A simple non-parametric reconstruction of parton distributions from limited Fourier information

TL;DR

This paper introduces a Bayesian non-parametric method using Gaussian processes to reconstruct parton distributions from limited Fourier data, providing a regularized, efficient, and uncertainty-aware solution.

Contribution

It presents a novel physically motivated Gaussian process approach to regularize inverse Fourier problems in parton distribution reconstruction.

Findings

Effective regularization of inverse Fourier problems

Physically meaningful hyperparameter fixing

Enhanced numerical efficiency and uncertainty control

Abstract

Some calculations of parton distributions from first principles only give access to a limited range of Fourier modes of the function to reconstruct. We present a physically motivated procedure to regularize the inverse integral problem using a Gaussian process as a Bayesian prior. We propose to fix the hyperparameters of the prior in a meaningful physical fashion, offering a simple implementation, great numerical efficiency, and allowing us to understand and keep control easily of the uncertainty of the reconstruction.