Neural Network Representation of Generalized Parton Distributions (NNGPD)

TL;DR

This paper introduces a neural network framework for modeling generalized parton distributions (GPDs) that leverages physical constraints and integral relations, validated through a benchmark with synthetic data.

Contribution

The authors develop a flexible neural network approach to GPD modeling that does not rely on specific functional forms, incorporating experimental and lattice QCD constraints.

Findings

Neural network GPDs reproduce key features of underlying models.

The approach effectively constrains GPDs using integral observables.

The framework is suitable for future experimental and lattice QCD data integration.

Abstract

We present a neural-network-based framework for modeling generalized parton distributions, referred to as NNGPD, in which GPDs are represented as flexible functions constrained through physically motivated integral relations. In this approach, experimental and theoretical information is incorporated into the training procedure via loss functions enforcing convolution integrals that define Compton form factors, as well as Mellin moments related to generalized form factors accessible in lattice QCD. This formulation reflects the inverse-problem character of GPD phenomenology without assuming a specific functional ansatz. As a proof of concept, we benchmark the NNGPD framework using a phenomenological spectator-based GPD model, from which synthetic training data for Compton form factors and Mellin moments are generated. The neural network is trained solely on these aggregate observables, and the resulting GPDs are compared directly with the underlying model distributions in a closure-type test. We find that the neural-network representation reproduces the main features of the GPDs over the relevant kinematic domain, despite being constrained only by their integral projections. This study demonstrates the viability of neural-network representations of GPDs constrained by global physical observables and provides a basis for future phenomenological applications combining experimental measurements of deeply virtual Compton scattering, including those anticipated at the Electron Ion Collider, with lattice QCD inputs for Mellin moments and generalized form factors.