Using Markov chain Monte Carlo, each randomly generated model will be assessed in regards to how well they fit the available thermochronology data. This is done to obtain an updated set of modeling parameters with reduced uncertainty. The resulting, more robust model can then be used to re-interpret the thermochronological data and find alternative drivers of cooling for certain samples.We apply this approach to a simple synthetic model to test the methodology, and then to the Eastern Alps triangle zone in the Bavarian Subalpine Molasse. Results show that it is possible to translate low-temperature thermochronology data into a likelihood function to obtain a 3-D kinematic model with updated, more probable parameters. The thermochronological data by itself, however, may not be informative enough to reduce the parameter uncertainty. The method is useful, however, to study alternative mechanisms of exhumation for the thermochronological samples that are not respected by the modeling, even when uncertainty is considered.

The societal importance of geothermal energy is significantly increasing because of its low carbon-dioxide footprint. However, geothermal exploration is also subject to high risks. For a better assessment of these risks, extensive parameter studies are required that improve the understanding of the subsurface. This yields computationally demanding analyses. Often this is compensated by constructing models with a small vertical extent. This paper demonstrates that this leads to entirely boundary-dominated and hence uninformative models. It demonstrates the indispensable requirement to construct models with a large vertical extent to obtain informative models with respect to the model parameters. For this quantitative investigation, global sensitivity studies are essential since they also consider parameter correlations. To compensate for the computationally demanding nature of the analyses, a physics-based machine learning approach is employed, namely the reduced basis method, instead of reducing the physical dimensionality of the model. The reduced basis method yields a significant cost reduction while preserving the physics and a high accuracy, thus providing a more efficient alternative to considering, for instance, a small vertical extent. The reduction of the mathematical instead of physical space leads to less restrictive models and, hence, maintains the model prediction capabilities. The combination of methods is used for a detailed investigation of the influence of model boundary settings in typical regional-scale geothermal simulations and highlights potential problems.

Geothermal energy plays an important role in the energy transition by providing a renewable energy source with a low CO2 footprint. For this reason, this paper uses state-of-the-art simulations for geothermal applications, enabling predictions for a responsible usage of this earth's resource. Especially in complex simulations, it is still common practice to provide a single deterministic outcome although it is widely recognized that the characterization of the subsurface is associated with partly high uncertainties. Therefore, often a probabilistic approach would be preferable, as a way to quantify and communicate uncertainties, but is infeasible due to long simulation times. We present here a method to generate full state predictions based on a reduced basis method that significantly reduces simulation time, thus enabling studies that require a large number of simulations, such as probabilistic simulations and inverse approaches. We implemented this approach in an existing simulation framework and showcase the application in a geothermal study, where we generate 2D and 3D predictive uncertainty maps. These maps allow a detailed model insight, identifying regions with both high temperatures and low uncertainties. Due to the flexible implementation, the methods are transferable to other geophysical simulations, where both the state and the uncertainty are important.