标题： 变分自编码器逆映射器用于提取康普顿形式因子：基准测试和条件学习 显示英文标题

标题： Variational autoencoder inverse mapper for extraction of Compton form factors: Benchmarks and conditional learning

摘要： 深度虚拟单态散射过程（DVES）作为探测核子在坐标空间中的夸克和胶子分布的精确探针。这些分布通过相对于质子动量转移的傅里叶变换从广义部分子分布（GPDs）中得出。QCD因子化定理使DVES能够通过康普顿形式因子（CFFs）进行参数化，CFFs是GPDs与微扰可计算的核函数的卷积。从深度虚康普顿散射（DVCS）中准确提取CFFs，得益于与贝特-海特定理（BH）过程的干涉以及更简单的末态结构，这对于推断GPDs至关重要。本文重点在于使用变分自编码器逆映射器（VAIM）及其约束变体（C-VAIM）从DVCS数据中提取CFFs。VAIM被证明在针对给定运动学条件提取多个CFF解方面与马尔可夫链蒙特卡罗（MCMC）方法一致，而C-VAIM有效捕捉了不同运动学值下CFFs之间的相关性，提供了更受约束的解。这项研究代表了向全面分析流程迈进的关键第一步，以实现GPDs的提取。 显示英文摘要

摘要： Deeply virtual exclusive scattering processes (DVES) serve as precise probes of nucleon quark and gluon distributions in coordinate space. These distributions are derived from generalized parton distributions (GPDs) via Fourier transform relative to proton momentum transfer. QCD factorization theorems enable DVES to be parameterized by Compton form factors (CFFs), which are convolutions of GPDs with perturbatively calculable kernels. Accurate extraction of CFFs from DVCS, benefiting from interference with the Bethe-Heitler (BH) process and a simpler final state structure, is essential for inferring GPDs. This paper focuses on extracting CFFs from DVCS data using a variational autoencoder inverse mapper (VAIM) and its constrained variant (C-VAIM). VAIM is shown to be consistent with Markov Chain Monte Carlo (MCMC) methods in extracting multiple CFF solutions for given kinematics, while C-VAIM effectively captures correlations among CFFs across different kinematic values, providing more constrained solutions. This study represents a crucial first step towards a comprehensive analysis pipeline towards the extraction of GPDs.