Bjørn Christian Skov Jensen: It often happens that we are curious about things we cannot observe directly, and while there might be ways to directly observe these things, they might require destructive action that cannot be condoned. Examples could be looking inside a person, or perhaps determining the toy inside a kinder egg. Thus we device ways to try to spy at these unobservables by indirect measures.
The link between these indirect measures and the unobservables is established by a mathematical model, which explains to us what our indirect measures would be if we knew the unobservable. Equipped with this we attempt to recover our unobservable from the indirect measures; we call problems like these Inverse Problems. Unluckily for us, the link, in general, might be highly unstable and our indirect measure inaccurate. This combination makes inverse problems very hard to solve; sometimes even impossible. Often though, while we might not for sure determine the unobservable, we can obtain a probability on the unobservable; i.e. we might be able to answer questions like: how likely is it that the unobservable is A compared to B?
As it happens, we are often not actually interested in the uncertain unobservable A coming from the model but rather some derived quantity, say, how many pieces does the toy in the kinder egg consist of? Information like this might be much more stably determined than the unobservable itself. In this project we would like to uncover more about what information we might derive stably and what might not be determinable at all.
PhD project title: Quantity of Interest Tomography
Effective start/end date 01/01/2017 → 31/03/2020
DTU supervisors: Kim Knudsen and Martin Skov Andersen from the Section for Scientific Computing