Some inverse problems in particle physics

Inverse problems play a central role in current areas of research in particle phenomenology. In these lectures, we focus on two examples, the extraction of Parton Distribution Functions (PDFs) from experimental data (or, equivalently, from pseudo- and quasi-PDFs computed in lattice QCD), and the extraction of spectral functions from lattice Euclidean time correlators. We investigate in detail three different approaches, namely Backus-Gilbert, Gaussian Processes, and fits based on Neural Network parametrizations.