Inverse problems for fractional models have become an active field of research in the recent years. These serve as prototypical examples of nonlocal models, which enjoy strong unique continuation properties. One may consider, for instance, data generated by exterior sources that interact with a domain of interest. In the fractional Calderón problem, one aims to recover information on the coefficients of a nonlocal equation based on nonlocal exterior interactions. We discuss the basic theory of such inverse problems, and present results on theoretical guarantees for numerical and statistical methods to analyze such data. These results are obtained in collaboration with Pu-Zhao Kow, Janne Nurminen (https://arxiv.org/abs/2511.11068), and Mukul Dwivedi, Andreas Rupp (https://arxiv.org/abs/2603.26287).
