Information Field Theory -- Concepts, Applications, and AI-Perspective

TL;DR

This paper introduces Information Field Theory (IFT) and the NIFTy framework, which enable probabilistic inference of continuous fields using domain knowledge, scalable algorithms, and AI perspectives, with applications in astrophysics and telescope imaging.

Contribution

It presents the foundational concepts of IFT and NIFTy, including novel variational inference schemes and their application to astrophysics and AI.

Findings

IFT enables optimal field inference exploiting domain regularities.

NIFTy implements probabilistic neural operator models for field inference.

UBIK customizes NIFTy for astrophysical telescope data analysis.

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 artificial intelligence (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.