用于重离子碰撞中分布重建的神经网络最大熵框架
Neural network maximum entropy framework for distribution reconstruction in heavy-ion collisions
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中文总结 AI 辅助
该研究开发了NN+MaxEnt框架，将神经网络与香农熵正则化结合，用于从重离子碰撞有限可观测量重建分布，经闭合测试验证后，成功应用于多重数和喷注能量损失分布重建，结果与传统方法一致。
中文摘要 AI 辅助
我们开发了一种神经网络最大熵（NN+MaxEnt）框架，用于从重离子碰撞中的有限可观测量重建概率分布。该方法将灵活的神经网络表示与香农熵正则化相结合，在不假设固定解析形式的情况下保持正性和归一化。在通过高斯、泊松和混合泊松闭合测试验证后，我们将该框架应用于两个物理动机的逆问题：一是受函数重整化群（fRG）累积量约束的有效多重数重建，用作闭合测试；二是从质心系能量√s_NN=2.76 TeV的铅-铅（Pb+Pb）碰撞中单举喷注核修饰因子R_AA数据中提取的条件喷注能量损失分布。对于fRG闭合测试，NN+MaxEnt准确复现了给定的累积量，且得到的分布与传统MaxEnt解一致；对于喷注，重建的能量损失分布复现了测量的R_AA，在初始喷注动量x=50 GeV时，条件平均能量损失为⟨Δp_T⟩≈11.8 GeV，其中值16%–84%区间为9.0–15.0 GeV，提取的能量损失轮廓在定性上与贝叶斯MCMC和LBT结果一致。因此，NN+MaxEnt提供了一种灵活、较少依赖假设的框架，用于通过可微正向映射与基础分布关联的可观测量进行正则化分布重建。
英文摘要
We develop a neural-network maximum-entropy (NN+MaxEnt) framework for reconstructing probability distributions from limited observables in heavy-ion collisions. The method combines flexible neural-network representations with Shannon-entropy regularization, preserving positivity and normalization without assuming a fixed analytic form. After validation with Gaussian, Poisson, and mixed-Poisson closure tests, we apply the framework to two physics-motivated inverse problems: an effective multiplicity reconstruction constrained by functional renormalization group cumulants, used as a closure test, and the conditional jet-energy-loss distribution extracted from single-inclusive jet $R_{AA}$ data in Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$~TeV. For the fRG closure test, NN+MaxEnt accurately reproduces the imposed cumulants and yields distributions consistent with conventional MaxEnt solutions. For jets, the reconstructed energy-loss distributions reproduce the measured $R_{AA}$; at an initial jet momentum $x=50~\mathrm{GeV}$, the conditional mean energy loss is $\langleΔp_T\rangle\simeq11.8~\mathrm{GeV}$, with a central $16\text{--}84\%$ interval of $9.0\text{--}15.0~\mathrm{GeV}$. The extracted energy-loss profile is qualitatively consistent with Bayesian MCMC and LBT results. NN+MaxEnt thus provides a flexible, less ansatz-dependent framework for regularized distribution reconstruction from observables connected to the underlying distribution through differentiable forward maps.
