标题： 中子星状态方程的神经后验估计 显示英文标题

标题： Neural Posterior Estimation of Neutron Star Equations of State

摘要： 我们提出了一种基于仿真的推断（SBI）框架，使用神经后验估计（NPE）与条件归一化流（CNF），从天体物理观测的质量、半径和潮汐变形性中约束中子星（NS）的状态方程（EoS）。为了确保模型符合现实，物理信息约束被直接嵌入到训练损失中。这使得在观测数据的条件下，能够对关键热力学量（包括压力、声速平方和迹异常）的完整后验分布进行高效的、无需似然的推断。我们的模型是在从两种无偏EoS先验生成的合成数据集上训练的：多项式参数化（PT）和高斯过程（GP）重构。这些数据集涵盖了各种情况，包括潮汐变形性信息的存在或缺失以及观测噪声。在所有设置中，该方法产生了准确且校准良好的后验分布，当包含潮汐变形性约束时，不确定性会降低。此外，我们发现归一化预测离散度的行为与NS内部的最大中心密度高度相关，这表明模型可以间接推断这一物理上有意义的量。该方法在EoS家族中具有良好的泛化能力，并能准确重构如多项式指数等导出量，展示了其在探测NS核心致密物质方面的鲁棒性和潜力。 显示英文摘要

摘要： We present a simulation-based inference (SBI) framework to constrain the neutron star (NS) equation of state (EoS) from astrophysical observations of masses, radii and tidal deformabilities, using Neural posterior estimation (NPE) with Conditional Normalising Flows (CNF). To ensure that the model conforms with reality, physics-informed constraints are embedded directly into the training loss. This enables efficient, likelihood-free inference of full posterior distributions for key thermodynamic quantities-including pressure, squared speed of sound, and the trace anomaly-conditioned on observational data. Our models are trained on synthetic datasets generated from two agnostic EoS priors: polytropic parametrizations (PT) and gaussian process (GP) reconstructions. These datasets span various scenarios, including the presence or absence of tidal deformability information and observational noise. Across all settings, the method produces accurate and well-calibrated posteriors, with uncertainties reduced when tidal deformability constraints are included. Furthermore, we find that the behavior of normalized predictive dispersions is strongly correlated with the maximum central density inside NSs, suggesting that the model can indirectly infer this physically meaningful quantity. The approach generalizes well across EoS families and accurately reconstructs derivative quantities such as the polytropic index, demonstrating its robustness and potential for probing dense matter in NS cores.