Field inference with information field theory

In many scientific, industrial, and economical applications, knowledge of fields, quantities that vary as a function of position, is essential.Inferring a physical field from data, however, is an ill posed problem, as the finite data can not alone constrain the infinite number of degrees of freedom of a function over continuous space. Domain knowledge has to regularise the set of possible solutions. Usually significant uncertainties remain and need to be quantified. This can be done via information field theory (IFT), which is a mathematical formulation of probabilistic field inference. IFT is related to modern AI/ML methodologies like generative models, however, it does not require training, despite being self-adaptive, as domain knowledge is systematically used. Here, the basic concepts of IFT and its numerical implementation are introduced and some of its recent application to astrophysical datasets are presented that probe space plasma in various environments and ways ranging from gamma ray astronomy over Galactic tomography to black hole filming.