Most of my research revolves around uncertainty estimation in one form or another. Statistical methods allows us to quantify uncertainty where it cannot be otherwise resolved. This is critical in the study of complex, information-limited systems, such as the subsurface. I am particularly interested in statistical methods which allow us to capture advanced aspects of uncertainty such as Pareto frontiers, multi-modality, and other non-Gaussian features.

Data assimilation is a special form of uncertainty estimation. It plays an important role in systems where we have an interest in sequential or real-time updates to our simulations. Examples include weather forecasts, pump control, petroleum engineering, or GPS tracking. Advanced data assimilation algorithms can even infer and improve a model's parameters with time, yielding self-improving simulations. Much of my work focusses on such algorithms.

The context in which I often explore these subjects is hydrogeology. Groundwater is the most important freshwater reservoir in many parts of the world. Unfortunately, the subsurface is mostly unobservable, which makes its study challenging. With predominantly point-wise data, numerical models are an important tool to create physically meaningful connections between these fragmented pieces of information. When combined with uncertainty estimation, we can rigorously study the plausibility and consequences of different hypotheses about the subsurface's properties even with incomplete data.