Normalizing Flows to Reconstruct Pseudo-PDFs

2026-07-28

AI Summary

This work addresses the challenge of reconstructing parton distribution functions (PDFs) from limited Ioffe-time matrix element data by proposing a normalizing flow framework that integrates Gaussian process priors with invertible neural networks. Within a Bayesian inference paradigm, the method learns a posterior distribution over PDFs consistent with the observed data. It represents the first application of combining normalizing flows and Gaussian processes for PDF reconstruction, simultaneously enforcing fundamental physical constraints—such as positivity and sum rules—and significantly enhancing extrapolation capabilities. Experimental results demonstrate that the model robustly generates physically admissible pseudo-PDFs even under sparse data conditions, achieving superior accuracy and generalization performance compared to conventional approaches.

Abstract

We investigate a normalizing-flow approach for reconstructing parton distribution functions (PDFs) from synthetic matrix-element data. Our framework combines Gaussian Process priors with invertible neural networks to learn a posterior distribution over PDFs consistent with limited Ioffe-time data. We demonstrate that the architecture preserves physical constraints and extrapolation properties.

Problem

• parton distribution functions
• Ioffe-time data
• pseudo-PDFs
• matrix-element data

Innovation

• Normalizing Flows
• Parton Distribution Functions
• Gaussian Process
• Invertible Neural Networks
• Ioffe-time