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

Data assimilation is a special form of uncertainty estimation. It is focussed on systems for which we have an interest in sequential or real-time updates to our uncertainty estimates. Examples include weather forecasts, pump control, petroleum engineering, or GPS tracking. Advanced data assimilation algorithms can also infer and improve a model's parameters with time, yielding a form of semi-autonomous machine learning. Much of my research focusses on such algorithms.

The context in which I explore these subjects is generally hydrogeology. Groundwater is the most important and ubiquitous freshwater reservoir in many parts of the world. Unfortunately, the subsurface is mostly beyond direct observation. With limited and predominantly point-wise information, numerical modelling is an important tool to create physically meaningful links between fragmented insights. When combined with uncertainty estimation, we can rigorously explore varying hypotheses about the subsurface even with incomplete data.