Information Field Theory -- Concepts, Applications, and AI-Perspective (2508.17269v1)

Abstract: Information field theory (IFT) is the application of probabilistic reasoning to fields. Physical fields are mathematical functions over continuous spaces that exhibit certain properties of regularity, such as limited variance and finite gradients. Inferring a field from an observational dataset should exploit these regularities. However, the finite number of constraints that the data provides is insufficient to determine the infinite number of degrees of freedom of a field. IFT enables us to derive optimal field inference algorithms that explicitly exploit domain knowledge. These algorithms can be implemented via Numerical Information Field Theory (NIFTy). In NIFTy, neural operator forward models can be written and inverted probabilistically. NIFTy thereby infers fields and their remaining uncertainties. This is achieved using novel variational inference schemes that scale quasi-linearly, even for ultra-high dimensional problems. This paper introduces the basic concepts of IFT and NIFTy, highlights a few of their astrophysical applications, and discusses their AI perspective. Finally, UBIK (the Universal Bayesian Imaging Kit), an emerging customisation of NIFTy for a suite of astrophysical telescopes, is presented as a central tool to the topic of the UniversAI conference.