Probabilistic GeomodelingUrheberrecht: CGRE
In CGRE, we develop novel methods to address complex geometrical objects in structural geology. Our methods are specifically tuned to work in cases with scarce data in a formal probabilistic manner. We investigate different mathematical models to construct complex geometries, e.g. gaussian processes, NURBS and subdivision surfaces. In addition, we work on innovative probabilistic methods, such as probabilistic maschine learning and gradient based samplers as well as optimised visualisation and interfacing with these methods, e.g. using methdos of virtual and augmented reality (VR/AR).
In geology we find environments and shapes but not everything is possible. We investigate possible numerical models that help us to construct these expected shapes with as few parameters as possible. In a sense, we aim to encode information by model selection without oversimplifying the model. Specific methods we work on are:
- Implicit modeling using gaussian processes and radial basis functions
- Explicit modeling using NURBS and subdivison surfaces.
- Kinematic modeling.
Latest advances on probabilistic programming allow us to outsource much of the data integration and estimation calculation to computers. In CGRE, we treat most of the models as stochastic. This enables us to perform inferences which in turn will yield a range of plausible models. This probabilistic view can be used not only to quantify uncertainty, but also to improve the overall understanding of a specific setting. Within this topic we are interested in:
- Probabistic Machine Learning (Probabilsitic Inversion)
- Novel gradient-based samplers
- Risk analysis
- Uncertainty quantification
Complex geometris in 3-D are often difficult to understand. Adding multiple 3-D objects - lines, planes, points - and soon enough one ends up with a variety of shapes and colours on the screen. We investigate the use of novel AR/VR methods for an optimized visualization and manipulation of data in a more intuitive environment. This extra dimension enhances exploratory processes as well as a novel level of data and model manipulation directly in 3-D.