In 1976 Keller formulated the following very general definition of inverse problems, which is often cited in the literature:
"We call two problems inverses of one another if the formulation of each involves all or part of the solution of the other. Often, for historical reasons, one of the two problems has been studied extensively for some time, while the other is newer and not so well understood. In such cases, the former problem is called the direct problem, while the latter is called the inverse problem."
Inverse problems appear in many situations in physics, engineering, biology and medicine. The main mathematical problem is the well (ill) – posedness of the inversion process. Indeed, in practice most inverse problems are ill-posed in terms of non-uniqueness or lack of stability of the inversion.
This one-day meeting is one of four LMS meetings on inverse problems every year that brings together researchers who work on advancing the field of inverse problems, both from a theoretical and from an applied point of view.
The meeting will concentrate on learning in inverse problems. Appropriate inversion models are used to still be able to compute reliable solutions to ill-posed problems which maximise the information gain from the data. The solution accuracy thereby depends on our certainty in the model, the accuracy with which we can realise it and the amount of sensible prior information we can integrate in the model. We will discuss recent advances on analysing and optimising inversion models using data learning, model design under uncertainties and parameter choice rules.
