High-dimensional maximum-entropy phase space tomography

TL;DR

This paper reviews two recent methods for high-dimensional phase space tomography using entropy maximization, addressing the challenge of reconstructing complex distributions in particle accelerators.

Contribution

It compares two novel approaches—normalizing flows with differentiable simulations and Lagrange multipliers with MCMC—for high-dimensional entropy maximization in phase space reconstruction.

Findings

Normalizing flows enable differentiable simulation-based reconstruction.

Lagrange multipliers combined with MCMC facilitate high-dimensional entropy maximization.

Several open problems remain in phase space tomography.

Abstract

Reconstructing 4D or 6D phase space distributions from 1D or 2D measurements is a challenging inverse problem encountered in particle accelerators. Entropy maximization is an established method to incorporate prior information in the reconstruction, but it is typically infeasible in high-dimensional spaces. In this paper, I review two recent approaches to high-dimensional entropy maximization. The first approach utilizes differentiable simulations and a class of generative models known as \textit{normalizing flows}, whereas the second approach employs the method of Lagrange multipliers and Markov Chain Monte Carlo (MCMC) sampling. My aim is to provide a short explanation of each method using a common notation. I conclude by mentioning several unsolved problems in phase space tomography.